Integrated simulation design pushing method, device and equipment for internal optimization of solver

Abstract

The application discloses an integrative simulation design pushing method and device for solver internal optimization, and equipment, and relates to the technical field of computer aided engineering, and comprises the following steps: performing structural optimization design based on a preset simulation analysis model, and determining optimization design scheme information; based on the optimization design scheme information, recognizing geometric feature information by selecting a node identifier on a grid model to perform inverse geometric parameterization, and combining model material attribute information and model unit attribute information to determine optimization design parameter information; performing iterative simulation solving and grid smoothing correction on the optimization design parameter information based on shape sensitivity in a preset shared memory space by calling an application program interface embedded in a solver kernel, until a preset convergence condition is met, and determining simulation design analysis results; and pushing stress nephograms, displacement nephograms and optimization convergence curves in the simulation design analysis results.

Description

Technical Field

[0001] This application relates to the field of computer-aided engineering technology, and in particular to an integrated simulation design push method, apparatus and equipment for solver internal optimization. Background Technology

[0002] Structural optimization is a crucial technique in modern product design, encompassing topology optimization (using element density as a variable), dimensional optimization (using element thickness as a variable), and shape / morphology optimization (using nodal coordinates as a variable). These methods optimize for a single variable type, yielding conceptual configurations or preliminary design schemes. However, as product development progresses into the detailed design phase, comprehensive performance improvements often require simultaneous optimization of multiple parameters, including geometric features, material properties, and load conditions. This involves a mix of continuous / discrete variables, parameter calibration, multi-objective trade-offs, and stochastic analysis. At this stage, single-variable structural optimization is no longer sufficient to meet design requirements.

[0003] In engineering practice involving joint optimization of multiple types of parameters, geometric parametric modeling is the primary step, its core being the establishment of the driving relationship between design variables and geometric features. However, there is a severe disconnect between current CAD and CAE models: once geometric design parameters change, the entire CAE preprocessing process (such as mesh generation, load and constraint application, contact definition, etc.) must be re-executed, resulting in significant time consumption. Even more challenging is the existence of numerous validated engineering models in industry, retaining only the finite element mesh model without the corresponding CAD geometric model, rendering parametric modeling from a geometric perspective without a basis. Furthermore, existing alternative methods have significant limitations: while free-form optimization based on mesh deformation or Morph techniques can directly move nodes, their perturbation methods struggle to accurately characterize specific engineering geometric features such as the radius / center position of a circular hole, chamfer radius, line length, and the length and width of a rectangle, often resulting in irregular freeform shapes lacking manufacturability; and while some commercial software offers geometric parametric functions, their applicability is limited to simple, regular models, failing to effectively support complex topologies commonly encountered in real-world engineering.

[0004] Current practices utilize general-purpose multidisciplinary optimization platforms to handle complex variable combinations. However, lacking a solver kernel and finite element preprocessing environment, these platforms rely on external calls. Users must build workflows to establish connections between modules, exchanging data with the solver via text files to drive optimization iterations. This approach requires frequent switching between multiple software programs. Building workflows within the finite element preprocessing environment is cumbersome and time-consuming, resulting in fragmented design processes, a disjointed user experience, and low efficiency. Therefore, how to push simulation designs before finite element analysis begins is a pressing issue.

[0005] The above content is only used to help understand the technical solution of this application and does not represent an admission that the above content is prior art. Summary of the Invention

[0006] The main purpose of this application is to provide an integrated simulation design push method, device and equipment for solver internal optimization, which aims to solve the technical problem of how to push the simulation design before the start of finite element analysis.

[0007] To achieve the above objectives, this application proposes an integrated simulation design push method for solver internal optimization, the method comprising: In one embodiment, the step of performing structural optimization design based on a preset simulation analysis model and determining the optimized design scheme information includes: Structural optimization design is performed based on a preset simulation analysis model to determine at least one of the following: topology optimization design scheme information, shape optimization design scheme information, size optimization design scheme information, and morphology optimization design scheme information. The structural optimization design includes at least one of topology optimization, shape optimization, size optimization, and morphology optimization. The feature parameters of at least one of the topology optimization design scheme information, the shape optimization design scheme information, the size optimization design scheme information, and the morphology optimization design scheme information are extracted to determine the optimization design scheme information. The feature parameters include any type of geometric parameters and non-geometric parameters.

[0008] In one embodiment, the step of determining the optimization design parameter information based on the optimized design scheme information, by selecting node identifiers on the mesh model for inverse geometric parameterization to identify the model's geometric feature information, and combining the model's material property information and model element property information, includes: Obtain optimization objective information and constraint information; Receive a set of node identifiers at the boundary of the target geometric feature on the mesh model specified by the user, perform geometric primitive fitting based on the set of node identifiers, calculate the geometric parameters in reverse, and use the geometric parameters as design variables; Based on the model's geometric features, material properties, and unit properties, other design variables are determined. Discrete variables in these design variables include thickness values ​​from the standard sheet metal thickness library, composite material ply angles, composite material ply thicknesses, material grade selection, and parameters limited by engineering specifications. The optimization design parameter information is obtained based on the design variable information, the optimization objective information, and the constraint information.

[0009] In one embodiment, the step of fitting geometric primitives based on the node identifier set and inversely calculating geometric parameters includes: The least squares method is used to fit the set of node identifiers into a circle, a straight line, or an arc, and the corresponding radius of the hole and the center position, the length of the straight line and the position of the endpoints, or the radius of the arc and the central angle are calculated. The geometric parameters are used as continuous or discrete design variables, and include at least one of the following: circular hole radius, center position, arc radius, straight line length, rectangle length and width, cylindrical hole radius, and reinforcing rib height.

[0010] In one embodiment, the step of performing iterative simulation and mesh smoothing correction based on shape sensitivity on the optimized design parameter information by calling the application programming interface embedded in the solver kernel in a preset shared memory space until a preset convergence condition is met, and determining the simulation design analysis results, includes: The robust model evaluation results are obtained by calling the application programming interface embedded in the solver kernel; Based on the robust model evaluation results, the optimized design parameter information is globally explored and iteratively corrected in a preset shared memory space until the preset convergence condition is met, and the first simulation design analysis result is determined. A semi-analytical method is used to perform local optimization and iterative correction of the optimized design parameter information in a preset shared memory space until the preset convergence condition is met, and the second simulation design analysis result is determined. The simulation design analysis result is obtained based on at least one of the first simulation design analysis result and the second simulation design analysis result.

[0011] In one embodiment, the solver kernel integrates an optimization engine consisting of an experiment design module, a surrogate model module, an optimization algorithm module, a stochastic analysis module, and an application programming interface between the solver; The steps for obtaining robust model evaluation results by calling the application programming interface embedded in the solver kernel include: The model data interaction information is obtained by calling the application programming interface of the optimization engine. The model data interaction information includes element information, node information, stiffness matrix, mass matrix and analysis results. Monte Carlo simulation and reliability analysis are performed based on the data interaction information of the model to obtain robust model evaluation results.

[0012] In one embodiment, the step of performing global exploration and iterative correction of the optimized design parameter information in a preset shared memory space based on the robust model evaluation results until a preset convergence condition is met, and determining the first simulation design analysis result includes: Based on the evaluation results of the robust model, determine the corresponding approximate mapping relationship information; Based on the approximate mapping relationship information, at least one of the corresponding genetic discrete variable information and particle swarm discrete variable information is determined. Based on at least one of the genetic discrete variable information and the particle swarm discrete variable information, global exploration and iterative correction are performed in a preset shared memory space until the preset convergence condition is met, and the first simulation design analysis result is obtained.

[0013] In one embodiment, the step of using a semi-analytical method to perform local optimization and iterative correction of the optimized design parameter information in a preset shared memory space until a preset convergence condition is met, and determining the second simulation design analysis result, includes: Obtain design response parameter information, which includes compliance, stress, frequency, displacement, temperature, and buckling; When the optimized design parameter information includes geometric design variables obtained through inverse geometric parameterization, a cooperative perturbation is applied to the boundary node set corresponding to the geometric design variables, and the shape sensitivity derivative of the stiffness matrix is ​​approximately calculated using the central difference method. The adjoint variables corresponding to all design variables are solved at once using the adjoint method, and the sensitivity of each design variable is obtained by combining the shape sensitivity derivative. Based on the sensitivity, local optimization and iterative correction are performed in the preset shared memory space to update the boundary node positions. The internal mesh nodes are then smoothed using Laplace smoothing or Helmholtz filtering until the preset convergence condition is met, and the second simulation design analysis result is obtained.

[0014] Furthermore, to achieve the above objectives, this application also proposes an integrated simulation design delivery device with solver internal optimization, the integrated simulation design delivery device with solver internal optimization comprising: The acquisition module is used to perform structural optimization design based on a preset simulation analysis model and determine the information of the optimization design scheme. The processing module is used to identify the geometric feature information of the model by selecting the node identifiers on the mesh model for inverse geometric parameterization based on the optimized design scheme information, and to determine the optimized design parameter information by combining the model material property information and the model element property information. The processing module is also used to perform iterative simulation and mesh smoothing correction based on shape sensitivity on the optimized design parameter information in a preset shared memory space by calling the application programming interface embedded in the solver kernel until the preset convergence condition is met, and to determine the simulation design analysis results. The execution module is used to push the stress cloud map, displacement cloud map and optimization convergence curve from the simulation design analysis results.

[0015] Furthermore, to achieve the above objectives, this application also proposes an integrated simulation design delivery device for solver internal optimization, the device comprising: a memory, a processor, and a computer program stored in the memory and executable on the processor, the computer program being configured to implement the steps of the integrated simulation design delivery method for solver internal optimization as described above.

[0016] One or more technical solutions proposed in this application have at least the following technical effects: This embodiment proposes an integrated simulation design push method for solver internal optimization. Based on a preset simulation analysis model, structural optimization design is performed to determine the optimized design scheme information. Based on the optimized design scheme information, inverse geometric parameterization is performed by selecting node identifiers on the mesh model to identify the model's geometric features. Combined with model material properties and model element properties, optimized design parameters are determined. The optimized design parameters are then iteratively simulated and solved based on shape sensitivity in a preset shared memory space by calling the application programming interface embedded in the solver kernel, along with mesh smoothing correction, until a preset convergence condition is met, thus determining the simulation design analysis result. Finally, the stress contour plot, displacement contour plot, and optimization convergence curve from the simulation design analysis result are pushed to the solver. This application utilizes structural optimization design to obtain superior design information from a pre-set simulation analysis model. Furthermore, through inverse geometric parameterization, it can directly identify engineering geometric features such as the radius of a circular hole, the center position of a circle, and the length of a straight line, using only the mesh model, even without a CAD geometric model. This breaks through the dependence on geometric models and solves the problem of existing mesh models being unable to be parameterized for optimization. Simultaneously, it can integrate multiple types of parameters, such as material properties and element properties, as optimization design variables, overcoming the limitation of only being able to handle single geometric variables. This allows for more comprehensive parameterized definition and flexible control of the design scheme. By calling the application programming interface embedded in the solver kernel, it directly performs iterative simulation solutions and mesh smoothing correction based on shape sensitivity in a shared memory space, further improving computational efficiency while ensuring solution accuracy. At this point, the stress cloud map, displacement cloud map, and convergence curve from the obtained simulation design analysis results are directly pushed to the same post-processing interface, eliminating the need for frequent switching between multiple software programs to view the results. This significantly simplifies the operation process and achieves a seamless integrated experience for analysis, optimization, and result viewing. Attached Figure Description

[0017] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application.

[0018] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, for those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0019] Figure 1 A flowchart is provided for Embodiment 1 of the integrated simulation design push method for internal optimization of the solver in this application; Figure 2 A schematic diagram illustrating the structural optimization of the integrated simulation design push method for optimizing the solver internal structure in this application; Figure 3 This is a schematic diagram of inverse geometric parameterization picking based on mesh model node identifiers in the integrated simulation design push method for internal optimization of the solver in this application. Figure 4 A schematic diagram of a design scenario for the integrated simulation design push method for optimizing the solver in this application; Figure 5 A schematic diagram showing the selection of node identifier positions for the integrated simulation design push method optimized within the solver of this application; Figure 6 A schematic diagram of the internal relationships of the optimization engine for the integrated simulation design push method for optimizing the solver in this application; Figure 7 A schematic diagram of the probability distribution curve of the integrated simulation design push method for the internal optimization of the solver in this application; Figure 8 The post-processing method for the integrated simulation design push method for the internal optimization of the solver in this application allows for intuitive viewing of the optimization result cloud map; Figure 9 A schematic diagram showing the optimized radius and position of the circular hole in the integrated simulation design push method for optimizing the solver in this application; Figure 10 A schematic diagram of the simulation design and analysis results of the integrated simulation design push method for the internal optimization of the solver in this application; Figure 11 A flowchart is provided for Embodiment 2 of the integrated simulation design push method for internal optimization of the solver in this application; Figure 12 This is a schematic diagram of the module structure of the integrated simulation design push device for solver internal optimization in an embodiment of this application; Figure 13 This is a schematic diagram of the hardware operating environment involved in the integrated simulation design push method for solver internal optimization in the embodiments of this application.

[0020] The purpose, features, and advantages of this application will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation

[0021] It should be understood that the specific embodiments described herein are merely illustrative of the technical solutions of this application and are not intended to limit this application.

[0022] To better understand the technical solution of this application, a detailed description will be provided below in conjunction with the accompanying drawings and specific implementation methods.

[0023] The main solution of this application embodiment is as follows: Structural optimization design is performed based on a preset simulation analysis model to determine the optimization design scheme information; based on the optimization design scheme information, inverse geometric parameterization is performed by selecting node identifiers on the mesh model to identify the model's geometric feature information, and combined with the model's material property information and model element property information, the optimization design parameter information is determined; the optimization design parameter information is subjected to iterative simulation solution based on shape sensitivity and mesh smoothing correction in a preset shared memory space by calling the application programming interface embedded in the solver kernel until the preset convergence condition is met, and the simulation design analysis result is determined; the stress cloud map, displacement cloud map, and optimization convergence curve from the simulation design analysis result are pushed out.

[0024] In this embodiment, for ease of description, the following description will focus on the integrated simulation design push device that identifies the optimization within the solver.

[0025] Because existing technologies require frequent switching between multiple software programs, workflow setup in finite element preprocessing environments is cumbersome and has a high learning curve, leading to fragmented design processes, disjointed user experiences, and low efficiency. More critically, there is a severe disconnect between CAD and CAE models: once geometric design parameters change, the entire CAE preprocessing process must be re-executed, resulting in significant time consumption. Furthermore, many existing engineering models in industry only retain finite element mesh models without corresponding CAD geometric models, rendering parametric modeling from a geometric perspective without a basis. Existing freeform optimization or Morph techniques based on mesh deformation are insufficient to accurately characterize specific engineering geometric features such as hole radius / center position, chamfer radius, and line length. The geometric parametric functions of some commercial software are limited to simple, regular models and cannot be used for complex topological structures.

[0026] This application provides a solution that, through structural optimization design, can obtain better design scheme information from a preset simulation analysis model. Based on this, through inverse geometric parameterization, it can directly identify engineering geometric features such as the radius of a circular hole, the center position of a circle, and the length of a straight line using only the mesh model, even without a CAD geometric model. This breaks through the dependence on geometric models and solves the problem of existing mesh models being unable to be parameterized for optimization. Simultaneously, it can integrate multiple types of parameters, such as material properties and element properties, as optimization design variables, overcoming the limitation of only being able to handle single geometric variables. This allows for more comprehensive parameterized definition and flexible control of the design scheme. Furthermore, by calling the application programming interface embedded in the solver kernel, it directly performs iterative simulation solutions and mesh smoothing correction based on shape sensitivity in a shared memory space, further improving computational efficiency while ensuring solution accuracy. At this point, the stress cloud map, displacement cloud map, and convergence curve from the obtained simulation design analysis results are directly pushed to the same post-processing interface, eliminating the need to frequently switch between multiple software programs to view the results. This significantly simplifies the operation process and achieves a seamless integrated experience of analysis, optimization, and result viewing.

[0027] Based on this, embodiments of this application provide an integrated simulation design push method for solver internal optimization, referring to... Figure 1 , Figure 1 This is a flowchart illustrating the first embodiment of the integrated simulation design push method for internal optimization of the solver in this application.

[0028] In this embodiment, the integrated simulation design push method optimized within the solver includes steps S10~S40: Step S10: Perform structural optimization design based on the preset simulation analysis model to determine the optimization design scheme information; It should be noted that the optimized design scheme information is a set of product design scheme data generated within the solver after performing one or more structural optimization iterations on a preset simulation analysis model. It represents the mathematical solution seeking the optimal performance under the current engineering constraints. Its form depends on the type of structural optimization used. For example, when performing topology optimization on a preset simulation analysis model of an automobile control arm, the determined optimized design scheme information is no longer the original solid block model data, but rather geometric and material distribution description data of a hollow skeleton structure containing material removal paths and load transfer paths.

[0029] It is understood that the preset simulation analysis model is an initial digital prototype model of the product that the user imports or establishes in a unified finite element preprocessing environment before starting the optimization process. It is a complete finite element analysis input file that has been meshed and has clearly assigned material properties (such as elastic modulus, Poisson's ratio, density), element types (such as shell elements, solid elements), and various engineering loads and displacement constraints. For example, a preset simulation analysis model for stiffness analysis of automotive body-in-white includes body mesh data composed of hundreds of thousands of shell elements, Young's modulus and yield strength of specific steel grades for each part, and boundary conditions and loads required for calculating bending and torsional stiffness under simulated real working conditions.

[0030] In a specific embodiment, structural optimization design is performed based on a preset simulation analysis model. At least one of the following is determined: topology optimization design scheme information, shape optimization design scheme information, size optimization design scheme information, and morphology optimization design scheme information. The structural optimization design includes at least one of topology optimization, shape optimization, size optimization, and morphology optimization. Specifically, the system can read preset simulation analysis models imported or created by the user. These models have completed mesh generation and are assigned complete finite element input data, including material properties, element types, load conditions, and displacement constraints. Based on the needs of the design stage, at least one structural optimization type (topology optimization, shape optimization, size optimization, and morphology optimization) can be selected in the solver interface. Figure 2 As shown, Figure 2 This diagram illustrates the structural optimization of the integrated simulation design push method for solving the internal optimization of the solver in this application. The diagram visually demonstrates the typical results of topology optimization, shape optimization, size optimization, and morphology optimization by dividing the data into four regions: Figure 2 (a) in the figure is a cloud map of the unit density distribution of topology optimization. The material retention and removal areas are displayed by color gradation, presenting the concept configuration of the optimal force transmission path with unit density as the variable. Figure 2 (b) shows the superimposed comparison of the boundary contours before and after shape optimization, demonstrating the fine adjustment of the local shape of the structure with node coordinates as variables; Figure 2 (c) in the figure represents the color-coded labels for the thickness of each region after size optimization, reflecting the optimal cross-sectional parameter distribution with unit thickness as the variable; Figure 2 (d) in the figure represents the distribution pattern of the stiffeners generated by the morphology optimization, showing the uneven morphology formed on the thin-walled surface with the nodal normal displacement as the variable.

[0031] It should be understood that topology optimization, shape optimization, size optimization, and morphology optimization methods all solve independently for a single variable type (element density, nodal coordinates, element thickness, or nodal normal displacement). The results are mainly conceptual configurations or preliminary design schemes described by geometric variables, and cannot cover the combined optimization of non-geometric parameters such as material grade, ply angle, and load conditions. Therefore, they are difficult to independently meet the engineering requirements for joint optimization of multiple types of variables in the detailed design stage. However, in the practical application of this application, the characteristic parameters of at least one of the topology optimization design scheme information, shape optimization design scheme information, size optimization design scheme information, and morphology optimization design scheme information are extracted to determine the optimization design scheme information. The characteristic parameters include any type of geometric and non-geometric parameters, which can also be combined according to actual engineering needs. The system can be used in combination, for example, by first obtaining the conceptual configuration of the material distribution path through topology optimization, and then by fine-tuning the detailed parameters through size optimization or shape optimization. The system extracts the feature parameters of at least one of the optimization design schemes, including topology optimization design scheme information, shape optimization design scheme information, size optimization design scheme information, and morphology optimization design scheme information. The feature parameters cover any type of geometric parameters (such as node coordinates, element thickness, cross-sectional size, hole position and shape, etc.) and non-geometric parameters (such as material grade, ply angle, ply thickness, etc.). These feature parameters are used as candidate design variables for multi-parameter optimization, so that joint iterative optimization is performed through the multi-parameter optimization engine embedded in the solver kernel. This breaks through the limitations of single variable types and achieves seamless connection from structural concept optimization to detailed multi-parameter collaborative optimization, meeting the needs of integrated simulation design push.

[0032] In one feasible implementation, step S10 may include steps A11-A12: Step A11: Based on the preset simulation analysis model, perform structural optimization design and determine at least one of the following: topology optimization design scheme information, shape optimization design scheme information, size optimization design scheme information, and morphology optimization design scheme information. The structural optimization design includes at least one of topology optimization, shape optimization, size optimization, and morphology optimization. It should be noted that the topology optimization design information can be obtained by iteratively solving the problem using the element density as a variable through the variable density method or the progressive structural optimization method, and outputting topology optimization design information describing the optimal material distribution path. For example, after topology optimization, the automotive control arm generates geometric and material distribution description data of a hollow skeleton structure containing material removal paths and load transfer paths from a solid block model. The shape optimization design information can be obtained by finely adjusting the structural boundary without changing the topological connection relationship, and outputting information describing the changes in node coordinates after boundary contour optimization, using node coordinates as variables. The size optimization design information can be obtained by using quantifiable parameters such as element thickness and cross-sectional dimensions as variables, and outputting size optimization design information describing the optimal thickness or cross-sectional dimensions of each region. The morphology optimization design information can be obtained by generating stiffeners or concave-convex morphologies on the surface of a thin-walled structure to improve stiffness, and outputting morphology optimization design information characterizing the distribution shape and height of the stiffeners.

[0033] It is understandable that topology optimization, shape optimization, size optimization, and morphology optimization are four basic solution strategies, which operate on different design variable spaces and are suitable for different design stages. They can be flexibly combined and applied in a unified finite element preprocessing environment according to engineering needs.

[0034] Step A12: Extract feature parameters of at least one of the topology optimization design scheme information, shape optimization design scheme information, size optimization design scheme information, and morphology optimization design scheme information to determine the optimization design scheme information. The feature parameters include any type of geometric parameters and non-geometric parameters.

[0035] It is understandable that geometric parameters are structural characteristic quantities that can be directly described by spatial geometric quantities. Their numerical changes directly characterize changes in the external or internal geometric shape of the structure. For example, in topology optimization design schemes, the element density distribution value, the spatial envelope range of the material retention area and the boundary contour coordinates; in shape optimization design schemes, the node coordinate displacement increment, the hole position and shape parameters, and the radius of curvature of the boundary curve; in size optimization design schemes, the shell thickness value, beam cross-sectional dimensions, stiffener height and spacing, and characteristic length and width; and in morphology optimization design schemes, the distribution position, orientation angle, stiffener height and draft angle of the stiffeners, etc., can be directly extracted numerically from the optimization result cloud map, node coordinate data table or cross-sectional parameter distribution data, and used as continuous or discrete variables in iterative optimization. Non-geometric parameters are structural characteristic quantities that are not directly represented by spatial geometric quantities but are related to material properties, load conditions, and process constraints. Their numerical changes represent changes in the structure's physical properties or engineering conditions. For example, material grade information and material constitutive parameters extracted from topology optimization or size optimization design schemes, ply angle and ply thickness values ​​extracted from shape or size optimization design schemes related to composite material structures, load condition parameters and displacement constraint types extracted from comparisons of multiple optimization design schemes under different load conditions, and process constraint parameters limited by engineering manufacturing specifications, can be obtained from the characteristic description data of each optimization design scheme and the associated material property database. This enables the optimization of actual decision quantities in engineering design such as material selection, ply scheme, and load parameters, so that the proposed design scheme not only has the optimal geometric configuration, but also achieves comprehensive optimization in non-geometric dimensions such as material utilization, process feasibility, and multi-condition adaptability, truly meeting the engineering needs of joint optimization of multiple types of variables in the detailed design stage.

[0036] Step S20: Based on the optimized design scheme information, inverse geometric parameterization is performed by selecting node identifiers on the mesh model to identify the geometric feature information of the model, and the optimized design parameter information is determined by combining the model material property information and the model element property information. It should be noted that inverse geometric parameterization is the core technical approach proposed in this application to solve the problems of fragmented CAD / CAE workflows and the lack of geometric parameterization for existing mesh models. Its core idea is that, in the case of having only a finite element mesh model but no corresponding CAD geometric model, the user only needs to specify the set of node identifiers at the boundary of the target geometric feature on the mesh model through a graphical interaction in a unified finite element preprocessing environment. The algorithm backend can automatically perform geometric primitive fitting based on the set of node identifiers, inversely calculate the geometric parameters, and use the geometric parameters as design variables. Thus, accurate geometric parameterization modeling can be achieved without relying on the CAD geometric model.

[0037] Understandably, model geometric feature information is a parametric description of all geometric shapes that constitute the optimized design scheme. In the inverse geometry parametric scenario, this information is not obtained from the CAD geometric model, but is obtained by inverse calculation after fitting geometric primitives to the user-specified boundary node set on the mesh model. It can include specific engineering geometric feature parameters such as the radius and center position of a circular hole, the length and endpoint position of a straight line, the radius and central angle of an arc, the length and width of a rectangle, the radius of a cylindrical hole, and the height of a reinforcing rib. Model material property information is the physical property data of the materials associated with each component or region in the optimized design scheme, such as the elastic modulus, Poisson's ratio, density, yield strength, and coefficient of thermal expansion. Model element attribute information is the inherent parametric characteristic data of various elements in the finite element model, independent of material and geometry. It can include the thickness of shell elements, the cross-sectional shape and size of beam elements (such as the flange width and web thickness of I-beams), and the layup information of composite materials (such as the thickness of each layer, layup angle, and material type).

[0038] Additionally, it should be noted that selecting node identifiers on the mesh model is done in the finite element preprocessing environment. Users use graphical interactive methods (such as box selection, point selection, or picking by feature corner points) to specify the set of node numbers corresponding to a certain target geometric feature boundary on the existing mesh model. This allows for the reverse identification of geometric primitives such as circular holes, straight lines, and arcs and their parameters based on the spatial coordinates of discrete nodes. This transforms the existing mesh model without parameterized information into a parameterized model that can be driven by the optimization engine.

[0039] In a specific embodiment, optimization target information and constraint information are obtained. That is, in a unified finite element preprocessing environment, the model can be directly picked up and optimization target information and constraint information can be obtained through graphical interaction. The optimization target information may include mass minimization, stiffness maximization or frequency target value, etc., and the constraint information may include stress constraints, displacement constraints, frequency constraints or manufacturing process constraints, etc.

[0040] The algorithm receives a set of node identifiers at the boundary of a target geometric feature on a user-specified mesh model. Based on this set, it performs geometric primitive fitting, reverse-calculates geometric parameters, and uses these parameters as design variables. For example, taking a two-dimensional model, when a user needs to perform parametric optimization on a circular hole, they only need to specify the set of node identifiers at the hole boundary on the mesh model by selecting a box or point. The background algorithm can then use the least squares method to fit the set of node identifiers into a circle and automatically calculate the corresponding hole radius and center position, using these as design variables for subsequent optimization. Similarly, for straight line features, the line length and endpoint positions can be calculated by fitting the straight line equation; for arc features, the arc radius and central angle can be calculated by fitting; for rectangular features, its length and width can be calculated by fitting. For three-dimensional models, this idea can be extended to the reverse identification of three-dimensional geometric feature parameters such as the radius of a cylindrical hole, the radius of a spherical hole, and the height of a reinforcing rib. In this way, as shown... Figure 3 As shown, Figure 3 This diagram illustrates the inverse geometric parameterization picking based on mesh model node identifiers in the integrated simulation design push method for solver internal optimization in this application. Figure 3 In this context, (a) represents the set of node identifiers selected by the user at the boundary of the circular hole on the mesh model. Figure 3 (b) indicates that the center position and hole radius are automatically identified through inverse geometric parameterization methods (such as least squares fitting) and used as design variables. Figure 3 (c) in the figure indicates that in the shape optimization iteration, a cooperative normal perturbation is applied to the boundary nodes to calculate the sensitivity, and mesh smoothing is combined to ensure that the internal mesh quality remains good after the boundary moves. This allows for a clear demonstration of the complete interactive process of the user selecting the set of boundary nodes for the circular hole on the mesh model, and the system automatically fitting and identifying the radius and center position of the circular hole. Thus, even without a CAD geometric model, precise geometric parameterization can be achieved solely based on the mesh model, fundamentally solving the engineering problem of the inability to parameterize and optimize existing mesh models. It can also accurately characterize specific engineering geometric features such as the radius / center position of the circular hole, the chamfer radius, and the length of the straight line, overcoming the limitations of traditional Morph technology or free shape optimization in determining the true geometric details.

[0041] Based on the model's geometric features, material properties, and element attributes from the optimized design scheme information, other design variables are determined. These discrete variables include thickness values ​​from the standard sheet metal thickness library, composite material ply angles, composite material ply thicknesses, material grade selection, and parameters constrained by engineering specifications. In other words, they are based on the model's geometric features, material properties, and element attributes from the optimized design scheme information, such as... Figure 4 As shown, Figure 4This document presents a schematic diagram of the integrated simulation design push method optimized within the solver of this application. It uses a graphical picking method to directly define various types of parameters in the model, such as geometric features, material properties, element properties, or load conditions, as design variable information. This enables comprehensive parameterization of the design scheme, covering geometric design variables obtained through inverse geometric parameterization (such as hole radius, center position, and line length), continuous variables, and commonly used discrete variables in engineering. The discrete variables include thickness values ​​from the standard sheet metal thickness library, composite material ply angles, composite material ply thicknesses, material grade selection, and parameters limited by engineering specifications. The optimization of these discrete variables is achieved collaboratively through a proxy model module and an optimization algorithm module, ensuring that the optimization results can be directly used in engineering manufacturing.

[0042] Based on the design variable information, the optimization target information, and the constraint information, the optimization design parameter information is obtained. That is, based on the design variable information, the optimization target information, and the constraint information, the optimization design parameter information that can be directly identified and driven by the multi-parameter optimization engine in the solver kernel is obtained, which can avoid the tedious operation of locating the row, column, and number of bits of the variable through a text file for parameter passing.

[0043] In one feasible implementation, step S20 may include steps B11 to B14: Step B11: Obtain optimization objective information and constraint information; It should be noted that the optimization target information refers to the optimal performance index expected to be achieved during the parameter optimization process. This may include target types such as minimizing mass, maximizing stiffness, maximizing or approaching the target value of the first-order natural frequency, and minimizing compliance. Minimizing the error between simulation results and experimental data can also be used as the optimization target in the parameter calibration scenario. The constraint information refers to the engineering restrictions that must be met during the optimization process. This may include the maximum stress not exceeding the allowable value of the material, the displacement of key points not exceeding the design limit, the first-order natural frequency avoiding the resonance range, and manufacturing process feasibility constraints (such as draft angle and minimum thickness limit).

[0044] It is understood that the optimization objectives and constraints can be set directly in the preprocessing interface without needing to be defined through text files or transferred across software.

[0045] Step B12: Receive the set of node identifiers at the boundary of the target geometric feature on the mesh model specified by the user, perform geometric primitive fitting based on the set of node identifiers, calculate the geometric parameters in reverse, and use the geometric parameters as design variables; like Figure 5 As shown, Figure 5The schematic diagram of the node marker position selection for the integrated simulation design push method optimized within the solver of this application shows that the length, width, and center point of the rectangle can be identified through inverse geometry based on the marker points.

[0046] It should be noted that the geometric primitive fitting is the process of identifying the analytical primitives (such as circles, lines, arcs, rectangles, etc.) and their parameters that best represent the geometric characteristics of a set of points from a discrete set of node coordinates using numerical methods. In specific implementations, the least squares method can be used for fitting: for circle fitting, the goal is to minimize the sum of the squared distances from all boundary nodes to the fitted circle, solving for the center coordinates and radius; for line fitting, the goal is to minimize the sum of the squared distances from all boundary nodes to the fitted line, solving for the line equation parameters and endpoint positions; for arc fitting, the radius of curvature and central angle are further solved based on the line fitting. After fitting, the obtained geometric parameters (such as the radius of a circular hole, the center position, the radius of an arc, the length of a line, the length and width of a rectangle, the radius of a cylindrical hole, the height of a reinforcing rib, etc.) are automatically created as design variables, which can participate in subsequent optimization iterations as continuous or discrete variables.

[0047] Understandably, the key advantages of this inverse geometry parameterization method are: firstly, it is completely independent of CAD geometric models, requiring only mesh models, making it suitable for large amounts of historical data with only mesh models; secondly, it is extremely user-friendly, requiring only the specification of node identifiers at the boundary of the target geometric features, without the need for manual measurement or input of geometric parameters; and thirdly, the identified geometric parameters have clear engineering significance (such as the radius of a circular hole and the position of the center), and the optimization results can be directly used for manufacturing, overcoming the shortcomings of free-form optimization or Morph technology, which can only produce irregular free shapes and lack manufacturability.

[0048] In one feasible implementation, step B12 may include steps C11-C12: Step C11: Use the least squares method to fit the set of node identifiers into a circle, a straight line, or an arc, and calculate the corresponding radius and center position of the circle, length and endpoint position of the straight line, or radius and central angle of the arc, etc. It should be noted that the radius of a circular hole is the distance from the center to the boundary of the hole, which determines the size of the hole; the position of the center is the coordinate of the center point of the hole in the model coordinate system, which determines the spatial positioning of the hole; the length of a straight line is the distance from the start point to the end point of the straight line, which determines the size of the linear feature; the position of the endpoints is the coordinate of the two endpoints of the straight line in the model coordinate system, which determines the orientation and range of the straight line; the radius of an arc is the radius of the circle in which the arc is located, which determines the curvature of the arc; and the central angle is the angle formed by the lines connecting the two endpoints of the arc to the center, which determines the range of the arc's curvature.

[0049] Understandably, the least squares method is a mathematical optimization technique that finds the best-fitting primitive and its parameters by minimizing the sum of the squares of the vertical distances from each discrete point in the node identifier set to the target geometric primitive (circle, line, or arc), thereby minimizing the fitting error in a statistical sense, and then reconstructing the accurate geometric feature parameters from the discrete grid nodes.

[0050] Step C12, the geometric parameters are used as continuous or discrete design variables, and the geometric parameters include at least one of the following: circular hole radius, center position, arc radius, straight line length, rectangle length and width, cylindrical hole radius, and reinforcing rib height.

[0051] It should be noted that the radius of a circular hole is the radius of a circular through hole or blind hole. As a continuous variable, it can vary continuously within a specified range, or as a discrete variable, it is limited by the standard drill bit specifications. The center position is the coordinate value of the center of the circular hole in a plane or space. It is usually used as a continuous variable in optimization to determine the arrangement of the holes. The radius of curvature of an arc feature determines the curvature of the arc boundary or chamfer. The straight line length is the straight line segment dimension of a linear boundary, stiffener, or a component on one side, which directly affects the geometric shape of the structure. The length and width of a rectangle refer to the length of the long side and the length of the short side of a rectangular feature. It is often used to describe the dimensional parameters of plates, openings, or cross-sectional shapes. The radius of a cylindrical hole is the feature radius of a cylindrical hole in a 3D model, which determines the cross-sectional size of a cylindrical cavity. The height of a stiffener is the height of the protruding stiffener along the normal direction on a thin-walled structure, which determines the degree of stiffening and the stiffness contribution of the stiffener.

[0052] Step B13: Based on the model geometric feature information, model material property information, and model unit property information of the optimized design scheme information, determine other design variable information. The discrete variables in the design variable information include thickness values ​​in the standard sheet metal thickness library, composite material ply angle, composite material ply thickness, material grade selection, and parameters limited by engineering specifications. It should be noted that the design variable information is a set of parameters extracted from the optimized design scheme and automatically adjusted by the multi-parameter optimization engine during the optimization iteration process. In addition to the geometric design variables obtained through inverse geometric parameterization, it also includes model material property information and model element property information. Among them, the model geometric feature information can be geometric parameters such as node coordinates, cross-sectional dimensions, and hole positions and shapes; the model material property information can be material constitutive parameters such as elastic modulus, density, and yield strength; and the model element property information can be element characteristic parameters such as shell element thickness, beam element cross-sectional parameters, and composite material layup definitions. This enables a comprehensive parameterized definition of the design scheme in the geometric, material, and element dimensions.

[0053] It is understood that the thickness values ​​in the standard sheet metal thickness library are discrete selectable thickness specifications that conform to industry standards (such as 0.8mm, 1.0mm, 1.2mm, 1.5mm, etc.), the composite material ply angles are discrete orientation values ​​of each ply in the composite laminate relative to a reference direction (such as 0°, ±30°, ±45°, 90°, etc.), the composite material ply thicknesses are discrete thickness specifications of each ply, the material grade selection is to select specific engineering material grades (such as specific grades of steel, aluminum alloys or composite materials) from the material database as design variables, and the parameters constrained by engineering specifications are discrete parameter options constrained by manufacturing process specifications, supply specifications or enterprise standards, so that the optimization results can directly have engineering manufacturability and avoid performance loss caused by human error.

[0054] Step B14: Obtain the optimization design parameter information based on the design variable information, the optimization target information, and the constraint information.

[0055] It should be noted that the optimized design parameter information is a set of parameters that transforms the optimized design scheme into a set that can be recognized and driven by the optimization engine in the solver kernel. This includes design variables, optimization objectives, and constraints. For example, for a car control arm scheme that has undergone topology optimization, the optimized design parameter information will explicitly specify that "the radius of the circular hole identified by inverse geometry parameterization can be continuously varied from 5 to 15 mm (design variable), the height of the reinforcing rib of the control arm can be continuously varied from 5 to 15 mm (design variable), the objective is to minimize the mass (optimization objective), but the maximum stress must be less than 200 MPa and the first natural frequency must be higher than 200 Hz (constraint)".

[0056] Step S30: By calling the application programming interface embedded in the solver kernel, the optimized design parameter information is subjected to iterative simulation and mesh smoothing correction based on shape sensitivity in the preset shared memory space until the preset convergence condition is met, and the simulation design analysis result is determined. It should be noted that the shape sensitivity-based iterative simulation solution, in each optimization iteration, directly retrieves low-level data such as the stiffness matrix and mass matrix from the shared memory space by calling the solver kernel's application programming interface. It calculates the sensitivity derivative of the objective function (such as compliance, stress, etc.) with respect to geometric design variables (such as nodal coordinates, hole radius), and determines the update direction and step size of the design variables based on this derivative value. This drives the solver to perform a new round of finite element simulation analysis, iterating repeatedly until the convergence condition is met, thereby achieving efficient and high-precision optimization of the structural shape. Meanwhile, the mesh light... Smoothing correction is a mesh quality maintenance operation performed after each update of the boundary node position based on sensitivity information (e.g., a change in the radius of a circular hole or a movement of the center). This is done to prevent the movement of boundary nodes from causing distortion or quality degradation of the internal mesh elements. For example, methods such as Laplace smoothing (adjusting the internal nodes to the average position of their neighboring nodes) or Helmholtz filtering (achieving a smoother finish by solving partial differential equations) can be used to readjust the coordinates of the internal mesh nodes. This ensures that the mesh maintains good element quality throughout the iteration process, thus ensuring the accuracy and stability of the simulation solution.

[0057] Understandably, general-purpose multidisciplinary optimization platforms lack a visual interface for finite element solvers and pre- and post-processing. They require complex workflows to establish connections between modules and necessitate data exchange via text files. This necessitates parsing these text files and parameterizing variables by defining their rows, columns, and number of bits. For example, the complex workflow structure, file transfer relationships between modules, and frequent switching between pre-processing, optimization monitoring, and post-processing software result in cumbersome processes, inefficient data exchange, and a fragmented user experience. Therefore, the application programming interface (API) embedded in the solver kernel is essentially a set of function call interfaces deeply integrated into the core code of the finite element solver, and is not compatible with general-purpose multidisciplinary optimization platforms. Optimization platforms (such as Isight and Optimus) employ a completely different external encapsulation method for driving solvers via command lines or text files. They can be directly compiled and linked within the solver's executable file by calling the aforementioned application programming interface (API), thus directly accessing the solver's runtime memory data structures. This allows direct reading of element information, node information, stiffness matrix, mass matrix, and intermediate calculation results from within the solver, without waiting for the solver to write the results to a text file for parsing. Alternatively, the solver can directly modify the model parameter values ​​corresponding to design variables (such as shell element thickness, material properties, and node coordinates) in memory, triggering incremental or complete reanalysis, or calling the solver kernel's gradient calculation function to provide accurate or semi-analytical derivative information for sensitivity analysis. For example, when the optimization engine needs to modify the thickness value of a shell element, it can call the API interface SetShellThickness(element_id, new_thickness) to complete the modification in memory. The solver will directly use the new value in the next analysis, and the entire process does not require reading or writing any intermediate files.

[0058] Additionally, it should be noted that the preset shared memory space is a physical memory region allocated by the operating system when the solver process starts. It can be accessed by both the solver kernel and the optimization engine. It can be created when the optimization task is initialized and its lifecycle spans the entire optimization iteration process until the simulation design analysis results are determined. The preset shared memory space stores core data that needs to be frequently exchanged during the optimization iteration process, including the current values ​​of design variables, response quantities of each iteration (such as compliance, stress, frequency, displacement, temperature, buckling critical load), sensitivity matrix, and coefficients of surrogate models. Since all data exchange is completed within the process through memory pointers, the file I / O overhead and cross-process communication latency in the external call mode can be avoided.

[0059] In a specific embodiment, robust model evaluation results are obtained by calling the application programming interface (API) embedded in the solver kernel. That is, the solver kernel integrates an optimization engine consisting of an experiment design module, a surrogate model module, an optimization algorithm module, a stochastic analysis module, and the API between the solver and the surrogate model. Figure 6 As shown, Figure 6 This diagram illustrates the internal relationships of the optimization engine in the integrated simulation design push method for solving the solver in this application. The optimization engine is embedded within the solver kernel and shares memory with the solver. It integrates experimental design modules, surrogate model modules, optimization algorithm modules, and stochastic analysis modules. Each module achieves association and data interaction by automatically calling the solver kernel's application programming interface (API), eliminating the need for users to manually build external workflows. The optimization engine API allows defining design variables, design responses, optimization objectives, and constraints in the optimization problem through interfaces such as PanaDv, PamResponse, PamOptobj, and PamOptCons, and configuring the OptAlg optimization algorithm. The program employs various solution strategies, including the Design of Experiments (DOE), the Design of Experiments (DOE), and the Responsive Surface Model (RSM). After completing all definitions, the program initializes these modules through a series of Initial calls. It then executes GetVar_DOE to obtain experimental design sample points and drives the solver for simulation analysis. GetVar_RSM is used to construct a surrogate model based on the sample data to approximate the mapping relationship between variables and responses. GetVar_OptAlg calls genetic algorithms, particle swarm optimization, or gradient-based algorithms to iteratively correct global exploration and local optimization within the surrogate model or directly based on solver analysis. The entire process achieves internal closed-loop data exchange within the solver kernel's shared memory space via APIs.

[0060] Based on the robust model evaluation results, the optimized design parameters are globally explored and iteratively corrected in a preset shared memory space until the preset convergence condition is met. The first simulation design analysis result is then determined. That is, based on the robust model evaluation results, the optimization engine can automatically call the multi-parameter optimization engine embedded in the solver kernel and sharing the solver's memory space. Initial sample points are generated using the optimal Latin hypercube design, covering the discrete variable combination space. A Kriging surrogate model is constructed based on these sample points to approximately represent the relationship between mass, frequency, stress, and other responses and thickness variables. The discrete variable optimization function of the genetic algorithm is used to perform a global search on the surrogate model to locate the optimal region. At this point, the optimization result of the discrete variables can be expressed as:

[0061] like Figure 7 As shown, Figure 7This diagram illustrates the probability distribution curve of the integrated simulation design push method optimized within the solver of this application. The optimization objective is to minimize the error between the simulation and experimental stress curves. The embedded optimization engine is invoked for parameter calibration. After calibration, the material parameters are defined as random variables following a normal distribution. The stochastic analysis module can be called to perform Monte Carlo simulations to evaluate the statistical distribution of component stiffness and reliability. The entire process involves parameter definition in a unified preprocessing stage, with the optimization engine automatically calling the solver for iteration. Post-processing directly displays the probability curves without requiring software switching, achieving an integrated process from parameter identification to robustness assessment. At this point, Monte Carlo simulations and reliability analyses are performed by directly reading the model data interaction information within the solver from shared memory, yielding robust model evaluation results. The model data interaction information includes element information, node information, stiffness matrix, mass matrix, and analysis results. The robust model evaluation results can be expressed as:

[0062] The entire iteration process is completed within the process itself, fundamentally eliminating the overhead and error risk of file parsing.

[0063] A semi-analytical method is used to perform local optimization and iterative correction of the optimized design parameters in a preset shared memory space until a preset convergence condition is met, thus determining the second simulation design analysis result, i.e., as shown below. Figure 8 As shown, Figure 8 The post-processing optimization result cloud map of the integrated simulation design push method optimized within the solver of this application is shown. The figure shows the post-processing optimization result cloud map obtained by calling the stiffness matrix and mass matrix information of the solver kernel and using a semi-analytical method to efficiently calculate the ply thickness and ply angle sensitivity. This demonstrates the advantage of this application in computational efficiency. The optimization engine obtains the contribution of each layer element to the overall stiffness matrix through the API interface and directly calculates the derivative of the thickness change with the buckling eigenvalue using a semi-analytical method. During the calculation process, the analytical method is used for simple physical quantities, and a semi-analytical strategy combining the central difference method and the analytical method is used for complex field variables to ensure a balance between accuracy and efficiency. Compared to Isight's finite difference method (which requires N additional solver calls), for example, when N=8, the efficiency is improved by 8 times. That is, before optimization, the angles of each layer are: 0.0, 30.0, -30.0, 30.0, -30.0, 30.0, -30.0, 30.0, and after optimization, the angles of each layer are: -27.0, 0.31, 9.01, 0.31, 9.01, 0.12, -0.44, -0.95.

[0064] When the optimized design parameter information includes geometric design variables (such as the radius of a circular hole and the position of the center) obtained through inverse geometric parameterization, a cooperative perturbation is applied to the boundary node set corresponding to the geometric design variables. The shape sensitivity derivative of the stiffness matrix is ​​approximated using the central difference method, and the adjoint method is used to solve for the adjoint variables corresponding to all design variables at once to obtain the complete process of the sensitivity of each design variable, demonstrating the advantage of this application in the efficiency of shape sensitivity calculation. Specifically, when the design variable is the radius of a circular hole, all nodes on the boundary of the circular hole are perturbed by the same step size ΔR along their respective node normals (or the radial direction of the fitted circle), and the shape sensitivity of the stiffness matrix to the radius variable is solved by difference. When the design variable is the center position, all nodes on the boundary of the circular hole generate the same rigid displacement perturbation ΔX and ΔY relative to the new center, and the shape sensitivity of the stiffness matrix to the center position variable is solved by difference. After optimizing the new radius and center position, the new positions of the nodes at the geometric boundary of the circular hole are first determined, and then the internal mesh nodes are smoothed by Laplace smoothing or Helmholtz filtering to ensure mesh quality. Figure 9 As shown, Figure 9 This diagram illustrates the optimized radius and position of the circular hole using the integrated simulation design push method optimized within the solver of this application. Other geometric parameters, such as arc radius, line length, rectangle length and width, and the radius of the cylindrical hole and the height of the reinforcing rib in the 3D model, can be handled in a similar manner. This semi-analytical sensitivity solution strategy is completed in a preset shared memory space. The optimization engine obtains the contribution of each element layer to the overall stiffness matrix through an API interface. For simple physical quantities, analytical methods are used; for complex field variables, a semi-analytical strategy combining central difference and analytical methods is employed to ensure a balance between accuracy and efficiency. Compared to the finite difference method of external multidisciplinary optimization platforms (which requires N additional solver calls), the method in this application has a significant efficiency advantage when the number of variables is large.

[0065] The simulation design analysis result is obtained based on at least one of the first simulation design analysis result and the second simulation design analysis result.

[0066] Step S40: Push the stress cloud map, displacement cloud map and optimized convergence curve from the simulation design analysis results.

[0067] It should be noted that the stress cloud map is a visualization of the stress tensor components (such as Mises equivalent stress, principal stress, or normal stress and shear stress in each direction) of each node in the model from the simulation design analysis results, rendered on the surface of the optimized three-dimensional geometric model in the form of a continuous color spectrum mapping. The color spectrum, from cool colors (such as blue) to warm colors (such as red), corresponds to the distribution of stress values ​​from low to high, allowing designers to intuitively identify high-stress areas and low-stress areas. It can be dynamically updated during the optimization iteration process. For example, when performing multi-parameter optimization of an engine connecting rod, after each iteration, the solver post-processing interface will automatically refresh the stress cloud map of the current design scheme. Designers can monitor the evolution trend of stress concentration areas in the structure in real time during the weight reduction process without switching to third-party software, and determine whether there is a potential risk of strength failure.

[0068] It is understood that the displacement cloud map is a visual graph that superimposes the displacement vectors (usually the resultant displacement amplitude or a component in a specified direction) of each node of the model in the simulation design analysis results onto the original geometric configuration with a deformation amplification factor. The displacement cloud map represents the displacement magnitude at each position through a color spectrum and intuitively displays the overall deformation mode of the structure through mesh deformation. It can directly reflect the stiffness characteristics of the optimization scheme. For example, when performing multi-parameter optimization on a body-in-white, the post-processing interface can simultaneously display the displacement cloud maps under bending and torsional conditions. Designers can observe the maximum displacement value of the loading point and the overall deformation distribution to judge in real time whether the stiffness of the current optimization scheme meets the design target. Since the push and optimization solution are completed in the same software environment, designers can compare the displacement cloud maps of different optimization iteration steps to quickly understand the influence of design variables on structural stiffness.

[0069] Additionally, it should be noted that the optimization convergence curve is a numerical visualization graph that displays the trend of key performance indicators changing with the number of iterations in real time during the optimization iteration process in the form of a two-dimensional line graph or scatter plot. Typical convergence curves include the objective function change curve (e.g., mass decreases with the number of iterations until convergence), the constraint function change curve (e.g., maximum stress fluctuates around the allowable value with the number of iterations and eventually satisfies the constraint), and the design variable change curve (e.g., a key thickness parameter tends to a stable value with the number of iterations). The optimization convergence curve has a dynamic appending characteristic, that is, new data points are added after each iteration. The post-processing interface can instantly add curves to the end and refresh the display. For example, when performing multi-parameter optimization on a composite wing skin, the post-processing interface can simultaneously push three convergence curves: one showing the process of the total structural mass gradually decreasing from the initial 82.5 kg to the convergence value of 75.2 kg; another showing the process of the maximum buckling load factor gradually increasing from 0.85 and converging to 1.05 to meet the stability constraint; and the third showing the process of the critical ply angle iteratively converging from the initial 45° to -27°. This allows for real-time evaluation of the optimization progress, determination of whether oscillations or stagnation occur, and early termination of optimization or adjustment of the optimization strategy when necessary.

[0070] In a specific embodiment, such as Figure 10 As shown, Figure 10 This diagram illustrates the simulation design analysis results of the integrated simulation design push method optimized within the solver of this application. It shows the stress cloud map, displacement cloud map, and optimization convergence curve displayed in real-time within the same finite element post-processing interface. This demonstrates a seamless integrated process where optimization model definition, optimization solution, and result viewing occur within the same software environment. In the unified finite element post-processing interface of the solver, the stress cloud map, displacement cloud map, and optimization convergence curve from the simulation design analysis results can be pushed to the user for dynamic display in a synchronously refreshed and interactive manner. The optimization effect can be intuitively evaluated without switching to third-party software, achieving a seamless integrated process where optimization model definition, optimization solution, and result viewing occur within the same software environment. For example, after the optimization engine writes the design variable values ​​and response quantities of the current iteration into the result area in the shared memory space, the post-processing module directly reads the data from memory through the API interface, renders the graphical interface, and completes the push, fundamentally eliminating the operational gaps caused by frequent switching between multi-disciplinary optimization platforms, solvers, and post-processing software.

[0071] This embodiment proposes an integrated simulation design push method for solver internal optimization. Based on a preset simulation analysis model, structural optimization design is performed to determine the optimized design scheme information. Based on the optimized design scheme information, inverse geometric parameterization is performed by selecting node identifiers on the mesh model to identify the model's geometric features. Combined with model material properties and model element properties, optimized design parameters are determined. The optimized design parameters are then iteratively simulated and solved based on shape sensitivity in a preset shared memory space by calling the application programming interface embedded in the solver kernel, along with mesh smoothing correction, until a preset convergence condition is met, thus determining the simulation design analysis result. Finally, the stress contour plot, displacement contour plot, and optimization convergence curve from the simulation design analysis result are pushed to the solver. This invention addresses the technical challenge of pushing simulation designs before finite element analysis begins. Compared to existing technologies, this application achieves superior design information from a pre-set simulation analysis model through structural optimization design. Furthermore, by employing inverse geometric parameterization, it can directly identify engineering geometric features such as hole radius, center position, and straight line length using only the mesh model, even without a CAD geometric model. This overcomes the dependence on geometric models and solves the problem of existing mesh models being unable to be parameterized. Simultaneously, it integrates multiple types of parameters, including material properties and element properties, as optimization design variables, overcoming the limitation of handling only single geometric variables and enabling more comprehensive parameterized definition and flexible control of the design scheme. By calling the application programming interface embedded in the solver kernel, it directly performs shape sensitivity-based iterative simulation and mesh smoothing correction in shared memory space, further improving computational efficiency while ensuring solution accuracy. Finally, the stress cloud map, displacement cloud map, and convergence curve from the obtained simulation design analysis results are directly pushed to the same post-processing interface, eliminating the need for frequent switching between multiple software programs to view results. This significantly simplifies the operation process and achieves a seamless integrated experience for analysis, optimization, and result viewing.

[0072] Based on the first embodiment of this application, in the second embodiment of this application, the same or similar content as the first embodiment can be referred to the above description, and will not be repeated hereafter.

[0073] In this embodiment, refer to Figure 11 , Figure 11 This is a flowchart illustrating Embodiment 2 of the integrated simulation design push method for solver internal optimization in this application. Step S30 specifically includes steps S31 to S34: Step S31: Obtain robust model evaluation results by calling the application programming interface embedded in the solver kernel; It should be noted that the robust model evaluation results are a comprehensive data report obtained after quantitatively evaluating the performance robustness of the current design scheme during the multi-parameter optimization process. It may include the mean, standard deviation and coefficient of variation of key responses, the probability that the design scheme still meets all constraints under given parameter fluctuations, and the sensitivity ranking that identifies the greatest impact on performance fluctuations. For example, after conducting a robust evaluation on a batch of automotive sheet metal parts with a manufacturing tolerance of ±0.05mm, the evaluation results will clearly inform the designers that the current design scheme has a 99.7% probability of meeting the stiffness requirements in the simulation of 3 million sample points, but the probability of the maximum stress exceeding the standard is 3.2%, and the risk point is concentrated at the root of the inner plate stiffener.

[0074] Understandably, the application programming interface (API) is a series of function call interfaces that the solver kernel exposes to the stochastic analysis module in the multi-parameter optimization engine. It can directly and efficiently obtain the core computational data required to perform Monte Carlo simulations or reliability analyses without the need for external file exchange or restarting the solver process.

[0075] In a specific embodiment, model data interaction information is obtained by calling the application programming interface (API) of the optimization engine. This model data interaction information includes element information, node information, stiffness matrix, mass matrix, and analysis results. Monte Carlo simulation and reliability analysis are performed based on this model data interaction information to obtain robust model evaluation results. This can be achieved by calling the API embedded in the solver kernel. The solver kernel integrates an optimization engine consisting of an experimental design module, a surrogate model module, an optimization algorithm module, a stochastic analysis module, and an API between the solver and the solver. Each module in the optimization engine shares element libraries, material libraries, load libraries, and intermediate data during the solution process with the solver by calling the API of the solver kernel. The optimization engine can directly read data from within the solver. The model data interaction information stored in the data structure includes element information, node information, stiffness matrix, mass matrix, and analysis results, without the need for data exchange through an external file system. Based on this, design variables can be defined as random variables that follow a specific probability distribution (such as normal distribution, uniform distribution, etc.). The stochastic analysis module can be called to perform Monte Carlo simulation or reliability analysis to obtain the statistical distribution characteristics and failure probability of the design scheme performance under the influence of manufacturing tolerances, material property fluctuations, or load uncertainties. In other words, robust model evaluation results are obtained. There is no need to build workflows externally to establish the relationship between modules, nor is there a need to parse text files for parameter transmission. This fundamentally avoids the problems of cumbersome workflows and low data exchange efficiency of multidisciplinary optimization platforms (such as Isight).

[0076] In one feasible implementation, step S31 may include steps D11~D12: Step D11: Obtain model data interaction information by calling the application programming interface of the optimization engine. The model data interaction information includes element information, node information, stiffness matrix, mass matrix, and analysis results. It should be noted that the model data interaction information is a set of computational data directly transferred between the multi-parameter optimization engine and the solver kernel in the shared memory space to support optimization iteration and stochastic analysis. Essentially, it is a structured mapping in memory of the underlying mathematical model and physical field results built and generated by the solver during the finite element analysis process.

[0077] Understandably, the element information includes the discretized structural description of each element in the finite element model, such as the type identifier, topological connection relationship, material assignment, and geometric properties. The node information includes the spatial coordinates, degree of freedom number, boundary constraint state, and load application of each node. The stiffness matrix is ​​an assembly matrix of overall stiffness coefficients that characterizes the structure's resistance to deformation. The mass matrix is ​​an assembly matrix of overall mass coefficients that characterizes the structure's inertial properties. The analysis results include all physical response data output by the solver after completing a full analysis, such as displacement field, stress field, strain field, frequency, and buckling modes.

[0078] Step D12: Based on the model data interaction information, perform Monte Carlo simulation and reliability analysis to obtain robust model evaluation results.

[0079] Understandably, Monte Carlo simulation is a random sampling numerical method based on the law of large numbers. It randomly selects a large number of sample points from the probability distribution of design variables, calls the solver for deterministic analysis on each sample point, and statistically analyzes the distribution, mean, variance, and quantiles of the response. Reliability analysis, on the other hand, is based on Monte Carlo simulation to calculate the probability that the design scheme will not fail under a given function, or to solve the probabilistic constraint boundary corresponding to the target reliability index. Since model data interaction information can be directly obtained from shared memory through the application programming interface, stochastic analysis can drive the solver to complete tens of thousands of sample analyses with extremely high efficiency. Unlike traditional external platforms, it does not require cumbersome file preparation, solver calls, and result parsing for each sample calculation. This allows for the rapid acquisition of robust model evaluation results containing the mean, standard deviation, coefficient of variation, failure probability, and sensitivity ranking of key responses. This enables designers to identify areas where parameter fluctuations affect performance early in the optimization iteration process, ensuring that the proposed design scheme is optimally performed and robustly reliable.

[0080] Step S32: Based on the robust model evaluation results, the optimized design parameter information is globally explored and iteratively corrected in a preset shared memory space until the preset convergence condition is met, and the first simulation design analysis result is determined. It should be noted that the first simulation design analysis result is a set of optimal or near-optimal design schemes that meet the preset convergence conditions. It represents the convergence of design variable values ​​and their corresponding performance response values ​​after iterative optimization by global search strategies such as genetic algorithms or particle swarm optimization under the current surrogate model confidence level. For example, in the optimization of sheet metal thickness of automotive body-in-white, the first simulation design analysis result can be the optimal thickness combination of each sheet metal area (such as 1.2mm for the engine hood, 1.5mm for the front bulkhead, and 0.8mm for the floor) and the corresponding performance indicators such as vehicle mass, bending stiffness, torsional stiffness, and modal frequency determined after global search by a genetic algorithm guided by a Kriging surrogate model.

[0081] Understandably, the preset convergence condition is a set of quantitative criteria used in the optimization iteration process to determine whether the current design scheme has reached an acceptable optimal level. It has hard termination conditions such as a maximum iteration limit (e.g., 100 generations) and a computation time limit to prevent getting stuck in infinite iteration in complex multi-peak problems and to ensure that the optimization process is completed within an acceptable time cost for engineering.

[0082] In a specific embodiment, the corresponding approximate mapping relationship information is determined based on the robust model evaluation results; at least one of the corresponding genetic discrete variable information and particle swarm discrete variable information is determined based on the approximate mapping relationship information; global exploration and iterative correction are performed in a preset shared memory space based on at least one of the genetic discrete variable information and the particle swarm discrete variable information until a preset convergence condition is met, and a first simulation design analysis result is obtained. That is, the first simulation design analysis result is the simulation design analysis result obtained after iterative solution based on the global optimization strategy guided by the surrogate model within the multi-parameter optimization engine. For example, in the preset shared memory space shared by the multi-parameter optimization engine and the solver, the approximate mapping relationship information between the design variables and the response is determined based on the obtained model data interaction information. A surrogate model, constructed using methods such as the Kriging model, radial basis function neural network, or response surface model in the surrogate model module, approximates the time-consuming simulation to accelerate global exploration. Based on the approximate mapping information, global optimization algorithms such as genetic algorithms or particle swarm optimization algorithms in the optimization algorithm module perform global exploration search within the design space. The global exploration strategy can effectively handle complex optimization problems involving a mixture of discrete and continuous variables, including standard sheet metal thickness, composite material layup angle, and material grade selection. In each iteration, the optimized design parameters are corrected based on the response values ​​predicted by the surrogate model. When the prediction accuracy of the surrogate model is insufficient, the finite element solver is triggered to perform accurate analysis to update the surrogate model. This process is repeated until the preset convergence condition is met, and the first simulation design analysis result is determined.

[0083] In one feasible implementation, step S32 may include steps E11 to E13: Step E11: Determine the corresponding approximate mapping relationship information based on the robust model evaluation results; It should be noted that the approximate mapping information uses an explicit functional relationship with minimal computational cost to approximate the implicit input-output mapping that originally required calling the solver for time-consuming finite element analysis. This includes the type identifier of the surrogate model (such as a Kriging model, radial basis function neural network, or response surface model), the model coefficient matrix, kernel function parameters, correlation length vector, and internal structural parameters such as the prediction variance distribution. This allows for the prediction of the corresponding mass, stress, frequency, displacement, and other response values ​​and their prediction uncertainties within milliseconds for any given combination of design variables without restarting the finite element solver.

[0084] Step E12: Based on the approximate mapping relationship information, determine at least one of the corresponding genetic discrete variable information and particle swarm discrete variable information; It should be noted that the genetic discrete variable information refers to the information required by the genetic algorithm when performing selection, crossover, and mutation operations, such as chromosome encoding schemes, discrete variable gene bit definitions, population size, crossover probability, mutation probability, and fitness evaluation rules. For example, thickness values ​​(0.8mm, 1.0mm, 1.2mm, 1.5mm, etc.) in the standard sheet metal thickness library are encoded as integer gene bits, and the population evolves in the discrete combination space through single-point crossover and bit mutation operations. The particle swarm discrete variable information refers to the information required by the particle swarm algorithm when processing discrete variables, such as particle position discretization rules, discrete mapping operators in the velocity update formula, discrete variable storage structures for individual optima and global optima, and neighborhood topological relationships. For example, continuous velocity update results are mapped to the nearest discrete thickness specification through rounding or probabilistic selection mechanisms, enabling particles to effectively track the optimal region in the mixed continuous-discrete space, thereby driving the global optimization algorithm to perform efficient searches in complex design spaces with extremely low computational cost.

[0085] Step E13: Based on at least one of the genetic discrete variable information and the particle swarm discrete variable information, perform global exploration and iterative correction in a preset shared memory space until the preset convergence condition is met, and obtain the first simulation design analysis result.

[0086] Understandably, global exploration is the process by which a multi-parameter optimization engine, within the complete multi-dimensional space composed of design variables, uses a surrogate model to approximate the time-consuming finite element simulation analysis, and collaborates with optimization algorithms with global search capabilities such as genetic algorithms and particle swarm optimization to find the optimal solution in a complex design space containing a mixture of continuous and discrete variables. The aim is to overcome the defect of gradient-based algorithms being prone to getting trapped in local optima and to locate advantageous regions in the design space where a global optimum may exist. Iterative correction, on the other hand, is a closed-loop adaptive mechanism that, during global exploration, adjusts the values ​​of design variables and improves the accuracy of the surrogate model round by round based on the feedback of the deviation between the predicted values ​​of the surrogate model and the accurate results of the finite element analysis. This mechanism does not require data exchange through an external file system.

[0087] Step S33: Use a semi-analytical method to perform local optimization and iterative correction on the optimized design parameter information in a preset shared memory space until the preset convergence condition is met, and determine the second simulation design analysis result. It should be noted that the second simulation design analysis result is a set of high-precision local optimal design schemes that meet the preset convergence conditions. It represents the precise values ​​of the design variables and their corresponding performance response values ​​determined after fast convergence within the advantageous region located by the current surrogate model by directly calculating the sensitivity derivatives of the design variables to the response using the underlying data such as the stiffness matrix and mass matrix of the solver kernel. This ensures the accuracy and reliability of the local optimal solution and is suitable for optimization problems in the detailed design stage where continuous variables dominate and high-precision convergence is required.

[0088] In a specific embodiment, design response parameter information is obtained, including compliance, stress, frequency, displacement, temperature, and buckling. When the optimized design parameter information includes geometric design variables obtained through inverse geometric parameterization, a cooperative perturbation is applied to the boundary node set corresponding to the geometric design variables. The shape sensitivity derivative of the stiffness matrix is ​​approximated using the central difference method. For example, when the design variable is the radius of a circular hole, all nodes on the boundary of the circular hole are perturbed by the same step size ΔR along their respective node normals (or the radial direction of the fitted circle), and the shape sensitivity of the stiffness matrix to this radius variable is solved using the difference method. When the design variable is the center position, all boundary nodes of the circular hole generate the same rigid displacement perturbation ΔX and ΔY relative to the new center, and the shape sensitivity of the stiffness matrix to the center position variable is solved using the difference method. The adjoint variables corresponding to all design variables are solved at once based on the adjoint method, and the sensitivity of each design variable is obtained by combining the shape sensitivity derivative. Based on the aforementioned sensitivity, local optimization and iterative correction are performed in a preset shared memory space to update the boundary node positions. After optimizing the new geometric parameters, the new positions of the nodes at the geometric boundaries are first determined. Then, Laplace smoothing or Helmholtz filtering is applied to the internal mesh nodes to smooth the mesh and ensure mesh quality until the preset convergence condition is met, thus obtaining the second simulation design analysis result. Other geometric parameters, such as arc radius, line length, rectangle length and width, and the radius of cylindrical holes and the height of reinforcing ribs in the 3D model, can be handled in a similar manner. For example, when the design variable is the line length, the boundary nodes at the endpoints of the line are perturbed by the corresponding step size along the line direction; when the design variable is the rectangle length and width, the boundary nodes on the corresponding sides are perturbed by the corresponding step size along their respective normal directions. This semi-analytical sensitivity solution strategy is performed within a pre-defined shared memory space. The optimization engine obtains the contribution of each element layer to the overall stiffness matrix through an API interface. For simple physical quantities, such as compliance, stress, frequency, displacement, and temperature, the derivatives of the design variables with respect to the response are directly calculated analytically. For complex physical field variables, a semi-analytical strategy combining the central difference method and analytical methods is used to ensure a balance between accuracy and efficiency. Compared to external multidisciplinary optimization platforms that require additional solver calls N times per step (N being the number of variables) using the difference method, the semi-analytical method significantly reduces computational costs, making gradient optimization practically efficient for large-scale design variable problems. Furthermore, the coordinated operation of inverse geometric parameterization, shape sensitivity solution, and mesh smoothing enables accurate geometric parameter optimization of the mesh model even without a CAD geometric model, and the optimization results have clear engineering geometric significance and manufacturability.

[0089] Shape sensitivity: Shape sensitivity is the derivative of the mechanical field with respect to the nodal coordinates. That is, the derivative of the element stiffness matrix K with respect to the design variables depends not only on the elastic coefficients D, but also on the geometric matrix B.

[0090] In one feasible implementation, step S33 may include steps F11 to F14: Step F11: Obtain design response parameter information, which includes compliance, stress, frequency, displacement, temperature, and buckling. It should be noted that the design response parameter information is a set of physical quantities output used to quantitatively evaluate the mechanical performance, thermal performance and stability characteristics of the structure under specific load and boundary conditions, and to determine the evaluation criteria and optimization direction of the design scheme.

[0091] Understandably, compliance characterizes the ease with which a structure deforms under external forces, and is numerically equal to the integral of strain energy density over volume or the inner product of force and displacement vectors. Minimizing compliance is equivalent to maximizing stiffness. Stress characterizes the intensity of internal forces generated at each point within the structure by external forces, typically output as Mises equivalent stress, principal stress, or normal and shear stress components in each direction, used to verify strength and safety. Frequency characterizes the inherent characteristics of free vibration of the structure, described by first-order or multiple-order natural frequency values ​​and corresponding mode shapes, used to avoid resonance or meet dynamic performance indicators. Displacement characterizes the change in position of each node of the structure under load, output as the resultant displacement amplitude or a component in a specified direction, used to verify stiffness constraints. Temperature characterizes the steady-state or transient temperature field distribution of the structure under thermal load or thermal boundary conditions, used for thermal stress analysis or thermal management design. Buckling characterizes the critical load factor or characteristic value at which the structure becomes unstable under compressive load, used to assess stability margin.

[0092] Step F12: When the optimized design parameter information includes geometric design variables obtained through inverse geometric parameterization, a cooperative perturbation is applied to the boundary node set corresponding to the geometric design variables, and the shape sensitivity derivative of the stiffness matrix is ​​approximately calculated using the central difference method. It should be noted that the aforementioned coordinated perturbation refers to the overall coordinated perturbation of all nodes on the geometric feature boundary according to the deformation mode that conforms to the physical meaning of the geometric parameter when the design variable is a parameter with a clear geometric meaning (such as the radius of a circular hole, the position of the center, the length of a straight line, the radius of an arc, etc.), rather than applying arbitrary perturbations to each node independently. For example, for the variable of the radius of a circular hole, all circular hole boundary nodes are perturbed by the same step size ΔR along their respective node normals (or the radial direction of the fitted circle), ensuring that the boundary remains circular after perturbation; for the variable of the position of the center, all circular hole boundary nodes generate the same rigid displacement perturbations ΔX and ΔY relative to the new center, ensuring that the boundary shape remains unchanged and only translation occurs after perturbation; for the variable of the length of a straight line, the boundary nodes at the endpoints of the straight line are perturbed by the corresponding step size along the straight line direction. This coordinated perturbation method can ensure a clear physical correspondence between the shape sensitivity of the differential solution and the geometric parameter variables, providing an accurate stiffness matrix derivative basis for the subsequent adjoint method to solve the sensitivity of all design variables at once.

[0093] Step F13: Solve for the adjoint variables corresponding to all design variables at once based on the adjoint method, and obtain the sensitivity of each design variable by combining the shape sensitivity derivative; It should be noted that the adjoint method is a highly efficient sensitivity calculation method. By introducing adjoint variables and solving the adjoint equations once, the sensitivity information corresponding to all design variables can be obtained at once, without needing to perturb and reanalyze each design variable individually as required by the direct difference method. In specific implementation, the adjoint variables are obtained by solving the system of adjoint linear equations related to the original stiffness matrix. Then, the adjoint variables are combined with the shape sensitivity derivative of the stiffness matrix approximated by cooperative perturbation and central difference method in step F12 to efficiently obtain the sensitivity values ​​of the objective function or constraints to each design variable. The entire solution process is completed through interface calls in a preset shared memory space.

[0094] Step F14: Based on the sensitivity, perform local optimization and iterative correction in the preset shared memory space, update the boundary node positions, and perform mesh smoothing processing on the internal mesh nodes using Laplace smoothing or Helmholtz filtering until the preset convergence condition is met, and obtain the second simulation design analysis result.

[0095] Understandably, local optimization is a refined search process that utilizes gradient information of the response quantity to guide the optimization algorithm towards a local optimum near the advantageous region identified during the global exploration phase. This differs from the broad search characteristics of global exploration. The key is to obtain the derivative information of the objective function and constraints with respect to the design variables through sensitivity analysis, determining the direction of the fastest decrease in function values, thus giving the optimization iteration a clear direction and efficient convergence speed. In scenarios based on geometric design variables obtained through inverse geometric parameterization, after each local optimization iteration updates the design variable values, the new positions of nodes at the corresponding geometric feature boundaries (such as the coordinates of new circular hole boundary nodes) must be determined based on the new geometric parameter values. Then, the internal mesh nodes are smoothed using Laplace smoothing or Helmholtz filtering. Laplace smoothing eliminates mesh distortion by iteratively moving each internal node to the average position of its neighboring nodes, while Helmholtz filtering achieves mesh smoothing in a more optimal way by solving partial differential equations. Both can effectively prevent the degradation of internal mesh quality caused by boundary node movement, ensuring the effectiveness of the mesh and the accuracy of the solution during the iteration process.

[0096] Step S34: Obtain simulation design analysis results based on at least one of the first simulation design analysis results and the second simulation design analysis results.

[0097] It is understood that the simulation design analysis results are a collection of optimal design schemes that satisfy all engineering constraints and objectives, along with their performance verification data. This may include design variable values, performance response data, and convergence history data of the entire optimization process. The design variable values ​​may be the precise thickness of each sheet metal part (e.g., 1.2 mm) determined after optimization, the optimal angle sequence of composite material layups, geometric parameters such as the radius and center position of the circular hole identified and optimized through inverse geometric parameterization, and the selected material grade. The performance response data may include mass, maximum stress, natural frequency, displacement, etc. The convergence history data of the entire optimization process may be the curve of the objective function value changing with the number of iterations, which is used to directly visualize the data in the post-processing environment without any data export or format conversion.

[0098] In a specific embodiment, the simulation design analysis result is the final optimization scheme data determined by selecting or combining two analysis results based on actual engineering needs and optimization strategy configuration. For example, experimental design, surrogate models, and optimization algorithms can be used independently or in combination according to the optimization strategy selected by the user. When the optimization problem is mainly composed of discrete variables and the design space is complex and multimodal, a global exploration strategy based on a surrogate model can be used alone, with the first simulation design analysis result as the simulation design analysis result. The surrogate model provides response surface models, Kriging models, radial basis function neural networks, etc., to construct an approximate mapping relationship between design variables and responses, approximating the time-consuming simulation and accelerating global exploration. When the optimization problem is mainly composed of continuous variables and requires a high-precision local optimum solution, a semi-analytical sensitivity-driven local optimization strategy in experimental design can be used alone, with the second simulation design analysis result as the simulation design analysis result. The experimental design can provide full factorial design, optimal Latin... Hypercubic design and orthogonal design methods are used to generate initial sample points within the design space to explore the main and interaction effects of variables on the response. Hybrid optimization strategies can also be employed, offering gradient-based optimization algorithms (such as sequential quadratic programming), genetic algorithms, particle swarm optimization, and multi-objective optimization algorithms. These strategies support the optimization of both continuous and discrete variables. In the global exploration phase, a surrogate model module is used to construct an approximate relationship between design variables and the response, guiding the genetic algorithm or particle swarm optimization algorithm to globally search for and determine the optimal region. In the local refinement phase, a semi-analytical sensitivity-driven gradient optimization algorithm is used for rapid convergence. The first simulation design analysis result is used as the input for the global phase, and the second simulation design analysis result is used as the final simulation design analysis result, balancing global search capability and local convergence efficiency. At this point, the obtained simulation design analysis results include the optimized design variable values ​​(including geometric parameters optimized through inverse geometric parameterization) and the corresponding stress contour plots, displacement contour plots, and optimized convergence curve data, which can be dynamically displayed directly within the same finite element post-processing interface.

[0099] This embodiment proposes an integrated simulation design push method for solver internal optimization. It obtains robust model evaluation results by calling an application programming interface embedded in the solver kernel; based on the robust model evaluation results, it performs global exploration and iterative correction of the optimized design parameters in a preset shared memory space until a preset convergence condition is met, thus determining a first simulation design analysis result; it then uses a semi-analytical method to perform local optimization and iterative correction of the optimized design parameters in the preset shared memory space until a preset convergence condition is met, thus determining a second simulation design analysis result; and finally, it obtains a simulation design analysis result based on at least one of the first and second simulation design analysis results. This application addresses the technical challenge of pushing simulation designs before finite element analysis begins. Compared to existing technologies, this application deeply embeds the optimization engine into the solver's underlying layer and shares memory with the solver. It directly calls the solver's application programming interface to obtain underlying data such as stiffness matrices and element information for robustness assessment. Based on the assessment results, it seamlessly coordinates optimization strategies within shared memory, achieving a seamless transition from global optimum location to local high-precision convergence. This breaks the dependence on external multidisciplinary optimization platforms. Combining global exploration using a surrogate model with efficient optimization using semi-analytical methods, it possesses the ability to escape local optima through global search. In gradient optimization, it directly calculates sensitivity using kernel data. In particular, for geometric design variables obtained through inverse geometric parameterization, it uses collaborative perturbation of boundary node sets, semi-analytical methods to approximate shape sensitivity, and adjoint methods to solve all variable sensitivities at once. After updating the boundary node positions, it uses Laplace smoothing or Helmholtz filtering for mesh smoothing. Thus, it achieves efficient and high-precision solutions for large-scale, multi-type variable complex engineering problems with extremely low computational cost, and the optimization results have clear engineering geometric significance and manufacturability.

[0100] This application also provides an integrated simulation design delivery device with internal solver optimization, please refer to... Figure 12 The integrated simulation design push device optimized within the solver includes: Module 10 is used to perform structural optimization design based on a preset simulation analysis model and determine the information of the optimization design scheme. Processing module 20 is used to identify model geometric feature information by selecting node identifiers on the mesh model for inverse geometric parameterization based on the optimized design scheme information, and to determine optimized design parameter information by combining model material property information and model element property information. The processing module 20 is also used to perform iterative simulation and mesh smoothing correction based on shape sensitivity on the optimized design parameter information in a preset shared memory space by calling the application programming interface embedded in the solver kernel until the preset convergence condition is met, and to determine the simulation design analysis result. The execution module 30 is used to push the stress cloud map, displacement cloud map and optimization convergence curve from the simulation design analysis results.

[0101] The acquisition module 10 is also used to perform structural optimization design based on a preset simulation analysis model, and determine at least one of topology optimization design scheme information, shape optimization design scheme information, size optimization design scheme information and morphology optimization design scheme information, wherein the structural optimization design includes at least one of topology optimization, shape optimization, size optimization and morphology optimization. The feature parameters of at least one of the topology optimization design scheme information, the shape optimization design scheme information, the size optimization design scheme information, and the morphology optimization design scheme information are extracted to determine the optimization design scheme information. The feature parameters include any type of geometric parameters and non-geometric parameters.

[0102] The processing module 20 is also used to acquire optimization target information and constraint information; Receive a set of node identifiers at the boundary of the target geometric feature on the mesh model specified by the user, perform geometric primitive fitting based on the set of node identifiers, calculate the geometric parameters in reverse, and use the geometric parameters as design variables; Based on the model's geometric features, material properties, and unit properties, other design variables are determined. Discrete variables in these design variables include thickness values ​​from the standard sheet metal thickness library, composite material ply angles, composite material ply thicknesses, material grade selection, and parameters limited by engineering specifications. The optimization design parameter information is obtained based on the design variable information, the optimization objective information, and the constraint information.

[0103] The processing module 20 is also used to fit the set of node identifiers into a circle, a straight line or an arc using the least squares method, and to calculate the corresponding radius of the hole and the center position, the length of the straight line and the end position or the radius of the arc and the central angle, etc. The geometric parameters are used as continuous or discrete design variables, and include at least one of the following: circular hole radius, center position, arc radius, straight line length, rectangle length and width, cylindrical hole radius, and reinforcing rib height.

[0104] The processing module 20 is also used to obtain robust model evaluation results by calling the application programming interface embedded in the solver kernel; Based on the robust model evaluation results, the optimized design parameter information is globally explored and iteratively corrected in a preset shared memory space until the preset convergence condition is met, and the first simulation design analysis result is determined. A semi-analytical method is used to perform local optimization and iterative correction of the optimized design parameter information in a preset shared memory space until the preset convergence condition is met, and the second simulation design analysis result is determined. The simulation design analysis result is obtained based on at least one of the first simulation design analysis result and the second simulation design analysis result.

[0105] The processing module 20 is further configured to include the following steps in obtaining robust model evaluation results by calling the application programming interface embedded in the solver kernel: The model data interaction information is obtained by calling the application programming interface of the optimization engine. The model data interaction information includes element information, node information, stiffness matrix, mass matrix and analysis results. Monte Carlo simulation and reliability analysis are performed based on the data interaction information of the model to obtain robust model evaluation results.

[0106] The processing module 20 is further configured to determine the corresponding approximate mapping relationship information based on the robust model evaluation result; Based on the approximate mapping relationship information, at least one of the corresponding genetic discrete variable information and particle swarm discrete variable information is determined. Based on at least one of the genetic discrete variable information and the particle swarm discrete variable information, global exploration and iterative correction are performed in a preset shared memory space until the preset convergence condition is met, and the first simulation design analysis result is obtained.

[0107] The processing module 20 is also used to acquire design response parameter information, which includes compliance, stress, frequency, displacement, temperature and buckling. When the optimized design parameter information includes geometric design variables obtained through inverse geometric parameterization, a cooperative perturbation is applied to the boundary node set corresponding to the geometric design variables, and the shape sensitivity derivative of the stiffness matrix is ​​approximately calculated using the central difference method. The adjoint variables corresponding to all design variables are solved at once using the adjoint method, and the sensitivity of each design variable is obtained by combining the shape sensitivity derivative. Based on the sensitivity, local optimization and iterative correction are performed in the preset shared memory space to update the boundary node positions. The internal mesh nodes are then smoothed using Laplace smoothing or Helmholtz filtering until the preset convergence condition is met, and the second simulation design analysis result is obtained.

[0108] The integrated simulation design push device with solver internal optimization provided in this application adopts the integrated simulation design push method with solver internal optimization in the above embodiments, which can solve the technical problem of how to push the simulation design before the start of finite element analysis. Compared with the prior art, the beneficial effects of the integrated simulation design push device with solver internal optimization provided in this application are the same as the beneficial effects of the integrated simulation design push method with solver internal optimization provided in the above embodiments, and other technical features in the integrated simulation design push device with solver internal optimization are the same as the features disclosed in the methods of the above embodiments, and will not be repeated here.

[0109] This application provides an integrated simulation design push device with solver internal optimization. The integrated simulation design push device with solver internal optimization includes: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions that can be executed by the at least one processor, and the instructions are executed by the at least one processor to enable the at least one processor to execute the integrated simulation design push method with solver internal optimization in the first embodiment described above.

[0110] The following is for reference. Figure 13 This document illustrates a schematic diagram of an integrated simulation design push device suitable for implementing solver internal optimization in the embodiments of this application. The integrated simulation design push device for solver internal optimization in the embodiments of this application may include, but is not limited to, mobile terminals such as mobile phones, laptops, digital broadcast receivers, PDAs (Personal Digital Assistants), PADs (Portable Application Description), PMPs (Portable Media Players), in-vehicle terminals (e.g., in-vehicle navigation terminals), and fixed terminals such as digital TVs and desktop computers. Figure 13 The integrated simulation design push device with internal optimization of the solver shown is merely an example and should not impose any limitations on the functionality and scope of use of the embodiments of this application.

[0111] like Figure 13As shown, the solver-optimized integrated simulation design delivery device may include a processing unit 1001 (e.g., a central processing unit, graphics processing unit, etc.), which can perform various appropriate actions and processes according to the program stored in ROM (Read Only Memory) 1002 or the program loaded from storage device 1003 into RAM (Random Access Memory) 1004. RAM 1004 also stores various programs and data required for the operation of the solver-optimized integrated simulation design delivery device. The processing unit 1001, ROM 1002, and RAM 1004 are interconnected via bus 1005. Input / output (I / O) interface 1006 is also connected to the bus. Typically, the following systems can be connected to I / O interface 1006: input devices 1007 including, for example, touchscreens, touchpads, keyboards, mice, image sensors, microphones, accelerometers, gyroscopes, etc.; output devices 1008 including, for example, liquid crystal displays (LCDs), speakers, vibrators, etc.; storage devices 1003 including, for example, magnetic tapes, hard disks, etc.; and communication devices 1009. Communication device 1009 allows the solver-optimized integrated simulation design push device to communicate wirelessly or wiredly with other devices to exchange data. Although the figure shows a solver-optimized integrated simulation design push device with various systems, it should be understood that it is not required to implement or have all the systems shown. More or fewer systems can be implemented alternatively.

[0112] Specifically, according to the embodiments disclosed in this application, the processes described above with reference to the flowcharts can be implemented as computer software programs. For example, embodiments disclosed in this application include a computer program product comprising a computer program carried on a computer-readable medium, the computer program containing program code for performing the methods shown in the flowcharts. In such embodiments, the computer program can be downloaded and installed from a network via a communication device, or installed from storage device 1003, or installed from ROM 1002. When the computer program is executed by processing device 1001, it performs the functions defined in the methods of the embodiments disclosed in this application.

[0113] The integrated simulation design push device with solver internal optimization provided in this application, employing the integrated simulation design push method with solver internal optimization in the above embodiments, can solve the technical problem of how to push the simulation design before the start of finite element analysis. Compared with the prior art, the beneficial effects of the integrated simulation design push device with solver internal optimization provided in this application are the same as the beneficial effects of the integrated simulation design push method with solver internal optimization provided in the above embodiments, and other technical features in this integrated simulation design push device with solver internal optimization are the same as those disclosed in the previous embodiment method, and will not be repeated here.

[0114] It should be understood that the various parts disclosed in this application can be implemented using hardware, software, firmware, or a combination thereof. In the description of the above embodiments, specific features, structures, materials, or characteristics can be combined in any suitable manner in one or more embodiments or examples.

[0115] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

[0116] The above description is only a part of the embodiments of this application and does not limit the patent scope of this application. All equivalent structural transformations made under the technical concept of this application and using the contents of the specification and drawings of this application, or direct / indirect applications in other related technical fields, are included in the patent protection scope of this application.

Claims

1. An integrated simulation design delivery method for solver internal optimization, characterized in that, The method includes: Structural optimization design is carried out based on a pre-set simulation analysis model to determine the information of the optimized design scheme; Based on the optimized design scheme information, inverse geometric parameterization is performed by selecting node identifiers on the mesh model to identify the geometric feature information of the model, and the optimized design parameter information is determined by combining the model material property information and the model element property information. By calling the application programming interface embedded in the solver kernel, the optimized design parameter information is subjected to iterative simulation and mesh smoothing correction based on shape sensitivity in a preset shared memory space until the preset convergence condition is met, and the simulation design analysis results are determined. The stress cloud map, displacement cloud map, and optimized convergence curve from the simulation design analysis results will be pushed out. The steps of determining the optimization design parameters based on the optimized design scheme information, including selecting node identifiers on the mesh model for inverse geometric parameterization to identify model geometric features, and combining model material properties and model element properties, include: Obtain optimization objective information and constraint information; Receive a set of node identifiers at the boundary of the target geometric feature on the mesh model specified by the user, perform geometric primitive fitting based on the set of node identifiers, calculate the geometric parameters in reverse, and use the geometric parameters as design variables; Based on the model's geometric features, material properties, and unit properties, other design variables are determined. Discrete variables in these design variables include thickness values ​​from the standard sheet metal thickness library, composite material ply angles, composite material ply thicknesses, material grade selection, and parameters limited by engineering specifications. Based on the design variable information, the optimization objective information, and the constraint information, the optimization design parameter information is obtained; The steps of performing iterative simulation and mesh smoothing correction based on shape sensitivity on the optimized design parameter information by calling the application programming interface embedded in the solver kernel in a preset shared memory space until the preset convergence condition is met, and determining the simulation design analysis results include: The robust model evaluation results are obtained by calling the application programming interface embedded in the solver kernel; Based on the robust model evaluation results, the optimized design parameter information is globally explored and iteratively corrected in a preset shared memory space until the preset convergence condition is met, and the first simulation design analysis result is determined. A semi-analytical method is used to perform local optimization and iterative correction of the optimized design parameter information in a preset shared memory space until the preset convergence condition is met, and the second simulation design analysis result is determined. The simulation design analysis result is obtained based on at least one of the first simulation design analysis result and the second simulation design analysis result.

2. The method as described in claim 1, characterized in that, The steps for determining the optimized design scheme information based on a preset simulation analysis model include: Structural optimization design is performed based on a preset simulation analysis model to determine at least one of the following: topology optimization design scheme information, shape optimization design scheme information, size optimization design scheme information, and morphology optimization design scheme information. The structural optimization design includes at least one of topology optimization, shape optimization, size optimization, and morphology optimization. The feature parameters of at least one of the topology optimization design scheme information, the shape optimization design scheme information, the size optimization design scheme information, and the morphology optimization design scheme information are extracted to determine the optimization design scheme information. The feature parameters include geometric parameters and non-geometric parameters.

3. The method as described in claim 1, characterized in that, The step of fitting geometric primitives based on the node identifier set and calculating geometric parameters in reverse includes: The node identifier set is fitted into a circle, a straight line, or an arc using the least squares method, and the corresponding radius and center position of the circular hole, the length and endpoint position of the straight line, or the radius and central angle of the arc are calculated. The geometric parameters are used as continuous or discrete design variables, and include at least one of the following: circular hole radius, center position, arc radius, straight line length, rectangle length and width, cylindrical hole radius, and reinforcing rib height.

4. The method as described in claim 1, characterized in that, The solver kernel integrates an optimization engine consisting of an experiment design module, a surrogate model module, an optimization algorithm module, a stochastic analysis module, and an application programming interface between the solver and the algorithm. The steps for obtaining robust model evaluation results by calling the application programming interface embedded in the solver kernel include: The model data interaction information is obtained by calling the application programming interface of the optimization engine. The model data interaction information includes element information, node information, stiffness matrix, mass matrix and analysis results. Monte Carlo simulation and reliability analysis are performed based on the data interaction information of the model to obtain robust model evaluation results.

5. The method as described in claim 1, characterized in that, The step of performing global exploration and iterative correction of the optimized design parameter information in a preset shared memory space based on the robust model evaluation results until a preset convergence condition is met, and determining the first simulation design analysis result includes: Based on the evaluation results of the robust model, determine the corresponding approximate mapping relationship information; Based on the approximate mapping relationship information, at least one of the corresponding genetic discrete variable information and particle swarm discrete variable information is determined. Based on at least one of the genetic discrete variable information and the particle swarm discrete variable information, global exploration and iterative correction are performed in a preset shared memory space until the preset convergence condition is met, and the first simulation design analysis result is obtained.

6. The method as described in claim 1, characterized in that, The step of using a semi-analytical method to perform local optimization and iterative correction of the optimized design parameter information in a preset shared memory space until a preset convergence condition is met, and determining the second simulation design analysis result, includes: Obtain design response parameter information, which includes compliance, stress, frequency, displacement, temperature, and buckling; When the optimized design parameter information includes geometric design variables obtained through inverse geometric parameterization, a cooperative perturbation is applied to the boundary node set corresponding to the geometric design variables, and the shape sensitivity derivative of the stiffness matrix is ​​approximately calculated using the central difference method. The adjoint variables corresponding to all design variables are solved at once using the adjoint method, and the sensitivity of each design variable is obtained by combining the shape sensitivity derivative. Based on the sensitivity, local optimization and iterative correction are performed in the preset shared memory space to update the boundary node positions. The internal mesh nodes are then smoothed using Laplace smoothing or Helmholtz filtering until the preset convergence condition is met, and the second simulation design analysis result is obtained.

7. An integrated simulation design delivery device with internal optimization of the solver, characterized in that, The device includes: The acquisition module is used to perform structural optimization design based on a preset simulation analysis model and determine the information of the optimization design scheme. The processing module is used to identify model geometric features by selecting node identifiers on the mesh model for inverse geometric parameterization based on the optimized design scheme information, and to determine optimized design parameters by combining model material properties and model element properties. It is also used to perform iterative simulation and mesh smoothing based on shape sensitivity in a preset shared memory space by calling the application programming interface embedded in the solver kernel until a preset convergence condition is met, thus determining the simulation design analysis results. Furthermore, it is used to acquire optimization target information and constraint information, receive a set of node identifiers at the target geometric feature boundaries on the mesh model specified by the user, perform geometric primitive fitting based on the node identifier set, inversely calculate geometric parameters, and use these geometric parameters as design variables. Based on the model geometric features, model material properties, and model element properties of the optimized design scheme information, it determines other design variables. The discrete variables in the design variable information include thickness values ​​in the standard sheet metal thickness library, composite material ply angles, composite material ply thicknesses, material grade selection, and parameters limited by engineering specifications. Based on the design variable information, the optimization objective information, and the constraint information, optimization design parameter information is obtained. It is also used to obtain robust model evaluation results by calling the application programming interface embedded in the solver kernel. According to the robust model evaluation results, the optimization design parameter information is globally explored and iteratively corrected in a preset shared memory space until a preset convergence condition is met, and a first simulation design analysis result is determined. A semi-analytical method is used to locally optimize and iteratively correct the optimization design parameter information in a preset shared memory space until a preset convergence condition is met, and a second simulation design analysis result is determined. The simulation design analysis result is obtained based on at least one of the first simulation design analysis result and the second simulation design analysis result. The execution module is used to push the stress cloud map, displacement cloud map and optimization convergence curve from the simulation design analysis results.

8. An integrated simulation design delivery device with internal solver optimization, characterized in that, The device includes: a memory, a processor, and a computer program stored in the memory and executable on the processor, the computer program being configured to implement the steps of the integrated simulation design push method for solver internal optimization as described in any one of claims 1 to 6.

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