Multi-model topological optimization method and system for complex geometric model

Abstract

The invention belongs to the field of structure optimization design, and particularly discloses a multi-model topological optimization method and system for a complex geometric model, and the method comprises the steps: building a corresponding finite element model according to a geometric model of a wing corrugated structure; dividing a design domain for the geometric model, and establishing a topological model corresponding to the finite element model; geometric mapping is carried out on the shared design domain through manufacturing constraints with repeated modes, a mapping relation of a local coordinate system for processing a large deformation area is established, a topology model capable of being synchronously optimized is formed, and an output file of the topology model is exported; and carrying out synchronous loop optimization on the plurality of topology models by utilizing a parallel computing interface, and judging optimization results of the topology models according to a convergence criterion until the topology models reach the convergence criterion, so as to obtain a final optimization model. According to the method, the geometric mapping effect and the multi-working-condition synchronous optimization effect of the complex geometric model can be improved.

Description

Technical Field

[0001] The present application belongs to the field of structural optimization design, and more specifically, relates to a multi-model topology optimization method and system for complex geometric models. Background Art

[0002] With the advancement of industrial technology, various products are becoming more diverse to meet consumer demand, resulting in a dramatic increase in the number of product parts. This increase in part count also increases product design costs and cycle times. However, some parts within a product, such as standard parts, are shared and standardized across a product family. Because shared parts are used across multiple finite element (FE) models, optimization methods that only consider a single FE model are unsuitable for the design of shared parts. The simultaneous optimization technique for multiple FE models is called multi-model optimization (MMO). MMO can share parts of the design domain by linking design variables, allowing multiple FE models to be processed in a single optimization.

[0003] Existing research on MMO can be divided into two categories: (1) different models have the same design domain; (2) different models have similar design domains, such as scaling, rigid body displacement, etc. However, for deformation / load / lightweight coordination problems such as variant wings, which have more complex geometric models and loads, different models share similar design domains, but not scaling or rigid body displacement, which leads to poor geometric mapping effects and poor multi-condition synchronous optimization effects. Summary of the Invention

[0004] In response to the defects of the existing technology, the purpose of this application is to provide a multi-model topology optimization method for complex geometric models, aiming to solve the problems of poor geometric mapping effect and poor multi-working condition synchronous optimization effect in the existing technology.

[0005] To achieve the above objectives, in a first aspect, the present application provides a multi-model topology optimization method for complex geometric models, comprising: Construct a corresponding finite element model based on the geometric model of the wing corrugated structure; Dividing the geometric model into a design domain and establishing a topological model corresponding to the finite element model, wherein the topological model includes a shared design domain, a non-shared design domain, and a non-design domain between the geometric models; Geometric mapping of the shared design domain is performed through manufacturing constraints of pattern repetition, a mapping relationship of a local coordinate system for processing large deformation areas is established, a topological model that can be optimized synchronously is formed, and an output file of the topological model is exported; A parallel computing interface is used to perform synchronous loop optimization on multiple topology models, and the optimization results of the topology models are judged according to the convergence criterion until the topology models reach the convergence criterion to obtain the final optimized model; the topology models are optimized based on the global optimization objectives and global constraints written in the output file.

[0006] Optionally, the cyclic optimization process of the topology model includes: Obtain the cell density file of the topology model optimization results and determine whether the optimization has converged based on the consistency and tolerance of the optimization results; When the consistency of the optimization results of multiple topology models is less than the expected value, determine whether there is flexible deformation between the shared design domains; The design domain is further discretized based on the judgment results, a local coordinate system is defined for the flexible deformation part of the design domain, and the topology model is iteratively optimized until the consistency of the optimization results meets the requirements.

[0007] Optionally, geometrically mapping the shared design domain using manufacturing constraints based on pattern repetition comprises: The selected mesh nodes are used as anchor points to determine the mapping starting position of the shared design domain of different geometric models; Select the global coordinate system or the local coordinate system to determine the spatial angle of the geometric mapping; The scaling ratio of the shared design domain is determined by scaling factors in the horizontal, vertical, and height directions to achieve accurate mapping of the shared design domain of multiple models.

[0008] Optionally, it also includes: Performing a single-model topology optimization of multiple working conditions on the geometric model, obtaining a first-order response based on a variable density method, and normalizing the first-order response to obtain a second-order response; The mathematical model of the secondary response is shown in the following formula:

[0009] in, represents the design variables of the topological model, Indicates the The value of the secondary response, Indicates the The value of the first-level response, Indicates the The ideal value of a target, such as the minimum value, Indicates the The worst value of the first-level response, such as the maximum value, Indicates the The weight of the first-level response, .

[0010] Optionally, the multi-model topology optimization process includes: Determine the shared design domains of each model and link the design domains one by one through pattern-repeated manufacturing constraints to ensure that at least one set of design variables is linked between different geometric models; The master-slave variable method is used to realize the association of variables, and the master design domain variables are converted into slave design domain variables through scaling, rotation and translation; Construct a multi-model optimization problem involving shared and non-shared variables, and set global optimization objectives and local constraints; Density filtering and projection processing are performed on design variables to ensure manufacturing feasibility; The secondary responses of different models are combined through the compromise planning method to achieve multi-model collaborative topology optimization.

[0011] Optionally, judging whether the optimization has converged based on the consistency and tolerance of the optimization results includes: Calculating the Hausdorff distance between the two optimization result geometric point sets, determining the maximum mismatch degree according to the Hausdorff distance, and setting a tolerance standard to judge the geometric consistency; For continuous surface models, the correlation between the Gaussian curvature distributions of the two models is compared to evaluate the curvature similarity, and a tolerance standard is set to judge the curvature consistency.

[0012] Optionally, the process of further discretizing the design domain includes: The global design domain is divided into multiple non-overlapping subdomains, a local coordinate system is defined for each flexible deformation subdomain, and the gradient consistency is guaranteed by the Jacobian matrix; A consistency penalty term is added during the optimization process of the topology model to minimize the sum of the objective function and the penalty term.

[0013] Optionally, use the parallel computing interface to perform simultaneous loop optimization of multiple topology models, including: When the number of parallel computing interface processes equals the number of models plus one, the domain decomposition method is not enabled for parallelism within each model, and only the main process and the single model process run; When the number of processes in the parallel computing interface is greater than the number of models plus one, one process is allocated to the main program, and the remaining processes are evenly distributed to each model. Each model is solved in parallel using the domain decomposition method.

[0014] Optionally, it also includes: The optimization result file is exported according to the final optimization result of the topology model, the geometry is reconstructed based on the optimization result file, and the mesh file is smoothed by a mesh smoothing program to realize conversion of the mesh file into a geometry file.

[0015] This application also provides a multi-model topology optimization system for complex geometric models, including: A finite element model building module is used to build a corresponding finite element model based on the geometric model of the wing corrugated structure; A topology model building module, configured to divide the geometric model into a design domain and establish a topology model corresponding to the finite element model, wherein the topology model includes a shared design domain, a non-shared design domain, and a non-design domain between the geometric models; A mapping module is used to geometrically map the shared design domain using manufacturing constraints of pattern repetition, establish a mapping relationship for processing large deformation regions in a local coordinate system, form a topological model that can be simultaneously optimized, and export an output file of the topological model; The optimization module is used to perform synchronous cyclic optimization on multiple topology models using a parallel computing interface, and to judge the optimization results of the topology models according to the convergence criteria until the topology models reach the convergence criteria to obtain the final optimized model; the topology models are optimized based on the global optimization objectives and global constraints written in the output file.

[0016] In a third aspect, the present application provides an electronic device comprising: at least one memory for storing programs; and at least one processor for executing the programs stored in the memory. When the program stored in the memory is executed, the processor is used to execute the method described in the first aspect or any possible implementation of the first aspect.

[0017] In a fourth aspect, the present application provides a computer-readable storage medium, which stores a computer program. When the computer program runs on a processor, the processor executes the method described in the first aspect or any possible implementation of the first aspect.

[0018] In a fifth aspect, the present application provides a computer program product, which, when executed on a processor, enables the processor to execute the method described in the first aspect or any possible implementation of the first aspect.

[0019] It can be understood that the beneficial effects of the second to fifth aspects mentioned above can be found in the relevant description of the first aspect mentioned above, and will not be repeated here.

[0020] In general, the above technical solutions conceived by this application have the following beneficial effects compared with the existing technologies: (1) This application maps the shared design domain through manufacturing constraints of pattern repetition, and establishes a local coordinate system in large deformation areas (such as corrugated transition areas and joints), accurately controls the mapping relationship, ensures the matching of geometric deformation and mechanical properties, avoids the distortion problem caused by traditional global mapping, and improves the mapping effect and mapping accuracy; the division and mapping strategy of this application ensures the consistency of different geometric models in the shared design domain, and at the same time, the establishment of the local coordinate system effectively handles the mapping problem of large deformation areas, providing an accurate basis for multi-model synchronous optimization. The optimization based on the written global optimization objectives and global constraints further ensures the coordination and consistency of the optimization results under multiple working conditions.

[0021] (2) This application performs synchronous cyclic optimization on multiple topological models, significantly shortening the calculation time. It is particularly suitable for complex scenarios with multiple objectives and multiple constraints. By pre-defining global objectives (such as maximum overall stiffness and minimum weight) and constraints (such as stress and displacement) in the output file, it ensures that the optimization direction of each sub-model is consistent and avoids local optimality.

[0022] (3) All topological models in this application follow the same convergence criterion in the synchronous optimization to ensure the overall design balance. The optimization results of the shared design domain are transmitted to each working condition model in real time to ensure that the corrugated structure meets the performance requirements under different loads. It supports the retention of non-design domains to facilitate compatibility with existing structures. The independent optimization of non-shared domains allows for local enhancement and improves the degree of design refinement.

[0023] (4) This application addresses the problem of multi-condition collaborative optimization of complex geometric models, improves the existing MMO method, and develops corresponding script language programs and visualization interfaces to achieve multi-model synchronous optimization design of hinged bridges and corrugated structures, which can quickly achieve cross-model synchronous optimization of products. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1 This is one of the flow diagrams of the multi-model topology optimization method for complex geometric models provided in an embodiment of the present application; Figure 2 is a flowchart illustrating implementation of multi-model topology optimization of a corrugated structure according to an exemplary embodiment; Figure 3 is a schematic diagram showing boundary conditions of multiple working conditions before and after deformation of a corrugated structure according to an exemplary embodiment; Figure 3 (a) is a schematic diagram of the first working condition of a simple corrugated plate composed of four corrugations. Figure 3 (b) is a schematic diagram of the second working condition of the continuously deflected corrugated plate; Figure 4 is a density cloud diagram showing two single-operating-condition optimization analysis results of a corrugated structure according to an exemplary embodiment; Figure 4(a) is a schematic diagram of the first working condition. Figure 4 (b) is a schematic diagram of the second working condition; Figure 5 is a cloud diagram illustrating an optimization density of a single design domain in an iterative process based on a multi-model topology optimization strategy according to an exemplary embodiment; Figure 5 (a) is a schematic diagram of the first working condition. Figure 5 (b) is a schematic diagram of the second working condition; Figure 6 is a density cloud diagram illustrating optimization of four design domains plus a local coordinate system in an iterative process based on a multi-model topology optimization strategy according to an exemplary embodiment; Figure 6 (a) is a schematic diagram of the first working condition. Figure 6 (b) is a schematic diagram of the second working condition; Figure 7 is a diagram illustrating a geometric reconstruction result of a final iteration of a multi-model optimization according to an exemplary embodiment; Figure 8 Schematic diagram of the structure of a multi-model topology optimization system for complex geometric models provided by an embodiment of the present application; Figure 9 It is a structural diagram of an electronic device provided in an embodiment of the present application. DETAILED DESCRIPTION

[0025] In order to make the purpose, technical solutions and advantages of this application more clear, the following further describes this application in detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain this application and are not intended to limit this application.

[0026] The term "and / or" as used herein describes an association between related objects, indicating that three possible relationships exist. For example, "A and / or B" can represent: A exists alone, A and B exist simultaneously, or B exists alone. The symbol " / " as used herein indicates that the related objects are in an "or" relationship, for example, A / B means either A or B.

[0027] The terms "first" and "second" in this specification and claims are used to distinguish different objects rather than to describe a specific order of objects. For example, "first response message" and "second response message" are used to distinguish different response messages rather than to describe a specific order of response messages.

[0028] In the embodiments of this application, words such as "exemplary" or "for example" are used to indicate examples, illustrations, or descriptions. Any embodiment or design described as "exemplary" or "for example" in the embodiments of this application should not be interpreted as being preferred or advantageous over other embodiments or designs. Rather, the use of words such as "exemplary" or "for example" is intended to present the relevant concepts in a concrete manner.

[0029] In the description of the embodiments of the present application, unless otherwise specified, "multiple" means two or more, for example, multiple processing units means two or more processing units, etc.; multiple elements means two or more elements, etc.

[0030] The embodiments of the present application are described below in conjunction with the drawings in the embodiments of the present application.

[0031] Reference Figure 1 , this application provides a multi-model topology optimization method for complex geometric models, including: S101. Constructing a corresponding finite element model based on the geometric model of the wing corrugated structure; S102. Divide the geometric model into a design domain and establish a topological model corresponding to the finite element model, wherein the topological model includes a shared design domain, a non-shared design domain, and a non-design domain between the geometric models; S103. Geometrically map the shared design domain using manufacturing constraints based on pattern repetition, establish a mapping relationship for a local coordinate system to process large deformation regions, form a topological model that can be simultaneously optimized, and export an output file of the topological model; S104. Utilize a parallel computing interface to perform synchronous loop optimization on multiple topology models, and determine the optimization results of the topology models according to a convergence criterion until the topology models reach the convergence criterion, thereby obtaining a final optimized model; the topology models are optimized based on the global optimization objectives and global constraints written in the output file.

[0032] Specifically, a suitable finite element discretization method is used to mesh the geometric model, ensuring localized densification in areas of high corrugation (such as crests and troughs) to improve computational accuracy. At the same time, material properties (such as isotropic / anisotropic material models) and boundary conditions (such as fixed supports and load application locations) can be defined, laying the foundation for subsequent topology optimization.

[0033] Secondly, the classification and definition of the design domain. Based on the optimization goal (such as weight reduction and stiffness improvement), the geometric model is divided into three types of areas: Shared Design Domain: A region with repetitive features (such as periodic corrugated elements) that needs to be geometrically consistent during optimization.

[0034] Non-shared design domains: Localized critical areas (e.g., connection joints, high stress areas) allow independent optimization to meet specific performance requirements.

[0035] Non-design domain: fixed structures (such as mounting holes and boundary areas) that are not involved in the optimization to maintain functionality.

[0036] The present application includes n geometric models, where n is a positive integer. These n geometric models can be identical or similar. Similarity can be categorized into three types: first, rigid motion such as spatial translation or rotation between the geometric models; second, proportional scaling between the design domains of different geometric models; and third, flexible deformation within the design domain, resulting in significant deflection or deformation.

[0037] Furthermore, pattern repetition constraints (such as translational and rotational symmetries) are leveraged to parametrically map the shared design domain, transforming the repeating units into a uniformly controllable template. For regions of large deformation (such as corrugated transitions), a local coordinate system is introduced to describe the deformation gradient, ensuring that the mapped geometry is both mechanically and manufacturably sound (e.g., avoiding self-intersections or distortion).

[0038] When rigid motion or proportional scaling occurs between geometric models, good consistency of cross-model optimization results can be achieved by discretizing the design domain step by step. When large flexible deformations exist in the design domains between different geometric models, the consistency of optimization results can be improved by establishing a local coordinate system and adjusting the geometric mapping angles of the design domains with large deflections.

[0039] The mapped topology model is converted into a standardized output file (.fem). This file contains the global optimization objective (such as flexibility minimization and volume fraction constraints), multi-case loads and constraints (such as stress limits and displacement limits), design variable ranges, and association rules for shared domains. This file serves as input for parallel optimization, ensuring that all computational nodes can synchronously read and update the model data.

[0040] It should be noted that the global optimization objectives and global constraints are written in the main program. Different finite element models have different working condition requirements. For example, Model 1 is a deformation condition with a load-bearing stiffness constraint, and the optimization objective is to minimize the specified deformation driving force. Model 2 is a load-bearing condition with a mass constraint, and the optimization objective is to minimize deformation under load. The responses of the different models are normalized mathematically and written into the main program in the form of global constraints and global optimization, transforming the multi-model, multi-condition optimization problem into a single-objective optimization problem.

[0041] Specifically, the embodiment of the present application is written in the scripting language Tcl subroutine and a visual interface is developed to read the .fem files of different finite element models, identify the mass, flexibility, frequency and other responses of different models, and normalize the different structural responses through mathematical methods such as compromise programming. Finally, through mathematical averaging, arithmetic mean, coefficient allocation and other methods, the optimization objectives and constraints are summarized into a function.

[0042] Finally, using parallel computing interfaces such as MPI (Message Passing Interface), multiple topology models (e.g., different load cases or local design domains) are distributed to different computing nodes for simultaneous optimization. Each node independently performs finite element analysis (e.g., FEA solver) and sensitivity calculations, but shares variable updates of the design domain in real time through MPI communication to ensure global consistency.

[0043] After each iteration, the objective function values, constraint violations, and other data for all nodes are summarized, and a unified convergence criterion is used to determine whether to terminate the optimization. If convergence has not occurred, the next round of parallel computing is initiated; if convergence has occurred, the final optimization model is output.

[0044] Optionally, the cyclic optimization process of the topology model includes: Obtain the cell density file of the topology model optimization results and determine whether the optimization has converged based on the consistency and tolerance of the optimization results; When the consistency of the optimization results of multiple topology models is less than the expected value, determine whether there is flexible deformation between the shared design domains; The design domain is further discretized based on the judgment results, a local coordinate system is defined for the flexible deformation part of the design domain, and the topology model is iteratively optimized until the consistency of the optimization results meets the requirements.

[0045] That is to say, in the embodiment of the present application, when the consistency of the optimization results of multiple models is poor, it is determined whether there is flexible deformation between the shared design domains, and the design domains are further discretized. A local coordinate system is defined for the flexible deformation design domain part to improve the consistency of the optimization results, and the iteration is repeated until the consistency of the optimization results meets the requirements.

[0046] Optionally, geometrically mapping the shared design domain using manufacturing constraints based on pattern repetition comprises: The selected mesh nodes are used as anchor points to determine the mapping starting position of the shared design domain of different geometric models; Select the global coordinate system or the local coordinate system to determine the spatial angle of the geometric mapping; The scaling ratio of the shared design domain is determined by scaling factors in the horizontal, vertical, and height directions to achieve accurate mapping of the shared design domain of multiple models.

[0047] The embodiment of the present application is based on the selected grid node as the anchor point. The shared design domain of different geometric models determines the mapping starting position through the anchor point link, selects the global coordinate system or the local coordinate system to determine the spatial angle of the geometric mapping, and determines the scaling ratio of the shared design domain through the scaling factors in the x, y, and z directions, thereby realizing accurate mapping of the shared design domain of multiple models.

[0048] Optionally, it also includes: Performing a single-model topology optimization of multiple working conditions on the geometric model, obtaining a first-order response based on a variable density method, and normalizing the first-order response to obtain a second-order response; The mathematical model of the secondary response is shown in the following formula:

[0049] in, represents the design variables of the topological model, Indicates the The value of the secondary response, Indicates the The value of the first-level response, Indicates the The ideal value of a target, such as the minimum value, Indicates the The worst value of the first-level response, such as the maximum value, Indicates the The weight of the first-level response, .

[0050] This application applies corresponding constraints, loading, and other boundary conditions based on different geometric models. A single-model optimization analysis is performed on the product under multiple operating conditions to obtain the flexibility and frequency response range of each model, define the corresponding secondary response, and normalize the primary response.

[0051] Optionally, the multi-model topology optimization process includes: Determine the shared design domains of each model and link the design domains one by one through pattern-repeated manufacturing constraints to ensure that at least one set of design variables is linked between different geometric models; The master-slave variable method is used to realize the association of variables, and the master design domain variables are converted into slave design domain variables through scaling, rotation and translation; Construct a multi-model optimization problem involving shared and non-shared variables, and set global optimization objectives and local constraints; Density filtering and projection processing are performed on design variables to ensure manufacturing feasibility; The secondary responses of different models are combined through the compromise planning method to achieve multi-model collaborative topology optimization.

[0052] Identify the shared design domains for each model and link them one by one using pattern-repeating manufacturing constraints. At least one set of design variables should be linked between different geometric models. Linking is accomplished by matching consistent optimization results to a single model using the same identification number (ID).

[0053] Assume that the optimization problem consists of p geometric models, each of which has a shared design domain, and each design domain has a variable vector , the pattern repetition constraint can be expressed as:

[0054] The association of variables is achieved through the master-slave method:

[0055] Where, is the main design domain variable, represents the scaling parameter, represents the translation coordinates, Represents a rotation matrix.

[0056] For multi-model topology optimization problems, the optimization problem form is transformed into:

[0057] Where, Indicates the number of models. are shared design variables, including , each model may share more than one design domain, so . are design variables that each model does not share with other models. is the flexibility objective function for each model, is an inequality constraint on the volume percentage of each model, is the load-bearing stiffness equality constraint for each model, is a global inequality constraint and is the weighted flexibility of each working condition. is the global stiffness equality constraint.

[0058] Use density filtering function to ensure smooth transition between adjacent variables and avoid discretization noise from destroying the repetitive consistency of the pattern. After filtering, it becomes :

[0059] Where, Indicates the unit is the center and the radius is All cells in the neighborhood of . is a weight function, usually a linear decay or Gaussian kernel function.

[0060] After filtering, the continuous density is projected Binarization (close to 0 or 1) while maintaining manufacturability. Using the Heaviside projection function:

[0061] Where, is the threshold, usually 0.5. is the steepness coefficient, which gradually increases during iteration and eventually approaches the binary solution.

[0062] The global optimization objectives and constraints are defined, and the secondary responses of different models are combined through the compromise programming method to form a new function.

[0063]

[0064] Where, is the penalty factor, .

[0065] Optionally, judging whether the optimization has converged based on the consistency and tolerance of the optimization results includes: Calculating the Hausdorff distance between the two optimization result geometric point sets, determining the maximum mismatch degree according to the Hausdorff distance, and setting a tolerance standard to judge the geometric consistency; For continuous surface models, the correlation between the Gaussian curvature distributions of the two models is compared to evaluate the curvature similarity, and a tolerance standard is set to judge the curvature consistency.

[0066] Specifically, the embodiment of the present application measures the maximum mismatch degree of the two optimization result geometric point sets by the Hausdorff distance method.

[0067] Where, is the Euclidean distance, is the geometric feature point set of different models. The tolerance standard is

[0068] For example , is the geometric characteristic length, then the optimization results are considered to be consistent. For continuous surface models, curvature similarity must also be considered to compare the correlation of Gaussian curvature distribution.

[0069]

[0070] Where, is the curvature of the two models, is the mean. The tolerance is generally .

[0071] Optionally, the process of further discretizing the design domain includes: The global design domain is divided into multiple non-overlapping subdomains, a local coordinate system is defined for each flexible deformation subdomain, and the gradient consistency is guaranteed by the Jacobian matrix; A consistency penalty term is added during the optimization process of the topology model to minimize the sum of the objective function and the penalty term.

[0072] Specifically, this embodiment further discretizes the design domain by splitting the design domain, and divides the global domain into Divided into N subdomains ,satisfy and , that is, there is no overlap between subdomains. For flexible deformation subdomains , define the local coordinate system , where Rotation matrix, is the translation vector.

[0073] Through the Jacobian matrix Ensure gradient consistency

[0074] Where, is the mapping function from reference unit to local coordinates, is the reference density field. Add a consistency penalty term to the optimization problem:

[0075] Where, represents the penalty factor, Represents function composition.

[0076] Optionally, use the MPI parallel computing interface to perform synchronous loop optimization on multiple topology models, including: When the number of MPI processes is equal to the number of models plus one, the domain decomposition method is not enabled for parallelism within each model, and only the master process and the single model process run; When the number of MPI processes is greater than the number of models plus one, one process is assigned to the main program, and the remaining processes are evenly distributed to each model. Each model is solved in parallel using the domain decomposition method.

[0077] Specifically, for the MPI process allocation rule, if the number of MPI processes (-np) is equal to the number of models n+1, the Domain Decomposition Method (DDM) parallelism is not enabled within each model, and only the master process + a single process for each model is used. If -np is greater than the number of models + 1, one process is allocated to the master program, and the remaining processes are evenly distributed among the models, with each model solved in parallel using DDM. You can also customize the process allocation by specifying the number of DDM processes for each model using the ASSIGN, MMO entry. For example: “-mmo –np 10 ASSIGN,MMO,model1,model1.fem,4 ASSIGN,MMO,model2,model2.fem,3" For the dual-model optimization described in the preceding code, four MPI processes are assigned to Model 1 and three to Model 2, respectively, based on the ASSIGN entries. In this case, the first MPI process is assigned to Main. Of the remaining nine MPI processes, four are assigned to Model 1 and three to Model 2. The remaining two MPI processes are evenly distributed between the two models. Therefore, Model 1 is assigned five MPI processes and Model 2 is assigned four MPI processes for DDM parallelization.

[0078] Optionally, it also includes: The optimization result file is exported according to the final optimization result of the topology model, the geometry is reconstructed based on the optimization result file, and the mesh file is smoothed by a mesh smoothing program to realize conversion of the mesh file into a geometry file.

[0079] Through mesh smoothing programs such as Polynurbs, based on the multi-model topology optimization results, discrete mesh files (such as STL files) are exported for geometric reconstruction and converted to continuous geometry display. The core principle is based on implicit surface reconstruction and NURBS fitting. The following is a detailed explanation.

[0080] The first step is to preprocess the STL file and define the triangular mesh surface (vertices + normal vectors) through Laplace smoothing, aiming to remove noise, fill holes and simplify the mesh.

[0081]

[0082] Where, is the smoothing coefficient, is the set of neighborhood vertices, Indicates the first triangle in a triangular mesh (such as an STL file). The coordinate vectors of the vertices.

[0083] The second step is mesh simplification, which uses the Quadratic Error Metric (QEM) algorithm to merge vertices by minimizing the geometric error. The core formula is to minimize the quadratic error after vertex transformation. The specific formula is as follows:

[0084] Where, are the new vertex coordinates to be optimized, is the equation of the plane associated with the original vertex, is the error quadratic matrix.

[0085] Radial Basis Function (RBF) interpolation, converting discrete point clouds into implicit functions The defined surface.

[0086] Where, is a kernel function (such as thin plate spline ), is a low-order polynomial. are the coordinates of any point in three-dimensional space, For the The coordinates of the control points (or center points), usually coming from an input point cloud (such as STL vertices). For the The weight coefficient of each control point.

[0087] Finally, the implicit surface is parameterized as NURBS (Non-Uniform Rational B-Splines). The NURBS surface is defined as follows:

[0088] Where, is the B-spline basis function, represents the control point, is the weight. Mapping to parameter domain (e.g. chord length parameterization). Solve for control points using least squares optimization With weight , improving the fitting accuracy.

[0089]

[0090] The present application is described in detail below with reference to specific examples.

[0091] Reference Figure 2 , Figure 2 This is the second flow chart of the embodiment of the present application, which includes the following steps: Import n geometric models; FE model 1, FE model 2, ... FE model n; Design domain segmentation; Shared design domain mapping; Local coordinate system construction; Fem file output; MPI parallel optimization; Convergence criterion judgment; If the judgment result is no, return to the design domain segmentation; If the judgment result is yes, the optimized configuration is output.

[0092] The detailed process is as follows: S1: Select the corrugated plate as the geometric model input. The two working conditions before and after the corrugated plate deformation are as follows: Figure 3 shown. Figure 3 (a) is a simple corrugated plate composed of two corrugations. The left end is fixed and a load F1 is applied to the right side. Figure 3 (b) shows a continuously deflected corrugated plate. A vertical upward load F2 is applied to the second section of the deformed plate, and the y degree of freedom of the node at the right end is constrained. The constraints are uniformly set to a 50% volume ratio. The optimization objective for the first case on the left is to maximize flexibility and improve the structural deformation capacity, while the optimization objective for the second case on the right is to minimize flexibility and ensure the load-bearing capacity of the corrugated structure after deformation.

[0093] The single model optimization results of the deformation condition and the load-bearing condition after deformation of the corrugated plate are as follows: Figure 4 As shown in the figure, the two optimization results are very inconsistent and have almost no similar geometric features. The output files of the optimization iterations are read to obtain the flexibility variation range of the two models. The flexibility response is normalized using the compromise programming method to generate the second type of response.

[0094] S2: Determine the shared design domain for the two models as the middle 70% of the corrugated plate width. For the initial optimization, assign only a single design domain to each model. Link the design domains of the two models using manufacturing constraints based on pattern repetition. Export a .fem file, define the global optimization objectives and constraints using TCL scripting subroutines, and write the main program for multi-model topology optimization.

[0095] S3: Run the multi-model optimization main program to obtain the multi-model optimization results of the corrugated structure single design domain as follows Figure 5 As shown in the figure, the optimization results of the first corrugation section are consistent between the two corrugated plate models, but there are certain differences between the optimized configurations of the corrugations in sections 2, 3, and 4. Therefore, the optimization iterations did not converge.

[0096] S4: Because the shared design domain between the two corrugated plates has a flexible deformation part, the entire domain is further divided into 4 design domains (corresponding to 4 sections of corrugation). At the same time, for the 2nd, 3rd, and 4th sections of corrugation with large deformation, a local coordinate system is added to improve the geometric mapping effect. The multi-model optimization is run again, and the results are as follows: Figure 6As shown, the optimization consistency is good.

[0097] S5: According to the final optimization results, the optimized mesh file is converted into a geometry file through the polynurbs program. Figure 7 shown.

[0098] Reference Figure 8 , the present application also provides a multi-model topology optimization system for complex geometric models, including: The finite element model building module 810 is used to build a corresponding finite element model according to the geometric model of the wing corrugated structure; A topology model building module 820 is configured to divide the geometric model into a design domain and establish a topology model corresponding to the finite element model, wherein the topology model includes a shared design domain, a non-shared design domain, and a non-design domain between the geometric models; A mapping module 830 is configured to geometrically map the shared design domain using manufacturing constraints based on pattern repetition, establish a mapping relationship for a local coordinate system to process large deformation regions, form a topological model that can be simultaneously optimized, and export an output file of the topological model; The optimization module 840 is used to perform synchronous loop optimization on multiple topology models using the MPI parallel computing interface, and to judge the optimization results of the topology models according to the convergence criterion until the topology models reach the convergence criterion to obtain the final optimized model; the topology models are optimized based on the global optimization objectives and global constraints written in the output file.

[0099] Optionally, the cyclic optimization process of the topology model includes: Obtain the cell density file of the topology model optimization results and determine whether the optimization has converged based on the consistency and tolerance of the optimization results; When the consistency of the optimization results of multiple topology models is less than the expected value, determine whether there is flexible deformation between the shared design domains; The design domain is further discretized based on the judgment results, a local coordinate system is defined for the flexible deformation part of the design domain, and the topology model is iteratively optimized until the consistency of the optimization results meets the requirements.

[0100] Optionally, geometrically mapping the shared design domain using manufacturing constraints based on pattern repetition comprises: The selected mesh nodes are used as anchor points to determine the mapping starting position of the shared design domain of different geometric models; Select the global coordinate system or the local coordinate system to determine the spatial angle of the geometric mapping; The scaling ratio of the shared design domain is determined by scaling factors in the horizontal, vertical, and height directions to achieve accurate mapping of the shared design domain of multiple models.

[0101] Optionally, it also includes: Performing a single-model topology optimization of multiple working conditions on the geometric model, obtaining a first-order response based on a variable density method, and normalizing the first-order response to obtain a second-order response; The mathematical model of the secondary response is shown in the following formula:

[0102] in, represents the design variables of the topological model, Indicates the The value of the secondary response, Indicates the The value of the first-level response, Indicates the The ideal value of a target, such as the minimum value, Indicates the The worst value of the first-level response, such as the maximum value, Indicates the The weight of the first-level response, .

[0103] Optionally, the multi-model topology optimization process includes: Determine the shared design domains of each model and link the design domains one by one through pattern-repeated manufacturing constraints to ensure that at least one set of design variables is linked between different geometric models; The master-slave variable method is used to realize the association of variables, and the master design domain variables are converted into slave design domain variables through scaling, rotation and translation; Construct a multi-model optimization problem involving shared and non-shared variables, and set global optimization objectives and local constraints; Density filtering and projection processing are performed on design variables to ensure manufacturing feasibility; The secondary responses of different models are combined through the compromise planning method to achieve multi-model collaborative topology optimization.

[0104] Optionally, judging whether the optimization has converged based on the consistency and tolerance of the optimization results includes: Calculating the Hausdorff distance between the two optimization result geometric point sets, determining the maximum mismatch degree according to the Hausdorff distance, and setting a tolerance standard to judge the geometric consistency; For continuous surface models, the correlation between the Gaussian curvature distributions of the two models is compared to evaluate the curvature similarity, and a tolerance standard is set to judge the curvature consistency.

[0105] Optionally, the process of further discretizing the design domain includes: The global design domain is divided into multiple non-overlapping subdomains, a local coordinate system is defined for each flexible deformation subdomain, and the gradient consistency is guaranteed by the Jacobian matrix; A consistency penalty term is added during the optimization process of the topology model to minimize the sum of the objective function and the penalty term.

[0106] Optionally, use the parallel computing interface to perform simultaneous loop optimization of multiple topology models, including: When the number of parallel computing interface processes equals the number of models plus one, the domain decomposition method is not enabled for parallelism within each model, and only the main process and the single model process run; When the number of processes in the parallel computing interface is greater than the number of models plus one, one process is allocated to the main program, and the remaining processes are evenly distributed to each model. Each model is solved in parallel using the domain decomposition method.

[0107] Optionally, it also includes: According to the final optimization result of the topology model, the optimization result file is exported, the geometry is reconstructed based on the optimization result file, the mesh file is smoothed by the polynurbs program, and the mesh file is converted into a geometry file.

[0108] Reference Figure 9 Based on the methods in the above embodiments, an embodiment of the present application provides an electronic device, which may include: a processor (Processor) 910, a communication interface (Communications Interface) 920, a memory (Memory) 930, and a communication bus 940. The processor 910, the communication interface 920, and the memory 930 communicate with each other via the communication bus 940. The processor 910 may call logic instructions in the memory 930 to execute the methods in the above embodiments.

[0109] In addition, the logic instructions in the aforementioned memory 930 can be implemented in the form of a software functional unit and, when sold or used as an independent product, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present application, or the portion that contributes to the prior art, or the portion of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes a number of instructions for enabling a computer device (which can be a personal computer, server, or network device, etc.) to execute all or part of the steps of the method described in each embodiment of the present application.

[0110] Based on the method in the above embodiment, an embodiment of the present application provides a computer-readable storage medium, which stores a computer program. When the computer program runs on a processor, the processor executes the method in the above embodiment.

[0111] Based on the method in the above embodiment, an embodiment of the present application provides a computer program product. When the computer program product runs on a processor, the processor executes the method in the above embodiment.

[0112] It is understood that the processor in the embodiments of the present application may be a central processing unit (CPU), other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field programmable gate arrays (FPGA), other programmable logic devices, transistor logic devices, hardware components, or any combination thereof. The general-purpose processor may be a microprocessor or any conventional processor.

[0113] The method steps in the embodiments of the present application can be implemented by hardware or by a processor executing software instructions. The software instructions can be composed of corresponding software modules, which can be stored in random access memory (RAM), flash memory, read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), registers, hard disks, mobile hard disks, CD-ROMs, or any other form of storage medium known in the art. An exemplary storage medium is coupled to the processor so that the processor can read information from the storage medium and write information to the storage medium. Of course, the storage medium can also be an integral part of the processor. The processor and storage medium can be located in an ASIC.

[0114] The above embodiments can be implemented in whole or in part using software, hardware, firmware, or any combination thereof. When implemented using software, they can be implemented in whole or in part in the form of a computer program product. The computer program product comprises one or more computer instructions. When loaded and executed on a computer, the computer program instructions fully or partially produce the processes or functions described in the embodiments of this application. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted via the computer-readable storage medium. The computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., coaxial cable, optical fiber, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium accessible by a computer or a data storage device such as a server or data center that integrates one or more available media. The available medium can be magnetic media (e.g., floppy disk, hard disk, tape), optical media (e.g., DVD), or semiconductor media (e.g., solid-state drive (SSD)).

[0115] It will be understood that the various numerical numbers involved in the embodiments of the present application are merely distinctions for the convenience of description and are not intended to limit the scope of the embodiments of the present application.

[0116] It is easy for those skilled in the art to understand that the above is only a preferred embodiment of the present application and is not intended to limit the present application. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present application should be included in the scope of protection of the present application.

Claims

1. A multi-model topology optimization method for complex geometric models, characterized in that: include: Construct a corresponding finite element model based on the geometric model of the wing corrugated structure; Dividing the geometric model into a design domain and establishing a topological model corresponding to the finite element model, wherein the topological model includes a shared design domain, a non-shared design domain, and a non-design domain between the geometric models; Geometric mapping of the shared design domain is performed through manufacturing constraints of pattern repetition, a mapping relationship of a local coordinate system for processing large deformation areas is established, a topological model that can be optimized synchronously is formed, and an output file of the topological model is exported; Using a parallel computing interface to perform synchronous cyclic optimization on multiple topology models, and judging the optimization results of the topology models according to a convergence criterion, until the topology models meet the convergence criterion, thereby obtaining a final optimized model; The topology model is optimized based on the global optimization objectives and global constraints written in the output file.

2. The multi-model topology optimization method for complex geometric models according to claim 1, characterized in that: The cyclic optimization process of the topology model includes: Obtain the cell density file of the topology model optimization results and determine whether the optimization has converged based on the consistency and tolerance of the optimization results; When the consistency of the optimization results of multiple topology models is less than the expected value, determine whether there is flexible deformation between the shared design domains; The design domain is further discretized based on the judgment results, a local coordinate system is defined for the flexible deformation part of the design domain, and the topology model is iteratively optimized until the consistency of the optimization results meets the requirements.

3. The multi-model topology optimization method for complex geometric models according to claim 1, characterized in that: The geometric mapping of the shared design domain by manufacturing constraints through pattern repetition includes: The selected mesh nodes are used as anchor points to determine the mapping starting position of the shared design domain of different geometric models; Select the global coordinate system or the local coordinate system to determine the spatial angle of the geometric mapping; The scaling ratio of the shared design domain is determined by scaling factors in the horizontal, vertical, and height directions to achieve accurate mapping of the shared design domain of multiple models.

4. The multi-model topology optimization method for complex geometric models according to claim 1, characterized in that: Also includes: Performing a single-model topology optimization of multiple working conditions on the geometric model, obtaining a first-order response based on a variable density method, and normalizing the first-order response to obtain a second-order response; The mathematical model of the secondary response is shown in the following formula: in, represents the design variables of the topological model, Indicates the The value of the secondary response, Indicates the The value of the first-level response, Indicates the The ideal value of a target, Indicates the The worst value of the first-level response, Indicates the The weight of the first-level response, .

5. The multi-model topology optimization method for complex geometric models according to claim 1, characterized in that: The multi-model topology optimization process includes: Determine the shared design domains of each model and link the design domains one by one through pattern-repeated manufacturing constraints to ensure that at least one set of design variables is linked between different geometric models; The master-slave variable method is used to realize the association of variables, and the master design domain variables are converted into slave design domain variables through scaling, rotation and translation; Construct a multi-model optimization problem involving shared and non-shared variables, and set global optimization objectives and local constraints; Density filtering and projection processing are performed on design variables to ensure manufacturing feasibility; The secondary responses of different models are combined through the compromise planning method to achieve multi-model collaborative topology optimization.

6. The multi-model topology optimization method for complex geometric models according to claim 2, characterized in that: The step of judging whether the optimization has converged based on the consistency and tolerance of the optimization results includes: Calculating the Hausdorff distance between the two optimization result geometric point sets, determining the maximum mismatch degree according to the Hausdorff distance, and setting a tolerance standard to judge the geometric consistency; For continuous surface models, the correlation between the Gaussian curvature distributions of the two models is compared to evaluate the curvature similarity, and a tolerance standard is set to judge the curvature consistency.

7. The multi-model topology optimization method for complex geometric models according to claim 3, characterized in that: The process of further discretizing the design domain involves: The global design domain is divided into multiple non-overlapping subdomains, a local coordinate system is defined for each flexible deformation subdomain, and the gradient consistency is guaranteed by the Jacobian matrix; A consistency penalty term is added during the optimization process of the topology model to minimize the sum of the objective function and the penalty term.

8. The multi-model topology optimization method for complex geometric models according to claim 1, characterized in that: Leverage parallel computing interfaces to perform simultaneous loop optimization on multiple topology models, including: When the number of parallel computing interface processes equals the number of models plus one, the domain decomposition method is not enabled for parallelism within each model, and only the main process and the single model process run; When the number of processes in the parallel computing interface is greater than the number of models plus one, one process is allocated to the main program, and the remaining processes are evenly distributed to each model. Each model is solved in parallel using the domain decomposition method.

9. The multi-model topology optimization method for complex geometric models according to claim 1, characterized in that: Also includes: The optimization result file is exported according to the final optimization result of the topology model, the geometry is reconstructed based on the optimization result file, and the mesh file is smoothed by a mesh smoothing program to realize conversion of the mesh file into a geometry file.

10. A multi-model topology optimization system for complex geometric models, characterized by: include: A finite element model building module is used to build a corresponding finite element model based on the geometric model of the wing corrugated structure; A topology model building module, configured to divide the geometric model into a design domain and establish a topology model corresponding to the finite element model, wherein the topology model includes a shared design domain, a non-shared design domain, and a non-design domain between the geometric models; A mapping module is used to geometrically map the shared design domain using manufacturing constraints of pattern repetition, establish a mapping relationship for processing large deformation regions in a local coordinate system, form a topological model that can be simultaneously optimized, and export an output file of the topological model; An optimization module is used to perform synchronous cyclic optimization on multiple topology models using a parallel computing interface, and to determine the optimization results of the topology models according to a convergence criterion until the topology models meet the convergence criterion, thereby obtaining a final optimized model; The topology model is optimized based on the global optimization objectives and global constraints written in the output file.

Images