3D model multi-scale lightweight method and system based on topological optimization

Abstract

The invention provides a 3D model multi-scale lightweight method and system based on topological optimization, and relates to the technical field of model lightweight, and the method comprises the steps: carrying out the mesh generation of a target 3D model, and generating a finite element model; a multi-scale topological optimization model is established, density distribution is adjusted through a density filtering function, and a macroscopic lightweight structure is obtained in combination with minimum size constraint and gray scale gradient projection processing; based on a macroscopic lightweight structure, a skeleton structure is obtained, based on an adaptive polygon segmentation rule, a porous filling unit is constructed, a multi-parameterized model is fused, a parameterized representation method of three variables of density, size and shape is established, and an intermediate scale structure is obtained through a multi-target genetic algorithm in combination with a sensitivity analysis technology; and embedding the intermediate-scale structure into the macroscopic lightweight structure, generating a multi-scale structure in combination with cascade optimization, calculating equivalent material attributes by adopting a homogenization method, iteratively adjusting model parameters, and finally obtaining a multi-scale lightweight result.

Description

Technical Field

[0001] The present invention relates to the technical field of model lightweighting, and in particular to a multi-scale lightweighting method and system for a 3D model based on topology optimization. Background Art

[0002] With the continuous development of industrial design and manufacturing technology, lightweight design has become one of the key factors to improve product performance and competitiveness. Traditional lightweight design methods mainly use experience and trial and error to optimize and reduce the weight of the structure locally, but it is difficult to take into account the overall performance and manufacturing feasibility of the structure at the same time.

[0003] However, existing topology optimization methods mainly focus on optimizing structures at a single scale, and fail to fully consider the multi-scale characteristics and lightweight potential of the structure. Engineering structures usually have complex morphologies and functional requirements across multiple scales, and it is difficult to obtain the optimal lightweight design by optimizing only at a single scale. In addition, the structures obtained by topology optimization usually have complex geometric shapes and topological structures, which brings challenges to subsequent manufacturing and processing. Existing technologies usually ignore the mutual influence and coupling relationship between different scales, making it difficult to obtain the globally optimal design solution, and face challenges such as high computational complexity and poor convergence, which limits its application in practical engineering.

[0004] In summary, there is an urgent need for a method that can simultaneously consider the multi-scale characteristics and lightweight requirements of the structure, while taking into account the manufacturing feasibility, to achieve efficient and reliable multi-scale lightweight design of 3D models. The present invention can solve the problems in the prior art. Summary of the invention

[0005] The present invention provides a 3D model multi-scale lightweight method and system based on topology optimization, which can solve the problems in the prior art.

[0006] A first aspect of the present invention, A multi-scale lightweight method for 3D models based on topology optimization is provided, including: Obtain a target 3D model to be lightweight, mesh the target 3D model, and generate a finite element model; based on the structural characteristics and load conditions of the target 3D model, combined with the SIMP interpolation model, introduce a non-uniform material property mapping function, establish a multi-scale topology optimization model, adjust the density distribution through a density filtering function, and combine the minimum size constraint and grayscale gradient projection processing to obtain a macro lightweight structure; Based on the macro lightweight structure, a skeleton structure is obtained through a skeleton extraction algorithm, and based on an adaptive polygon segmentation rule and combined with local feature information in the skeleton structure, a porous filling unit matching the skeleton structure is constructed, and based on the porous filling unit, a multi-parameter model of variable density, variable size and variable shape is integrated to establish a parameterized representation method of three variables of density, size and shape, and a multi-objective genetic algorithm is used in combination with a sensitivity analysis technique to collaboratively optimize and adjust topological parameters and morphological parameters to obtain an intermediate scale structure; Through the multi-scale coupling method, the intermediate-scale structure is embedded in the macro-lightweight structure. Combined with cascade optimization, a multi-scale structure is generated after connection and transition. Based on the multi-scale structure, the homogenization method is used to calculate the equivalent material properties, evaluate the mechanical properties and thermal response characteristics, and iteratively adjust the model parameters to finally obtain a multi-scale lightweight result.

[0007] Preferably, The target 3D model to be lightweight is obtained, and the target 3D model is meshed to generate a finite element model; based on the structural characteristics and load conditions of the target 3D model, combined with the SIMP interpolation model, a non-uniform material property mapping function is introduced to establish a multi-scale topology optimization model, and the density distribution is adjusted by the density filtering function. Combined with the minimum size constraint and grayscale gradient projection processing, a macro lightweight structure is obtained, including: Obtaining a target 3D model to be lightweight, meshing the target 3D model, generating a finite element model, and calculating and obtaining the stress-strain response of the finite element model under various working conditions through finite element static analysis based on the finite element model; Based on the structural characteristics and load conditions of the target 3D model, a relative density design variable is defined, a nonlinear mapping relationship between material properties and the relative density design variable is established through a SIMP interpolation model, and an exponential non-uniform material property mapping function is used to establish a nonlinear association between material properties of a microscopic filling area and macroscopic relative density; Based on the stress-strain response, taking the minimum structural flexibility as the optimization goal and the volume fraction as the constraint condition, a mathematical model is determined, the SIMP interpolation model and the exponential non-uniform material property mapping function are substituted into the mathematical model to optimize the mathematical model, and a multi-scale topology optimization model is established; The multi-scale topology optimization model is solved by a pre-constructed moving progressive optimization algorithm, and the optimal density distribution is obtained by iteratively updating the relative density design variables; A Helmholtz partial differential equation type density filter function is used to perform local averaging processing on the optimal density distribution to obtain a smooth density field; Performing mathematical morphological filtering on the smooth density field, combining density gradient control, performing minimum size constraint on the smooth density field, and obtaining a minimum size constrained density field; Based on the regularized Gaussian function, the lowest size constraint density field is subjected to grayscale gradient projection processing to obtain a macroscopic lightweight structure.

[0008] Preferably, Based on the stress-strain response, with the minimum structural flexibility as the optimization goal and the volume fraction as the constraint condition, the mathematical model is determined to include: The objective function formula is as follows: ; in, C represents the structural flexibility, u T represents the transpose of the strain displacement vector, i represents the element index of the finite element model, and B i T represents the transpose of the stress-strain matrix of the ith element, E min represents the minimum elastic modulus, E 0 represents the elastic modulus of the perfect material, k represents the parameter of the exponential function, ρ i Indicates i The relative density of the unit, B i represents the stress-strain matrix of the ith element, V i Indicates i The volume of a unit, u represents the strain displacement vector.

[0009] Preferably, Based on the macro lightweight structure, the skeleton structure is obtained by using a skeleton extraction algorithm, including: Based on the size and complexity of each part in the macro lightweight structure, the voxelization resolution is adaptively determined according to a preset resolution range to generate an adaptive voxel model; By using a distance transformation algorithm, the shortest geodesic distance from each voxel in the adaptive voxel model to the structure boundary is calculated to generate a geodesic distance field; Perform multi-scale smoothing on the geodesic distance field based on a Gaussian kernel function to obtain distance field representations at different scales, extract local maximum points of the distance field representation at each scale, and determine candidate skeleton points; Based on the local features of the candidate skeleton points, a skeleton point screening threshold is adaptively determined to obtain a screened skeleton point set, based on the centrality and connectivity information of each skeleton point in the skeleton point set, the contribution of the skeleton point to the skeleton as a whole is calculated, and according to a preset skeleton point elimination threshold, skeleton points are pruned to obtain a skeleton point pruned result set; Based on a preset local neighborhood search strategy, the local neighborhood range of each skeleton point in the skeleton point pruning result set is adaptively determined, a minimum spanning tree is constructed within the local neighborhood range to obtain a local connected skeleton structure, and combined with global connectivity optimization, the local connected skeleton structure is spliced ​​into a complete skeleton structure.

[0010] Preferably, Calculating the shortest geodesic distance from each voxel in the adaptive voxel model to the structure boundary by a distance transformation algorithm, and generating a geodesic distance field comprises: Each voxel in the adaptive voxel model corresponds to a node, and the adaptive voxel model is represented as a three-dimensional voxel grid; Initializing the geodesic distance value from the boundary node of the three-dimensional voxel grid to the structure boundary based on a preset fast marching algorithm, and adding the boundary node to the active node list; Selecting a node with the smallest geodesic distance value from the active node list as the current extended node, obtaining an adjacent node corresponding to the current extended node, measuring the node distance between the current extended node and the corresponding adjacent node, updating the geodesic distance value of the adjacent node to the sum of the geodesic distance value of the current extended node and the node distance, removing the current extended node from the active node list, and adding the adjacent node to the active node list if the updated geodesic distance value of the adjacent node is less than the geodesic distance value before the update; traversing the active node list and updating the geodesic distance value until the active node list is empty; The geodesic distance values ​​of all nodes in the three-dimensional voxel grid are normalized to obtain the geodesic distance field.

[0011] Preferably, Based on the adaptive polygon segmentation rule, combined with the local feature information in the skeleton structure, a porous filling unit matching the skeleton structure is constructed. Based on the porous filling unit, a multi-parameter model of variable density, variable size and variable shape is integrated to establish a parameterized representation method of three variables of density, size and shape. Through a multi-objective genetic algorithm, combined with sensitivity analysis technology, the topological parameters and morphological parameters are collaboratively optimized and adjusted to obtain an intermediate scale structure including: Based on the local feature information of the skeleton structure, skeleton feature parameters are obtained, and according to the skeleton feature parameters, generation parameters of the polygon segmentation map are adaptively adjusted to obtain adaptive polygon segmentation rules; based on the adaptive polygon segmentation rules, a porous filling unit matching the skeleton structure is constructed; Introducing variable density parameters, variable size parameters and variable shape parameters to respectively control the density distribution, size change and shape change of the porous filling unit, establishing a parametric mapping relationship between the variable density parameters, variable size parameters and variable shape parameters, and obtaining a multi-parameter model integrating variable density, variable size and variable shape; Based on multiple predetermined optimization objectives, a multi-objective optimization model is established, and the sensitivity analysis technology is used to determine the influence of topological parameters and morphological parameters on the multiple optimization objectives. Through a multi-objective genetic algorithm, the topological parameters and morphological parameters are encoded and optimized, and the topological parameters and morphological parameters are dynamically adjusted to generate the optimal combination of the topological parameters and morphological parameters. According to the optimal combination of topological parameters and morphological parameters, the density, size and shape of the porous filling unit are updated, and the updated porous filling unit is fused with the skeleton structure to generate an intermediate scale structure.

[0012] Preferably, Based on the multi-scale structure, the equivalent material properties calculated using the homogenization method include: Based on the multi-scale structure, selecting a periodic representative voxel and establishing a three-dimensional entity of the periodic representative voxel; Applying periodic boundary conditions and basic strain conditions to the three-dimensional entity, calculating the stress-strain response of the periodic representative volume element under each condition, and calculating each independent component of the equivalent elastic tensor through the stress-strain relationship according to the stress-strain response; Applying a uniaxial thermal load condition to the three-dimensional entity, calculating the temperature gradient and heat flux distribution of the periodic representative volume element, and calculating each component of the equivalent thermal conductivity tensor in combination with Fourier's heat conduction law; Assembling the calculated equivalent elastic tensor and the equivalent thermal conductivity tensor into an equivalent material property matrix of the multi-scale structure; Iterate different regions in the multi-scale structure, repeatedly assemble the equivalent material property matrix corresponding to each region, and calculate and obtain the equivalent material properties of each region.

[0013] The second aspect of the present invention, A 3D model multi-scale lightweight system based on topology optimization is provided, including: The first unit is used to obtain the target 3D model to be lightweight, mesh the target 3D model, and generate a finite element model; based on the structural characteristics and load conditions of the target 3D model, combined with the SIMP interpolation model, introduce a non-uniform material property mapping function, establish a multi-scale topology optimization model, adjust the density distribution through a density filtering function, and combine the minimum size constraint and grayscale gradient projection processing to obtain a macro lightweight structure; The second unit is used to obtain the skeleton structure based on the macro lightweight structure through a skeleton extraction algorithm, and to construct a porous filling unit matching the skeleton structure based on an adaptive polygon segmentation rule and in combination with local feature information in the skeleton structure. Based on the porous filling unit, a multi-parameter model of variable density, variable size and variable shape is integrated to establish a parameterized representation method of three variables of density, size and shape. Through a multi-objective genetic algorithm combined with sensitivity analysis technology, topological parameters and morphological parameters are collaboratively optimized and adjusted to obtain an intermediate scale structure. The third unit is used to embed the intermediate-scale structure into the macro lightweight structure through a multi-scale coupling method, combine cascade optimization, and generate a multi-scale structure after connection and transition. Based on the multi-scale structure, the homogenization method is used to calculate the equivalent material properties, evaluate the mechanical properties and thermal response characteristics, iteratively adjust the model parameters, and finally obtain a multi-scale lightweight result.

[0014] The third aspect of the present invention, An electronic device is provided, comprising: processor; a memory for storing processor-executable instructions; The processor is configured to call the instructions stored in the memory to execute the aforementioned method.

[0015] A fourth aspect of the present invention, A computer-readable storage medium is provided, on which computer program instructions are stored. When the computer program instructions are executed by a processor, the aforementioned method is implemented.

[0016] In the present invention, a high-precision finite element model is created to accurately reflect the geometric shape and structural characteristics of the target structure; the SIMP interpolation model and the non-uniform material property mapping function are used to realize the non-uniform distribution of material properties in the model to better adapt to the actual load requirements of the structure; through the establishment of a multi-scale topology optimization model, the microstructure characteristics and macrostructure requirements are comprehensively considered, and optimization is effectively performed at different scales to ensure the balance of performance and manufacturing in the final design; the skeleton extraction algorithm is used to accurately extract the skeleton structure from the macro lightweight structure, providing a clear structural skeleton for further optimization and analysis; based on the adaptive polygon segmentation rule and combined with the local characteristics of the skeleton structure, a topology optimization model is constructed. The porous filling units that match the skeleton ensure that the geometric characteristics of the filling units are consistent with the local details of the skeleton structure, thereby improving the accuracy and applicability of the model. By integrating multi-parametric models of variable density, variable size and variable shape, a parametric representation method of three variables is established to comprehensively optimize the structure, which can better adapt to different design requirements and usage scenarios. Through multi-scale coupling methods and cascade optimization, the intermediate-scale structure is embedded in the macroscopic lightweight structure to generate a seamless multi-scale structure, ensuring the effective connection and transition of structures of different scales and improving the comprehensive performance of the overall structure. The homogenization method is used to calculate the equivalent material properties of the multi-scale structure, providing an accurate evaluation of the mechanical properties and thermal response characteristics of the structure. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 A schematic diagram of a process of a multi-scale lightweight method for a 3D model based on topology optimization according to an embodiment of the present invention; Figure 2 It is a structural schematic diagram of a 3D model multi-scale lightweight system based on topology optimization according to an embodiment of the present invention. DETAILED DESCRIPTION

[0018] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0019] The technical solution of the present invention is described in detail with specific embodiments below. The following specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described in detail in some embodiments.

[0020] Figure 1 FIG. 1 is a flow chart of a multi-scale lightweight method for a 3D model based on topology optimization according to an embodiment of the present invention. Figure 1 As shown, the method includes: S101. Obtain a target 3D model to be lightweight, mesh the target 3D model, and generate a finite element model; based on the structural characteristics and load conditions of the target 3D model, combined with the SIMP interpolation model, introduce a non-uniform material property mapping function, establish a multi-scale topology optimization model, adjust the density distribution through a density filtering function, and combine the minimum size constraint and grayscale gradient projection processing to obtain a macro lightweight structure; In this embodiment, by creating a high-precision finite element model, the geometric shape and structural characteristics of the target structure can be accurately reflected, providing a reliable basis for subsequent optimization analysis; the SIMP interpolation model and non-uniform material property mapping function are used to achieve non-uniform distribution of material properties in the model to better adapt to the actual load requirements of the structure; through the establishment of a multi-scale topology optimization model, the microstructure characteristics and macrostructure requirements are comprehensively considered, and optimization is effectively performed at different scales to ensure the balance of performance and manufacturing in the final design; the density filter function is used to adjust the density distribution of the material to ensure the smoothness and continuity of the material distribution during the optimization process. Combined with the minimum size constraint, it can effectively avoid the appearance of too small or too fine structural features in the optimization results, improve the manufacturability and structural stability of the design; through grayscale gradient projection processing, the material distribution in the optimization results is converted into an actual manufacturable structural form, which helps to convert the theoretical optimization results into a design scheme in actual engineering and ensure the actual feasibility and performance of the structure.

[0021] In an optional embodiment, a target 3D model to be lightweight is obtained, the target 3D model is meshed, and a finite element model is generated; based on the structural characteristics and load conditions of the target 3D model, a non-uniform material property mapping function is introduced in combination with a SIMP interpolation model, a multi-scale topology optimization model is established, and the density distribution is adjusted by a density filtering function, and a macroscopic lightweight structure is obtained in combination with a minimum size constraint and grayscale gradient projection processing, including: Obtaining a target 3D model to be lightweight, meshing the target 3D model, generating a finite element model, and calculating and obtaining the stress-strain response of the finite element model under various working conditions through finite element static analysis based on the finite element model; Based on the structural characteristics and load conditions of the target 3D model, a relative density design variable is defined, a nonlinear mapping relationship between material properties and the relative density design variable is established through a SIMP interpolation model, and an exponential non-uniform material property mapping function is used to establish a nonlinear association between material properties of a microscopic filling area and macroscopic relative density; Based on the stress-strain response, taking the minimum structural flexibility as the optimization goal and the volume fraction as the constraint condition, a mathematical model is determined, the SIMP interpolation model and the exponential non-uniform material property mapping function are substituted into the mathematical model to optimize the mathematical model, and a multi-scale topology optimization model is established; The multi-scale topology optimization model is solved by a pre-constructed moving progressive optimization algorithm, and the optimal density distribution is obtained by iteratively updating the relative density design variables; A Helmholtz partial differential equation type density filter function is used to perform local averaging processing on the optimal density distribution to obtain a smooth density field; Performing mathematical morphological filtering on the smooth density field, combining density gradient control, performing minimum size constraint on the smooth density field, and obtaining a minimum size constrained density field; Based on the regularized Gaussian function, the lowest size constraint density field is subjected to grayscale gradient projection processing to obtain a macroscopic lightweight structure.

[0022] The SIMP interpolation model is a material interpolation model used in topology optimization. The core idea is to achieve a smooth transition of material properties by adjusting the relative density of the material, so as to flexibly control the material distribution during the optimization process. A relative density design variable, usually ranging from 0 to 1, is used to represent the existence state of the material, where 1 means that the material is completely present and 0 means that the material is completely absent. The relationship between the elastic modulus and relative density of the material is usually expressed as: ; Where E0 is the elastic modulus of the reference material, ρ represents the relative density design variable, and p is a penalty factor that is usually greater than 1 to encourage more consistent material distribution and reduce fuzzy areas.

[0023] The SIMP interpolation model adjusts the effective elastic modulus of the material, allowing a gradual transition of the material during the optimization process to achieve design optimization.

[0024] The Helmholtz partial differential equation density filter function is a smoothing technique used to process the material density distribution in the optimization results. Its purpose is to remove high-frequency noise or discontinuity that may appear in the optimization process and to smooth the density field.

[0025] Smooth density field refers to the smooth material density distribution obtained through density filtering and other smoothing techniques, such as morphological filtering. This density field has less high-frequency noise and smoother material distribution after optimization, which is convenient for actual manufacturing and structural analysis. The smooth density field is the density distribution field after density filtering. It has the characteristics of continuity and smoothness, avoiding the discretization and noise problems that may occur during the optimization process.

[0026] Obtain the target three-dimensional model to be lightweight, and select a suitable meshing method based on the geometric characteristics and accuracy requirements of the model. Common meshing methods include tetrahedral meshing and hexahedral meshing. Tetrahedral meshing is suitable for models with complex and irregular geometric shapes, while hexahedral meshing is suitable for models with regular geometric shapes and a high degree of structuring. According to the characteristics of the model, select the appropriate mesh size and unit type, mesh the model, and generate a high-quality finite element model. During the meshing process, key areas (such as stress concentration areas, load action areas, etc.) need to be meshed to improve calculation accuracy. At the same time, attention should be paid to the control of mesh quality to avoid the occurrence of distorted units or transition units to ensure the reliability of finite element analysis.

[0027] Using the finite element static analysis method, material properties, boundary conditions and load conditions are applied to the generated finite element model. Material properties include elastic modulus, Poisson's ratio, etc., which are set according to the actual mechanical properties of the material. Boundary conditions are defined according to the constraints of the model. Common boundary conditions include fixed constraints, symmetric constraints, periodic boundary conditions, etc. Load conditions are applied according to the actual force conditions, which can be force loads, displacement loads, pressure loads, etc. After defining the material properties, boundary conditions and load conditions, the finite element solver is used to perform static mechanical solutions on the model to calculate and obtain the stress and strain responses of the finite element model under various load conditions. Optionally, the results can be visualized through stress-strain cloud diagrams to analyze the mechanical behavior and potential weak areas of the model.

[0028] According to the structural characteristics and load conditions of the target three-dimensional model, the relative density design variable is defined. The relative density design variable represents the relative density of the material in each finite element unit, and its value range is from 0 to 1, indicating the change of the material from void to solid. The SIMP interpolation model is used to establish a nonlinear mapping relationship between material properties and relative density design variables. The SIMP interpolation model introduces a penalty factor, which makes the material properties of the intermediate density value lower, and promotes the optimization results to converge to the discrete distribution of "solid-void". At the same time, in order to describe the relationship between the material properties of the microscopic filling area and the macroscopic relative density in the multi-scale structure, an exponential non-uniform material property mapping function is used. This function describes the nonlinear change of the material properties of the microscopic filling area with the macroscopic relative density through an exponential function, reflecting the material heterogeneity of the multi-scale structure.

[0029] The mathematical optimization model is determined with the minimum structural flexibility as the optimization goal and the volume fraction as the constraint condition. Structural flexibility refers to the degree of deformation of the structure under a given load. Minimum flexibility means maximum structural stiffness. The volume fraction represents the ratio of the volume of the optimized structure to the volume of the initial design domain. Lightweight design can be achieved by controlling the volume fraction. The SIMP interpolation model and the exponential non-uniform material property mapping function are substituted into the optimization mathematical model to establish a multi-scale topology optimization model. This model comprehensively considers the topology optimization of the macroscopic structure and the microscopic filling area, and optimizes the material distribution by optimizing the relative density design variables.

[0030] The multi-scale topology optimization model is solved using a pre-built moving progressive optimization algorithm. The moving progressive optimization algorithm is a heuristic optimization algorithm that gradually improves the optimization target value by continuously iteratively updating the design variables. In each iteration, the structural response is calculated based on the current design variable values, the optimization target and constraints are evaluated, and the design variables are updated based on the sensitivity information. Through multiple iterations, the optimization process is gradually advanced, and finally the optimal design variable values ​​that meet the optimization target and constraints, that is, the optimal material relative density distribution, are obtained.

[0031] Since the optimal density distribution obtained by topology optimization usually contains a large number of "grayscale" units, that is, units with density between 0 and 1, post-processing is required to obtain clear structural boundaries. The optimal density distribution is locally averaged using the Helmholtz partial differential equation type density filter function. By solving the Helmholtz partial differential equation, the density field is smoothed, the "grayscale" units are eliminated, and a smooth density field is obtained. The Helmholtz partial differential equation controls the smoothness of the density field and the width of the transition region by introducing diffusion and convection terms.

[0032] In order to further improve the manufacturing feasibility of the structure, it is necessary to control the minimum size of the smooth density field. The mathematical morphological filtering method is used to eliminate structural features smaller than the minimum size by corroding and dilating the density field. At the same time, the density gradient control method is combined to ensure the continuity and smoothness of the structure by limiting the density gradient between adjacent units. After mathematical morphological filtering and density gradient control, a density field that meets the minimum size requirements is obtained.

[0033] Finally, based on the regularized Gaussian function, the density field that meets the minimum size constraint is projected with grayscale gradient. The regularized Gaussian function convolves the density field with the Gaussian kernel function to obtain a smooth grayscale gradient structure. By adjusting the parameters of the Gaussian function, the smoothness of the grayscale gradient and the width of the transition area are controlled. After the grayscale gradient projection process, a macroscopic lightweight structure with a smooth transition boundary is finally obtained.

[0034] In this embodiment, a high-quality finite element model is generated by finely meshing the target three-dimensional model to ensure that the model can accurately reflect the geometric characteristics and stress conditions; the stress and strain responses of the model under various working conditions are calculated by using finite element static analysis, so that the mechanical behavior of the structure and potential weak areas can be fully understood; the SIMP interpolation model and the exponential non-uniform material property mapping function are used to establish a nonlinear relationship between material properties and relative density design variables, and the material properties of the microscopic filling area in the multi-scale structure are accurately modeled to reflect the real behavior of the material under different densities; a mathematical model with minimum structural flexibility as the optimization goal and volume fraction as the constraint condition is established. By controlling the volume fraction, lightweight design is achieved and the structural stiffness is maximized to ensure the best mechanical properties and minimum structural deformation; the multi-scale topology optimization model is solved by a moving progressive optimization algorithm, and the optimization target value is gradually improved by iteratively updating the design variables. The algorithm effectively finds the optimal relative density distribution of materials to meet the optimization objectives and constraints. The generation of a smooth density field eliminates the grayscale units in the density field, improving the smoothness and continuity of the optimization results. Through mathematical morphological filtering and density gradient control, the minimum size of the smooth density field is further controlled, eliminating structural features smaller than the minimum size, ensuring the manufacturing feasibility of the structure. At the same time, combined with grayscale gradient projection processing, a macroscopic lightweight structure with a smooth transition boundary is obtained.

[0035] In an optional embodiment, based on the stress-strain response, with the minimum structural flexibility as the optimization goal and the volume fraction as the constraint condition, determining the mathematical model includes: The objective function formula is as follows: ; in, C represents the structural flexibility, u T represents the transpose of the strain displacement vector, i represents the element index of the finite element model, and B i T represents the transpose of the stress-strain matrix of the ith element, E min represents the minimum elastic modulus, E 0 represents the elastic modulus of the perfect material, k represents the parameter of the exponential function, ρ i Indicates i The relative density of the unit, B i represents the stress-strain matrix of the ith element, V i Indicates i The volume of a unit, u represents the strain displacement vector.

[0036] The calculation process of the formula is as follows: In the formula, the structural flexibility C It is calculated by the strain displacement vector u through a series of matrices and material properties; for each finite element i, the material properties of the finite element i are first calculated, involving the minimum elastic modulus E min and the elastic modulus of the complete material E 0; adjust material properties through exponential functions to reflect different relative densities ρ i The material properties are then used to calculate the stiffness matrix B for each element. i T and volume V i ; Finally, the results of all units are summarized and weighted by the strain displacement vector u to obtain the overall structural flexibility.

[0037] According to the formula, by optimizing the objective function, the structural flexibility is minimized and the stiffness and stability of the structure are improved; the nonlinear mapping of relative density is introduced to make the behavior of the material at different densities more realistic and accurate, which helps to optimize the accuracy of the design; the volume and stiffness of each finite element unit are comprehensively considered in the calculation process to ensure the balanced optimization of the overall structure in all parts; by adjusting the exponential function parameters and relative density, it can adapt to different design requirements and material properties and provide a flexible optimization solution.

[0038] S102. Based on the macro lightweight structure, a skeleton structure is obtained through a skeleton extraction algorithm. Based on an adaptive polygon segmentation rule and in combination with local feature information in the skeleton structure, a porous filling unit matching the skeleton structure is constructed. Based on the porous filling unit, a multi-parameter model of variable density, variable size and variable shape is integrated to establish a parameterized representation method of three variables of density, size and shape. A multi-objective genetic algorithm is used in combination with a sensitivity analysis technique to collaboratively optimize and adjust topological parameters and morphological parameters to obtain an intermediate scale structure. In this embodiment, the skeleton extraction algorithm is used to accurately extract the skeleton structure from the macro lightweight structure, providing a clear structural skeleton for further optimization and analysis; based on the adaptive polygon segmentation rule and combined with the local features of the skeleton structure, a porous filling unit matching the skeleton is constructed to ensure that the geometric features of the filling unit are consistent with the local details of the skeleton structure, thereby improving the accuracy and applicability of the model; by integrating the multi-parameterized model of variable density, variable size and variable shape, a three-variable parameterized representation method is established to comprehensively optimize the structure, which can better adapt to different design requirements and usage scenarios; a multi-objective genetic algorithm and sensitivity analysis technology are used to coordinately optimize and adjust the topological parameters and morphological parameters, thereby obtaining an optimized intermediate-scale structure. This structure achieves a balance between multiple optimization objectives and has excellent performance and design flexibility.

[0039] In an optional embodiment, based on the macro lightweight structure, obtaining the skeleton structure by using a skeleton extraction algorithm includes: Based on the size and complexity of each part in the macro lightweight structure, the voxelization resolution is adaptively determined according to a preset resolution range to generate an adaptive voxel model; By using a distance transformation algorithm, the shortest geodesic distance from each voxel in the adaptive voxel model to the structure boundary is calculated to generate a geodesic distance field; Perform multi-scale smoothing on the geodesic distance field based on a Gaussian kernel function to obtain distance field representations at different scales, extract local maximum points of the distance field representation at each scale, and determine candidate skeleton points; Based on the local features of the candidate skeleton points, a skeleton point screening threshold is adaptively determined to obtain a screened skeleton point set, based on the centrality and connectivity information of each skeleton point in the skeleton point set, the contribution of the skeleton point to the skeleton as a whole is calculated, and according to a preset skeleton point elimination threshold, skeleton points are pruned to obtain a skeleton point pruned result set; Based on a preset local neighborhood search strategy, the local neighborhood range of each skeleton point in the skeleton point pruning result set is adaptively determined, a minimum spanning tree is constructed within the local neighborhood range to obtain a local connected skeleton structure, and combined with global connectivity optimization, the local connected skeleton structure is spliced ​​into a complete skeleton structure.

[0040] The voxelization resolution is adaptively determined according to the size and structural complexity of each part in the macro lightweight structure. For areas with larger size and simpler structure, a lower resolution is used; for areas with smaller size and complex structure, a higher resolution is used. By reasonably selecting the resolution range, the data volume of the voxel model can be reduced while ensuring the accuracy of the model. According to the determined adaptive resolution, the macro lightweight structure is voxelized to generate an adaptive voxel model. The adaptive voxel model can use different resolutions in different areas to achieve a balance between accuracy and efficiency.

[0041] The distance transform algorithm is used to calculate the shortest geodesic distance from each voxel in the adaptive voxel model to the boundary of the structure. The distance transform algorithm calculates the shortest path distance from the voxel to the boundary by diffusion layer by layer. Starting from the boundary voxel, it gradually diffuses to the internal voxel. The distance value of each voxel is equal to the minimum distance value of its neighboring voxels plus the distance between voxels. The distance transform algorithm is used to obtain the geodesic distance field, which represents the shortest geodesic distance from each voxel to the boundary of the structure. The geodesic distance field can reflect the internal morphology and scale information of the structure.

[0042] The geodesic distance field is smoothed at multiple scales using a Gaussian kernel function. The Gaussian kernel function performs convolution operations on the distance field to obtain distance field representations at different scales. The scale and degree of smoothing are controlled by adjusting the parameters of the Gaussian kernel function. At each scale, the local maximum points of the distance field representation are extracted as candidate skeleton points. The local maximum points correspond to the peak areas in the distance field and represent the central axis position of the structure. Through multi-scale analysis, a set of candidate skeleton points at different scales is obtained, covering the main skeleton information of the structure.

[0043] According to the local features of the candidate skeleton points, the skeleton point screening threshold is adaptively determined. Local features may include distance field values, normal vector directions, curvatures, etc. By analyzing the local feature distribution of the candidate skeleton points, the screening threshold is adaptively determined to remove noise and redundant skeleton points. The candidate skeleton points that meet the screening threshold are retained to obtain a screened skeleton point set. In order to further optimize the skeleton structure, the contribution of the skeleton point to the skeleton as a whole is calculated based on the centrality and connectivity information of each skeleton point. The centrality reflects the importance of the skeleton point in the local area, and the connectivity information reflects the topological relationship between the skeleton point and other skeleton points. According to the preset skeleton point elimination threshold, the skeleton points with lower contribution are removed to obtain a skeleton point pruning result set. The pruned skeleton point set can better represent the main skeleton of the structure.

[0044] The preset local neighborhood search strategy is used to adaptively determine the local neighborhood range of each skeleton point in the skeleton point pruning result set. The local neighborhood range is adaptively adjusted according to the position and structural characteristics of the skeleton point to ensure that the neighborhood contains sufficient context information. Within the local neighborhood range of each skeleton point, a minimum spanning tree is constructed to obtain a locally connected skeleton structure. The minimum spanning tree algorithm generates a loop-free minimum connected subgraph by connecting the skeleton points in the neighborhood to represent the topological structure of the local skeleton. In order to obtain a complete skeleton structure, the locally connected skeleton structure needs to be globally optimized. By analyzing the connectivity relationship and geometric similarity between the local skeleton structures, they are spliced ​​into a complete skeleton structure. The global optimization process takes into account the continuity, smoothness and topological consistency of the overall skeleton to obtain the final skeleton structure representation.

[0045] In this embodiment, the voxel resolution is adaptively selected according to the size and complexity of different regions, and the generation of an adaptive voxel model is realized. This processing reduces the amount of data and optimizes the computational efficiency while ensuring the accuracy of the model; the shortest geodesic distance from each voxel to the structure boundary is calculated by the distance transformation algorithm, providing an accurate representation of the internal morphology and scale information of the structure; the geodesic distance field is multi-scale smoothed using the Gaussian kernel function, and the candidate sets of skeleton points at different scales are extracted, which enhances the details and continuity of the skeleton structure; the skeleton points are adaptively screened and pruned by analyzing the local features of the skeleton points and calculating the contribution, which improves the accuracy and reliability of the skeleton representation; the local skeleton structure is constructed using the minimum spanning tree algorithm, and it is spliced ​​into a complete skeleton structure through global optimization, ensuring the continuity, smoothness and topological consistency of the skeleton.

[0046] In an optional embodiment, calculating the shortest geodesic distance from each voxel in the adaptive voxel model to the structure boundary by a distance transformation algorithm, and generating the geodesic distance field includes: Each voxel in the adaptive voxel model corresponds to a node, and the adaptive voxel model is represented as a three-dimensional voxel grid; Initializing the geodesic distance value from the boundary node of the three-dimensional voxel grid to the structure boundary based on a preset fast marching algorithm, and adding the boundary node to the active node list; Selecting a node with the smallest geodesic distance value from the active node list as the current extended node, obtaining an adjacent node corresponding to the current extended node, measuring the node distance between the current extended node and the corresponding adjacent node, updating the geodesic distance value of the adjacent node to the sum of the geodesic distance value of the current extended node and the node distance, removing the current extended node from the active node list, and adding the adjacent node to the active node list if the updated geodesic distance value of the adjacent node is less than the geodesic distance value before the update; traversing the active node list and updating the geodesic distance value until the active node list is empty; The geodesic distance values ​​of all nodes in the three-dimensional voxel grid are normalized to obtain the geodesic distance field.

[0047] The adaptive voxel model is represented as a three-dimensional voxel grid. Each voxel in the adaptive voxel model corresponds to a node in the grid, and the adjacency relationship between voxels corresponds to the edge connection between nodes. In this way, the irregular adaptive voxel model is converted into a regular three-dimensional voxel grid representation. The three-dimensional voxel grid provides a convenient data structure and operation basis for the subsequent distance transformation and skeleton extraction algorithms.

[0048] The preset fast marching algorithm is used to initialize the geodesic distance values ​​from the boundary nodes of the 3D voxel grid to the structure boundary. First, the voxel nodes located on the structure boundary are identified and their geodesic distance values ​​are initialized to 0. Then, these boundary nodes are added to the active node list as the starting points of the distance transformation. The active node list is used to record the nodes currently participating in the distance transformation calculation in order to efficiently update the geodesic distance values.

[0049] Select the node with the smallest geodesic distance value from the active node list as the current expansion node. This node represents the node with the smallest known geodesic distance value and is the expansion starting point of the distance transformation. Get the adjacent nodes of the current expansion node, that is, the voxel nodes directly connected to it. Measure the node distance between the current expansion node and each adjacent node, that is, the Euclidean distance between the two nodes. Update the geodesic distance value of the adjacent node to the sum of the geodesic distance value of the current expansion node and the node distance, that is, propagate the distance information of the current expansion node to the adjacent nodes. Remove the current expansion node from the active node list, indicating that the distance information of the node has been processed. If the updated geodesic distance value of the adjacent node is less than the geodesic distance value before the update, it means that the distance to the adjacent node through the current expansion node is shorter, and the adjacent node needs to be added to the active node list for subsequent distance updates.

[0050] Repeat the process of traversing all nodes in the active node list and updating their geodesic distance values. Each time, select the node with the smallest geodesic distance value from the active node list as the current expansion node, update the geodesic distance values ​​of its adjacent nodes, and add or remove the adjacent nodes from the active node list according to the update results. Through continuous expansion and updating, the distance information is gradually propagated from the boundary nodes to the internal nodes until the active node list is empty, that is, the geodesic distance values ​​of all nodes have been calculated.

[0051] The geodesic distance values ​​of all nodes in the three-dimensional voxel grid are normalized. Due to different structural dimensions and voxel sizes, the range of geodesic distance values ​​may vary greatly. In order to facilitate subsequent skeleton extraction and analysis, the geodesic distance values ​​need to be normalized. Common normalization methods include maximum normalization and mean-variance normalization. Maximum normalization divides all geodesic distance values ​​by the maximum geodesic distance value and maps them to the range of [0, 1]. Mean-variance normalization subtracts the mean from the geodesic distance value and divides it by the standard deviation to obtain a standardized distance value with a mean of 0 and a variance of 1. The normalized geodesic distance field represents the relative distance relationship between each position inside the structure and the boundary, providing important prior information for skeleton extraction.

[0052] In this embodiment, the adaptive voxel model is converted into a regular three-dimensional voxel grid, which simplifies the data structure and makes subsequent processing more efficient and standardized; the geodesic distance from each voxel node in the three-dimensional voxel grid to the structure boundary is accurately calculated through the fast marching algorithm. The algorithm effectively propagates distance information and improves the computational efficiency and accuracy of distance transformation; through normalization, the range of geodesic distance values ​​is adjusted so that the geodesic distance field can maintain consistency under different structure sizes and voxel sizes. This process ensures the accuracy and consistency of the skeleton extraction process; the normalized geodesic distance field provides reliable prior information for skeleton extraction, enhances the effect and accuracy of the skeleton extraction algorithm, and helps to extract the main skeleton information of the structure.

[0053] In an optional embodiment, based on the adaptive polygon segmentation rule and in combination with the local feature information in the skeleton structure, a porous filling unit matching the skeleton structure is constructed. Based on the porous filling unit, a multi-parameter model of variable density, variable size and variable shape is integrated to establish a parameterized representation method of three variables of density, size and shape. Through a multi-objective genetic algorithm, combined with sensitivity analysis technology, the topological parameters and morphological parameters are collaboratively optimized and adjusted to obtain an intermediate scale structure, including: Based on the local feature information of the skeleton structure, skeleton feature parameters are obtained, and according to the skeleton feature parameters, generation parameters of the polygon segmentation map are adaptively adjusted to obtain adaptive polygon segmentation rules; based on the adaptive polygon segmentation rules, a porous filling unit matching the skeleton structure is constructed; Introducing variable density parameters, variable size parameters and variable shape parameters to respectively control the density distribution, size change and shape change of the porous filling unit, establishing a parametric mapping relationship between the variable density parameters, variable size parameters and variable shape parameters, and obtaining a multi-parameter model integrating variable density, variable size and variable shape; Based on multiple predetermined optimization objectives, a multi-objective optimization model is established, and the sensitivity analysis technology is used to determine the influence of topological parameters and morphological parameters on the multiple optimization objectives. Through a multi-objective genetic algorithm, the topological parameters and morphological parameters are encoded and optimized, and the topological parameters and morphological parameters are dynamically adjusted to generate the optimal combination of the topological parameters and morphological parameters. According to the optimal combination of topological parameters and morphological parameters, the density, size and shape of the porous filling unit are updated, and the updated porous filling unit is fused with the skeleton structure to generate an intermediate scale structure.

[0054] Analyze the local feature information of the skeleton structure and extract the skeleton feature parameters. The local feature information includes the geometric shape, size, direction, connectivity, etc. of the skeleton. By performing local analysis on the skeleton structure, parameters reflecting the skeleton features are obtained, such as the length of the skeleton line segment, the degree of the skeleton node, the curvature of the skeleton, etc. According to the extracted skeleton feature parameters, the generation parameters of the polygon segmentation map are adaptively adjusted. The generation parameters include the size, shape, density, etc. of the polygon. By establishing a mapping relationship between the skeleton feature parameters and the generation parameters, the matching polygon segmentation map is adaptively generated according to the skeleton features. The adjusted generation parameters can control the details and changes of the polygon segmentation map according to the local features of the skeleton. Based on the adaptive polygon segmentation rules, a porous filling unit matching the skeleton structure is constructed. The porous filling unit is determined by the polygon segmentation map and has a density, size and shape distribution that is adapted to the skeleton structure. Through the adaptive polygon segmentation driven by the skeleton features, the geometric matching and fusion of the skeleton structure and the porous filling unit are realized.

[0055] Variable density parameters, variable size parameters and variable shape parameters are introduced to control the density distribution, size change and shape change of the porous filling unit respectively. The variable density parameter achieves a gradient change in density by adjusting the porosity and material distribution of the porous filling unit. The variable size parameter achieves a gradual change in size by adjusting the scale and proportion of the porous filling unit. The variable shape parameter achieves the dynamic evolution of the shape by adjusting the shape and topological structure of the porous filling unit. A parametric mapping relationship between the variable density parameters, variable size parameters and variable shape parameters is established to obtain a multi-parameter model that integrates variable density, variable size and variable shape. Through parametric mapping, different parameter combinations are mapped to the density, size and shape of the corresponding porous filling unit. The multi-parameter model can flexibly control the performance and appearance of the porous filling unit through parameter adjustment to achieve structural diversity and optimization.

[0056] A multi-objective optimization model is established based on multiple predetermined optimization objectives. The optimization objectives may include mechanical properties, quality, manufacturing feasibility and other factors of the structure. By defining multiple optimization objective functions, the structural design is transformed into a multi-objective optimization problem. The sensitivity analysis technique is used to evaluate the influence of topological parameters and morphological parameters on the optimization objectives. By calculating the sensitivity of the parameters, the contribution and importance of different parameters to the optimization objectives are determined. According to the results of the sensitivity analysis, the key parameters with a greater impact on the optimization objectives are selected as the decision variables for optimization. A multi-objective genetic algorithm is used to encode and optimize the topological parameters and morphological parameters. The parameters are encoded as genotypes, and new parameter combinations are generated through the selection, crossover and mutation operations of the genetic algorithm. In the optimization search process, the topological parameters and morphological parameters are dynamically adjusted to explore the parameter space and find the optimal parameter combination. Through the iterative optimization of the multi-objective genetic algorithm, the optimal combination of topological parameters and morphological parameters that takes into account multiple optimization objectives is obtained.

[0057] According to the optimal combination of topological parameters and morphological parameters, the density, size and shape of the porous filling unit are updated. The optimal parameter combination is substituted into the multi-parameterized model to obtain the optimized porous filling unit. The updated porous filling unit has the optimal density distribution, size change and shape characteristics, which can meet the performance requirements and design constraints of the structure. The updated porous filling unit is integrated with the skeleton structure to generate an intermediate-scale structure. By embedding the porous filling unit into the skeleton structure, the seamless integration of the macroscopic skeleton and the microscopic porous structure is achieved. The intermediate-scale structure inherits the overall morphology and mechanical properties of the skeleton structure, and has the optimized density distribution and morphological characteristics of the porous filling unit, achieving the optimization of structural performance.

[0058] In this embodiment, by analyzing the local features of the skeleton and adaptively adjusting the generation parameters of the polygon segmentation map, the geometric precision matching of the porous filling unit and the skeleton structure is achieved, ensuring the seamless integration and effective fusion of the porous structure and the skeleton; variable density, variable size and variable shape parameters are introduced to flexibly adjust the density distribution, size and shape of the porous filling unit, and finely control the performance and appearance of the structure, thereby achieving structural optimization and diversity; by establishing a multi-objective optimization model, comprehensively considering factors such as the mechanical properties, quality and manufacturing feasibility of the structure, and using sensitivity analysis and multi-objective genetic algorithm for optimization. The optimization process accurately adjusts the topological parameters and morphological parameters based on multiple objectives to ensure the comprehensiveness and effectiveness of the optimization results; by fusing the optimized porous filling unit with the skeleton structure, the generated intermediate-scale structure not only inherits the overall morphology and mechanical properties of the skeleton, but also has optimized density distribution and morphological characteristics, thereby maximizing the structural performance and meeting the design requirements and performance standards.

[0059] S103. The intermediate-scale structure is embedded into the macroscopic lightweight structure through a multi-scale coupling method. Combined with cascade optimization, a multi-scale structure is generated after connection and transition. Based on the multi-scale structure, a homogenization method is used to calculate the equivalent material properties, evaluate the mechanical properties and thermal response characteristics, iteratively adjust the model parameters, and finally obtain a multi-scale lightweight result.

[0060] In this embodiment, the intermediate-scale structure is embedded in the macroscopic lightweight structure through a multi-scale coupling method and cascade optimization, generating a seamless multi-scale structure, ensuring the effective connection and transition of structures of different scales, and improving the comprehensive performance of the overall structure; the equivalent material properties of the multi-scale structure are calculated by a homogenization method, providing an accurate evaluation of the mechanical properties and thermal response characteristics of the structure; the mechanical properties and thermal response characteristics of the structure are optimized by iteratively adjusting the model parameters, and ultimately an efficient multi-scale lightweight result is obtained, thereby improving the performance and reliability of the structure in practical applications.

[0061] In an optional embodiment, based on the multi-scale structure, calculating the equivalent material properties using a homogenization method includes: Based on the multi-scale structure, selecting a periodic representative voxel and establishing a three-dimensional entity of the periodic representative voxel; Applying periodic boundary conditions and basic strain conditions to the three-dimensional entity, calculating the stress-strain response of the periodic representative volume element under each condition, and calculating each independent component of the equivalent elastic tensor through the stress-strain relationship according to the stress-strain response; Applying a uniaxial thermal load condition to the three-dimensional entity, calculating the temperature gradient and heat flux distribution of the periodic representative volume element, and calculating each component of the equivalent thermal conductivity tensor in combination with Fourier's heat conduction law; Assembling the calculated equivalent elastic tensor and the equivalent thermal conductivity tensor into an equivalent material property matrix of the multi-scale structure; Iterate different regions in the multi-scale structure, repeatedly assemble the equivalent material property matrix corresponding to each region, and calculate and obtain the equivalent material properties of each region.

[0062] The periodic boundary condition specifically refers to a boundary condition used to simulate a repetitive structure. Under the condition, the deformation and mechanical response of one face of the model are completely consistent with the adjacent faces. This ensures that the response of the model on the boundary is consistent with the actual situation of the periodic structure, so that infinite or periodically arranged structures can be effectively simulated in a finite model.

[0063] The basic strain condition specifically refers to the basic strain state applied to the periodic representative element, such as tension, compression or shear, which is used to test and calculate the stress response of the material under these strains. Through the condition, the elastic behavior of the material and the corresponding stress-strain relationship can be obtained.

[0064] The uniaxial thermal load condition specifically refers to a temperature gradient or heat flow applied to a periodic representative volume element, which has a single direction and magnitude. The condition is used to analyze the temperature response and heat conduction characteristics of a material under thermal stress in order to calculate the equivalent thermal conductivity.

[0065] Based on the multi-scale structure, a representative unit that can represent the periodic characteristics of the entire structure is selected, namely the periodic representative element. The periodic representative element usually selects the basic unit that appears repeatedly in the structure, which can reflect the geometric characteristics and material properties of the entire structure. According to the selected periodic representative element, a three-dimensional solid model is established. The three-dimensional solid model accurately describes the geometric shape, size and topological structure of the representative element, providing a basis for subsequent numerical analysis and calculation of equivalent material properties.

[0066] Apply periodic boundary conditions and basic strain conditions to the established three-dimensional entity. The periodic boundary conditions ensure that the representative element meets the periodic requirements during the deformation process, that is, the node displacements and forces on the relative boundary surfaces remain consistent. Basic strain conditions include uniaxial tension, shear, etc. By applying these conditions to the representative element, the mechanical behavior of the material under different deformation modes is simulated. Numerical methods, such as finite element analysis, are used to calculate the stress-strain response of the periodic representative element under various conditions. By solving the displacement field and stress field of the representative element, the stress-strain data under different conditions are obtained. According to the stress-strain response, the stress-strain relationship is used to calculate the independent components of the equivalent elastic tensor. The equivalent elastic tensor describes the elastic mechanical properties of the material. Through the linear elastic theory, the stress-strain data are converted into the component values ​​of the equivalent elastic tensor to obtain the equivalent elastic properties of the representative element.

[0067] Apply uniaxial thermal load conditions to three-dimensional entities to simulate the thermal conduction behavior of materials under temperature gradients. Establish a steady-state heat conduction problem by applying temperature boundary conditions on the boundary surfaces of representative volume elements. Use numerical methods to calculate the temperature gradient and heat flux distribution of periodic representative volume elements under thermal loads. By solving the temperature field and heat flow field of the representative volume element, the temperature and heat flow data at different positions are obtained. Combined with Fourier's law of heat conduction, calculate the components of the equivalent thermal conductivity tensor. Fourier's law of heat conduction describes the thermal conduction characteristics of materials and establishes a linear relationship between heat flux density and temperature gradient. According to the temperature gradient and heat flow data, the component values ​​of the equivalent thermal conductivity tensor are obtained by Fourier's law of heat conduction to characterize the equivalent thermal conduction properties of the representative volume element.

[0068] The calculated equivalent elastic tensor and equivalent thermal conductivity tensor are assembled into an equivalent material property matrix of the multi-scale structure. The equivalent material property matrix is ​​a matrix that comprehensively describes the mechanical and thermal properties of the material, and contains all independent components of the equivalent elastic tensor and equivalent thermal conductivity tensor. By assembling these components into the matrix according to certain arrangement rules, a complete equivalent material property matrix is ​​obtained. The equivalent material property matrix can comprehensively characterize the equivalent mechanical and thermal behaviors of multi-scale structures, providing convenience for subsequent structural analysis and optimization design.

[0069] For different regions in the multi-scale structure, the above steps are repeated to obtain the equivalent material property matrix corresponding to each region. Since multi-scale structures are usually inhomogeneous and anisotropic, the material properties of different regions may be different. By selecting representative units for each region, establishing a three-dimensional solid model, applying periodic boundary conditions and load conditions, and calculating equivalent material properties, the equivalent material property matrix of the region is obtained. Iterate through all regions in the multi-scale structure, repeat the process, and finally obtain the equivalent material property distribution of the entire structure. Regionalized equivalent material properties can more accurately describe the local mechanical and thermal properties of multi-scale structures, and provide regionalized material parameters for performance evaluation and optimal design of structures.

[0070] In this embodiment, by applying periodic boundary conditions, basic strain conditions and uniaxial thermal load conditions, the stress-strain response and thermal conduction characteristics of the periodic representative volume element can be accurately calculated, and the calculation results are used to derive the equivalent elastic tensor and the equivalent thermal conductivity tensor, thereby obtaining the macroscopic mechanical and thermal properties of the material; by assembling the calculated equivalent elastic tensor and the equivalent thermal conductivity tensor into an equivalent material property matrix, the mechanical and thermal properties of the multi-scale structure at the macroscopic scale can be accurately characterized, and the microscopic and macroscopic properties of the structure can be comprehensively considered to provide a more accurate description of the material properties; by iterative analysis and calculation of different regions in the multi-scale structure, the equivalent material properties of each region can be obtained, so that different regions of the structure can be optimized according to their specific performance requirements, thereby achieving performance improvement of the overall structure and optimization of design goals.

[0071] Figure 2 Schematic diagram of the structure of a 3D model multi-scale lightweight system based on topology optimization according to an embodiment of the present invention. Figure 2 As shown, the system comprises: The first unit is used to obtain the target 3D model to be lightweight, mesh the target 3D model, and generate a finite element model; based on the structural characteristics and load conditions of the target 3D model, combined with the SIMP interpolation model, introduce a non-uniform material property mapping function, establish a multi-scale topology optimization model, adjust the density distribution through a density filtering function, and combine the minimum size constraint and grayscale gradient projection processing to obtain a macro lightweight structure; The second unit is used to obtain the skeleton structure based on the macro lightweight structure through a skeleton extraction algorithm, and to construct a porous filling unit matching the skeleton structure based on an adaptive polygon segmentation rule and in combination with local feature information in the skeleton structure. Based on the porous filling unit, a multi-parameter model of variable density, variable size and variable shape is integrated to establish a parameterized representation method of three variables of density, size and shape. Through a multi-objective genetic algorithm combined with sensitivity analysis technology, topological parameters and morphological parameters are collaboratively optimized and adjusted to obtain an intermediate scale structure. The third unit is used to embed the intermediate-scale structure into the macro lightweight structure through a multi-scale coupling method, combine cascade optimization, and generate a multi-scale structure after connection and transition. Based on the multi-scale structure, the homogenization method is used to calculate the equivalent material properties, evaluate the mechanical properties and thermal response characteristics, iteratively adjust the model parameters, and finally obtain a multi-scale lightweight result.

[0072] According to a third aspect of the embodiments of the present invention, An electronic device is provided, comprising: processor; a memory for storing processor-executable instructions; The processor is configured to call the instructions stored in the memory to execute the aforementioned method.

[0073] A fourth aspect of the embodiments of the present invention is: A computer-readable storage medium is provided, on which computer program instructions are stored. When the computer program instructions are executed by a processor, the aforementioned method is implemented.

[0074] The present invention may be a method, an apparatus, a system and / or a computer program product. The computer program product may include a computer-readable storage medium carrying computer-readable program instructions for executing various aspects of the present invention.

[0075] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A multi-scale lightweight method for 3D models based on topology optimization, characterized in that: include: Obtaining a target 3D model to be lightweight, meshing the target 3D model, and generating a finite element model; Based on the structural characteristics and load conditions of the target 3D model, combined with the SIMP interpolation model, a non-uniform material property mapping function is introduced to establish a multi-scale topology optimization model, and the density distribution is adjusted by the density filtering function. Combined with the minimum size constraint and grayscale gradient projection processing, a macro lightweight structure is obtained; Based on the macro lightweight structure, a skeleton structure is obtained through a skeleton extraction algorithm, and based on an adaptive polygon segmentation rule and combined with local feature information in the skeleton structure, a porous filling unit matching the skeleton structure is constructed, and based on the porous filling unit, a multi-parameter model of variable density, variable size and variable shape is integrated to establish a parameterized representation method of three variables of density, size and shape, and a multi-objective genetic algorithm is used in combination with a sensitivity analysis technique to collaboratively optimize and adjust topological parameters and morphological parameters to obtain an intermediate scale structure; Through the multi-scale coupling method, the intermediate-scale structure is embedded in the macro-lightweight structure. Combined with cascade optimization, a multi-scale structure is generated after connection and transition. Based on the multi-scale structure, the homogenization method is used to calculate the equivalent material properties, evaluate the mechanical properties and thermal response characteristics, and iteratively adjust the model parameters to finally obtain a multi-scale lightweight result.

2. The method according to claim 1, characterized in that The target 3D model to be lightweight is obtained, and the target 3D model is meshed to generate a finite element model; based on the structural characteristics and load conditions of the target 3D model, combined with the SIMP interpolation model, a non-uniform material property mapping function is introduced to establish a multi-scale topology optimization model, and the density distribution is adjusted by the density filtering function. Combined with the minimum size constraint and grayscale gradient projection processing, a macro lightweight structure is obtained, including: Obtaining a target 3D model to be lightweight, meshing the target 3D model, generating a finite element model, and calculating and obtaining the stress-strain response of the finite element model under various working conditions through finite element static analysis based on the finite element model; Based on the structural characteristics and load conditions of the target 3D model, a relative density design variable is defined, a nonlinear mapping relationship between material properties and the relative density design variable is established through a SIMP interpolation model, and an exponential non-uniform material property mapping function is used to establish a nonlinear association between material properties of a microscopic filling area and macroscopic relative density; Based on the stress-strain response, taking the minimum structural flexibility as the optimization goal and the volume fraction as the constraint condition, a mathematical model is determined, the SIMP interpolation model and the exponential non-uniform material property mapping function are substituted into the mathematical model to optimize the mathematical model, and a multi-scale topology optimization model is established; The multi-scale topology optimization model is solved by a pre-constructed moving progressive optimization algorithm, and the optimal density distribution is obtained by iteratively updating the relative density design variables; A Helmholtz partial differential equation type density filter function is used to perform local averaging processing on the optimal density distribution to obtain a smooth density field; Performing mathematical morphological filtering on the smooth density field, combining density gradient control, performing minimum size constraint on the smooth density field, and obtaining a minimum size constrained density field; Based on the regularized Gaussian function, the lowest size constraint density field is subjected to grayscale gradient projection processing to obtain a macroscopic lightweight structure.

3. The method according to claim 1, characterized in that Based on the stress-strain response, with the minimum structural flexibility as the optimization goal and the volume fraction as the constraint condition, the mathematical model is determined to include: The objective function formula is as follows: ； in, C represents the structural flexibility, u T represents the transpose of the strain displacement vector, i represents the element index of the finite element model, and B i T represents the transpose of the stress-strain matrix of the ith element, E min represents the minimum elastic modulus, E 0 represents the elastic modulus of the perfect material, k represents the parameter of the exponential function, ρ i Indicates i The relative density of the unit, B i represents the stress-strain matrix of the ith element, V i Indicates i The volume of a unit, u represents the strain displacement vector.

4. The method according to claim 1, characterized in that Based on the macro lightweight structure, the skeleton structure is obtained by using a skeleton extraction algorithm, including: Based on the size and complexity of each part in the macro lightweight structure, the voxelization resolution is adaptively determined according to a preset resolution range to generate an adaptive voxel model; By using a distance transformation algorithm, the shortest geodesic distance from each voxel in the adaptive voxel model to the structure boundary is calculated to generate a geodesic distance field; Perform multi-scale smoothing on the geodesic distance field based on a Gaussian kernel function to obtain distance field representations at different scales, extract local maximum points of the distance field representation at each scale, and determine candidate skeleton points; Based on the local features of the candidate skeleton points, a skeleton point screening threshold is adaptively determined to obtain a screened skeleton point set, based on the centrality and connectivity information of each skeleton point in the skeleton point set, the contribution of the skeleton point to the skeleton as a whole is calculated, and according to a preset skeleton point elimination threshold, skeleton points are pruned to obtain a skeleton point pruned result set; Based on a preset local neighborhood search strategy, the local neighborhood range of each skeleton point in the skeleton point pruning result set is adaptively determined, a minimum spanning tree is constructed within the local neighborhood range to obtain a local connected skeleton structure, and combined with global connectivity optimization, the local connected skeleton structure is spliced ​​into a complete skeleton structure.

5. The method according to claim 4, characterized in that Calculating the shortest geodesic distance from each voxel in the adaptive voxel model to the structure boundary by a distance transformation algorithm, and generating a geodesic distance field comprises: Each voxel in the adaptive voxel model corresponds to a node, and the adaptive voxel model is represented as a three-dimensional voxel grid; Initializing the geodesic distance value from the boundary node of the three-dimensional voxel grid to the structure boundary based on a preset fast marching algorithm, and adding the boundary node to the active node list; Selecting a node with the smallest geodesic distance value from the active node list as the current extended node, obtaining an adjacent node corresponding to the current extended node, measuring the node distance between the current extended node and the corresponding adjacent node, updating the geodesic distance value of the adjacent node to the sum of the geodesic distance value of the current extended node and the node distance, removing the current extended node from the active node list, and adding the adjacent node to the active node list if the updated geodesic distance value of the adjacent node is less than the geodesic distance value before the update; traversing the active node list and updating the geodesic distance value until the active node list is empty; The geodesic distance values ​​of all nodes in the three-dimensional voxel grid are normalized to obtain the geodesic distance field.

6. The method according to claim 1, characterized in that Based on the adaptive polygon segmentation rule, combined with the local feature information in the skeleton structure, a porous filling unit matching the skeleton structure is constructed. Based on the porous filling unit, a multi-parameter model of variable density, variable size and variable shape is integrated to establish a parameterized representation method of three variables of density, size and shape. Through a multi-objective genetic algorithm, combined with sensitivity analysis technology, the topological parameters and morphological parameters are collaboratively optimized and adjusted to obtain an intermediate scale structure including: Based on the local feature information of the skeleton structure, skeleton feature parameters are obtained, and according to the skeleton feature parameters, generation parameters of the polygon segmentation map are adaptively adjusted to obtain adaptive polygon segmentation rules; based on the adaptive polygon segmentation rules, a porous filling unit matching the skeleton structure is constructed; Introducing variable density parameters, variable size parameters and variable shape parameters to respectively control the density distribution, size change and shape change of the porous filling unit, establishing a parametric mapping relationship between the variable density parameters, variable size parameters and variable shape parameters, and obtaining a multi-parameter model integrating variable density, variable size and variable shape; Based on multiple predetermined optimization objectives, a multi-objective optimization model is established, and the sensitivity analysis technology is used to determine the influence of topological parameters and morphological parameters on the multiple optimization objectives. Through a multi-objective genetic algorithm, the topological parameters and morphological parameters are encoded and optimized, and the topological parameters and morphological parameters are dynamically adjusted to generate the optimal combination of the topological parameters and morphological parameters. According to the optimal combination of topological parameters and morphological parameters, the density, size and shape of the porous filling unit are updated, and the updated porous filling unit is fused with the skeleton structure to generate an intermediate scale structure.

7. The method according to claim 1, characterized in that Based on the multi-scale structure, the equivalent material properties calculated using the homogenization method include: Based on the multi-scale structure, selecting a periodic representative voxel and establishing a three-dimensional entity of the periodic representative voxel; Applying periodic boundary conditions and basic strain conditions to the three-dimensional entity, calculating the stress-strain response of the periodic representative volume element under each condition, and calculating each independent component of the equivalent elastic tensor through the stress-strain relationship according to the stress-strain response; Applying a uniaxial thermal load condition to the three-dimensional entity, calculating the temperature gradient and heat flux distribution of the periodic representative volume element, and calculating each component of the equivalent thermal conductivity tensor in combination with Fourier's heat conduction law; Assembling the calculated equivalent elastic tensor and the equivalent thermal conductivity tensor into an equivalent material property matrix of the multi-scale structure; Iterate different regions in the multi-scale structure, repeatedly assemble the equivalent material property matrix corresponding to each region, and calculate and obtain the equivalent material properties of each region.

8. A 3D model multi-scale lightweight system based on topology optimization, used to implement the method described in any one of claims 1 to 7, characterized in that: include: The first unit is used to obtain the target 3D model to be lightweight, mesh the target 3D model, and generate a finite element model; based on the structural characteristics and load conditions of the target 3D model, combined with the SIMP interpolation model, introduce a non-uniform material property mapping function, establish a multi-scale topology optimization model, adjust the density distribution through a density filtering function, and combine the minimum size constraint and grayscale gradient projection processing to obtain a macro lightweight structure; The second unit is used to obtain the skeleton structure based on the macro lightweight structure through a skeleton extraction algorithm, and to construct a porous filling unit matching the skeleton structure based on an adaptive polygon segmentation rule and in combination with local feature information in the skeleton structure. Based on the porous filling unit, a multi-parameter model of variable density, variable size and variable shape is integrated to establish a parameterized representation method of three variables of density, size and shape. Through a multi-objective genetic algorithm combined with sensitivity analysis technology, topological parameters and morphological parameters are collaboratively optimized and adjusted to obtain an intermediate scale structure. The third unit is used to embed the intermediate-scale structure into the macro lightweight structure through a multi-scale coupling method, combine cascade optimization, and generate a multi-scale structure after connection and transition. Based on the multi-scale structure, the homogenization method is used to calculate the equivalent material properties, evaluate the mechanical properties and thermal response characteristics, iteratively adjust the model parameters, and finally obtain a multi-scale lightweight result.

9. An electronic device, characterized in that: include: processor; a memory for storing processor-executable instructions; The processor is configured to call the instructions stored in the memory to execute the method described in any one of claims 1 to 7.

10. A computer-readable storage medium having computer program instructions stored thereon, characterized in that: When the computer program instructions are executed by a processor, the method according to any one of claims 1 to 7 is implemented.

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