Complex design domain multi-scale isogeometric topology optimization method, device, equipment and medium

Abstract

The invention provides a complex design domain multi-scale isogeometric topology optimization method, a complex design domain multi-scale isogeometric topology optimization device, complex design domain multi-scale isogeometric topology optimization equipment and a medium, and relates to the technical field of isogeometric topology optimization. Constructing a material interpolation model based on a microstructure equivalent elastic tensor obtained according to the microstructure density and a preset equivalent elastic tensor prediction model, constructing a preset isogeometric topology optimization model, and updating design variables based on the macroscopic sensitivity and the microscopic sensitivity obtained through calculation; the method comprises the following steps: obtaining a target macroscopic design variable and a target microscopic design variable, respectively generating a target macrostructure and a target microstructure, carrying out smoothing processing on a rough optimization multi-scale structure formed by filling the target microstructure into the target macrostructure, and obtaining a target complex design domain multi-scale structure model; and the bottleneck that the complex multi-scale model is difficult to optimize by the existing isogeometric concurrent topological optimization is broken through.

Description

Technical Field

[0001] The present application relates to the technical field of isogeometric topology optimization, and in particular to a method, device, equipment and medium for multi-scale isogeometric topology optimization in a complex design domain. Background Art

[0002] Multiscale structures have excellent physical properties, such as light weight and high stiffness, high ionic conductivity, heat dissipation and thermal insulation, which makes them applicable to various complex engineering projects such as machinery, aerospace, optoelectronics and biomedicine. Multiscale concurrent topology optimization can design multiscale structures with better mechanical properties. As a research hotspot in the field of structural optimization, topology optimization is a numerical iterative process that follows specified objective functions and constraints in a predefined design domain to find the optimal material distribution. It has the advantages of more significant material savings and improved structural performance.

[0003] In recent years, many scholars have studied the concurrent topology optimization of multi-scale structures. The dual-scale concurrent optimization problem can be divided into two, which are associated with macro and micro design variables respectively. When the micro design variables are fixed, the sensitivity of the macro design variables is obtained, and the macro design variables are updated accordingly. In the same optimization step, the micro optimization problem is also solved in the same way, so that the design variables of both scales are updated. However, the existing traditional concurrent topology optimization methods based on the finite element method (FEM) and the like are difficult to ensure the smoothness of the discrete model on the surface boundary. The isogeometric analysis (IGA) method with non-uniform rational B-splines as the basis function is combined with topology optimization, namely the so-called isogeometric topology optimization. Although isogeometric topology optimization has been applied in many fields such as solid, fluid, electromagnetic, and thermal since it was proposed, it is still mostly theoretical research on multi-scale structures in regular design domains, and lacks multi-scale structure optimization in complex design domains for practical engineering.

[0004] Therefore, in order to solve the optimization design problem of complex multi-scale structures, a multi-scale isogeometric topology optimization method for complex design domain is needed. Summary of the invention

[0005] The purpose of this application is to provide a method, system, device and medium for multi-scale isogeometric topology optimization of a complex design domain in order to solve the problem that existing concurrent isogeometric topology optimization methods are difficult to design multi-scale models of complex design domains.

[0006] In a first aspect, the present application provides a method for multi-scale isogeometric topology optimization of a complex design domain, comprising: constructing a macro-structure design domain and a micro-structure design domain of a multi-scale structure of a complex design domain to be optimized based on optimization design parameter information of the multi-scale structure of the complex design domain to be optimized;

[0007] Obtaining a microstructure equivalent elastic tensor according to the microstructure density corresponding to the multi-scale structure of the complex design domain to be optimized and a preset equivalent elastic tensor prediction model;

[0008] Based on the microstructure equivalent elastic tensor, a material interpolation model is constructed; the material interpolation model includes a macro material interpolation sub-model and a micro material interpolation sub-model;

[0009] Based on the macro-design variables corresponding to the macro-structure design domain, the micro-design variables corresponding to the micro-structure design domain, the micro-structure equivalent elastic tensor and the material interpolation model, taking the minimum force compliance as the optimization goal and the volume fraction of the material as the constraint, a preset isogeometric topology optimization model of the multi-scale structure of the complex design domain to be optimized is constructed;

[0010] Calculating the macro sensitivity and micro sensitivity of the preset isogeometric topology optimization model, and updating the macro design variables and micro design variables of the preset isogeometric topology optimization model by using an optimization criterion method based on the macro sensitivity and micro sensitivity until a preset convergence condition is met, thereby obtaining target macro design variables and target micro design variables;

[0011] Based on the target macro-design variables and the target micro-design variables, a target macro-structure and a target micro-structure are generated respectively, the target micro-structure is filled into the target macro-structure to form a rough optimized multi-scale structure, and the rough optimized multi-scale structure is smoothed using an isosurface extraction method to obtain a target complex design domain multi-scale structure model.

[0012] According to the technical solution provided by the present application, the optimization design parameter information of the complex design domain multi-scale structure to be optimized is used to construct the macro-structure design domain and the micro-structure design domain of the complex design domain multi-scale structure to be optimized, including:

[0013] Obtaining optimization design parameter information of the multi-scale structure of the complex design domain to be optimized;

[0014] Based on the optimization design parameter information, the multi-scale structure of the complex design domain to be optimized is NURBS meshed to generate the macro-structure design domain;

[0015] Based on the optimization design parameter information, an initial microstructure is constructed and discretized into a NURBS grid to generate the microstructure design domain.

[0016] According to the technical solution provided by this application, the method also includes:

[0017] Collecting microstructure densities of a plurality of sample geometric structures and calculating microstructure equivalent elastic tensors of each of the sample geometric structures using an energy homogenization algorithm;

[0018] The microstructure density of the sample geometric structure is used as the model input, and the microstructure equivalent elastic tensor of the sample geometric structure is used as the model output, and a fully connected neural network model is trained to obtain the preset equivalent elastic tensor prediction model.

[0019] According to the technical solution provided by the present application, the material interpolation model is constructed based on the microstructure equivalent elastic tensor, including:

[0020] According to the formula:

[0021]

[0022] Construct the material interpolation model; wherein, E M is the macrostructure elastic tensor, is the macroscopic isogeometric unit density, E hom is the microstructure equivalent elastic tensor, E m is the microstructure elastic tensor, is the density of microscopic isogeometric units, E0 is the constitutive elastic tensor of the material, Δ is a constant, and p is the penalty parameter.

[0023] According to the technical solution provided by the present application, based on the macro-design variables corresponding to the macro-structure design domain, the micro-design variables corresponding to the micro-structure design domain, the micro-structure equivalent elastic tensor and the material interpolation model, the minimum force compliance is taken as the optimization goal, and the volume fraction of the material is taken as the constraint to construct a preset isogeometric topology optimization model of the multi-scale structure of the complex design domain to be optimized, including:

[0024] According to the formula:

[0025]

[0026] Construct a preset isogeometric topology optimization model of the multi-scale structure of the complex design domain to be optimized; wherein, ρ M is the macro design variable, i.e., the density of macro structural control points; N is the number of isogeometric units included in the macro structural design domain; ρ m is the micro-design variable, i.e., the density of micro-structure control points; n is the number of iso-geometric units included in the micro-structure design domain; C(ρ M ,ρ m ) is the target value of the multi-scale structure in the complex design domain to be optimized, i.e., force compliance; C Mech (ρ M ,ρ m ) is the mechanical flexibility; K(ρ M,ρ m ) is the stiffness matrix and thermal conductivity matrix of the global performance design domain, including the stiffness matrix and thermal conductivity matrix of the macrostructure design domain and the stiffness matrix and thermal conductivity matrix of the microstructure design domain; U M is the force load at the macrostructure control point, F is the displacement at the macrostructure control point, B M is the macrostructure strain displacement matrix, E M is the macrostructure elastic tensor, Ω M is the macrostructure design domain, Ω m is the microstructure design domain, V M is the specified structural volume of the macroscopic design variable, i.e., the maximum volume fraction of the macroscopic structure; V m is the prescribed structural volume of the micro-design variable, i.e., the maximum volume fraction of the microstructure; is the minimum value of the macro design variable, is the minimum value of the micro-design variable.

[0027] According to the technical solution provided by the present application, the calculation of the macroscopic sensitivity and microscopic sensitivity of the preset isogeometric topology optimization model includes:

[0028] According to the formula:

[0029]

[0030] Calculate the macroscopic sensitivity and microscopic sensitivity of the preset isogeometric topology optimization model, where C Mech (ρ M ,ρ m ) is the mechanical flexibility, ρ M is the macro design variable, i.e., the density of macro structure control points; S M is the macro design variable ρ M The set of cells affected by the corresponding control point, For S M The cell density of the i-th cell in , U M is the macrostructure control point force load, B M is the macrostructure strain displacement matrix, E hom is the microstructure equivalent elastic tensor; ρ m is the micro-design variable, i.e., the density of micro-structure control points; Δ is a constant, and p is the penalty parameter.

[0031] According to the technical solution provided by the present application, the macro design variables and micro design variables of the preset equal geometry topology optimization model are updated by using the optimization criterion method based on the macro sensitivity and micro sensitivity, including:

[0032] According to the formula:

[0033]

[0034] The macroscopic design variables and microscopic design variables of the preset geometric topology optimization model are updated; wherein, ρ M is the macro design variable, i.e., the density of macro structure control points; k is the current iteration number, is the macro design variable at the k+1th iteration, is the macro design variable at the kth iteration, is the update factor of the macro design variables at the kth iteration; ρ m is the micro-design variable, i.e., the density of micro-structure control points; is the micro-design variable at the k+1th iteration, is the micro-design variable at the kth iteration, is the update factor of the micro-design variables at the kth iteration, μ is a constant, is the Lagrange multiplier of the macro design variable, V M is the prescribed structural volume of the macroscopic design variable, i.e., the maximum volume fraction of the macroscopic structure; is the Lagrange multiplier of the microscopic design variable, V m is the prescribed structural volume of the micro-design variable, i.e., the maximum volume fraction of the microstructure.

[0035] In a second aspect, the present application provides a multi-scale isogeometric topology optimization device for a complex design domain, comprising:

[0036] The first construction module is used to construct a macro-structure design domain and a micro-structure design domain of the multi-scale structure of the complex design domain to be optimized based on the optimization design parameter information of the multi-scale structure of the complex design domain to be optimized;

[0037] A first acquisition module is used to acquire a microstructure equivalent elastic tensor according to the microstructure density corresponding to the multi-scale structure of the complex design domain to be optimized and a preset equivalent elastic tensor prediction model;

[0038] A second construction module is used to construct a material interpolation model based on the microstructure equivalent elastic tensor; the material interpolation model includes a macro material interpolation sub-model and a micro material interpolation sub-model;

[0039] A third construction module is used to construct a preset isogeometric topology optimization model of the multi-scale structure of the complex design domain to be optimized based on the macro-design variables corresponding to the macro-structure design domain, the micro-design variables corresponding to the micro-structure design domain, the micro-structure equivalent elastic tensor and the material interpolation model, with minimum force compliance as the optimization goal and the volume fraction of the material as the constraint;

[0040] A calculation update module, used for calculating the macro sensitivity and micro sensitivity of the preset isogeometric topology optimization model, and updating the macro design variables and micro design variables of the preset isogeometric topology optimization model by using an optimization criterion method based on the macro sensitivity and micro sensitivity until a preset convergence condition is met, thereby obtaining target macro design variables and target micro design variables;

[0041] The second acquisition module is used to generate a target macrostructure and a target microstructure based on the target macro-design variables and the target micro-design variables, respectively, fill the target microstructure into the target macrostructure to form a rough optimized multi-scale structure, and use the isosurface extraction method to smooth the rough optimized multi-size structure to obtain a target complex design domain multi-scale structure model.

[0042] In a third aspect, the present application provides an electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the method described above when executing the computer program.

[0043] In a fourth aspect, the present application provides a computer-readable storage medium having a computer program stored thereon, and the computer program implements the method described above when executed by a processor.

[0044] Compared with the prior art, the beneficial effects of the present application are as follows: the method, device, equipment and medium for multi-scale equigeometric topology optimization of a complex design domain provided by the present application construct a macro-structure design domain and a micro-structure design domain of a multi-scale structure of a complex design domain to be optimized based on the optimization design parameter information of the multi-scale structure of the complex design domain to be optimized, and construct a material interpolation model based on the micro-structure density corresponding to the multi-scale structure of the complex design domain to be optimized and the micro-structure equivalent elastic tensor obtained by the preset equivalent elastic tensor prediction model, and then construct a preset equigeometric topology optimization model based on the macro-design variables and the micro-design variables and the micro-structure equivalent elastic tensor, with the minimum force flexibility as the optimization goal and the volume fraction of the material as the constraint, and update the macro-design variables and the micro-design variables based on the calculated macro-sensitivity and micro-sensitivity using the optimization criterion method until the preset convergence conditions are met, and obtain the target macro-design variables and the target micro-design variables, generate the target macro-structure and the target micro-structure respectively, and smooth the rough optimized multi-scale structure formed by filling the target micro-structure into the target macro-structure to obtain the target complex design domain multi-scale structure model. Based on the gridded complex CAD surface model and the regular initial microstructure, a complex design domain multi-scale model for isogeometric concurrent topology optimization is constructed, breaking through the bottleneck that the existing isogeometric concurrent topology optimization is difficult to optimize complex multi-scale models; a fully connected neural network model is used to instantly predict the equivalent elastic tensor of the microstructure, avoiding the defect of excessive calculation of the equivalent elastic tensor of the microstructure by the traditional homogenization method, and reducing the time cost; by filling the microstructure into the macrostructure design domain and smoothing it using the isosurface extraction technology, a multi-scale structure model of the target complex design domain is obtained, which lays the foundation for subsequent additive manufacturing and is more conducive to engineering applications.

[0045] It should be understood that the description of technical features, technical solutions, beneficial effects or similar language in this application does not imply that all features and advantages can be realized in any single embodiment. On the contrary, it is understood that the description of features or beneficial effects means that specific technical features, technical solutions or beneficial effects are included in at least one embodiment. Therefore, the description of technical features, technical solutions or beneficial effects in this specification does not necessarily refer to the same embodiment. Furthermore, the technical features, technical solutions and beneficial effects described in the present embodiment can also be combined in any appropriate manner. Those skilled in the art will understand that the embodiment can be realized without one or more specific technical features, technical solutions or beneficial effects of a specific embodiment. In other embodiments, additional technical features and beneficial effects can also be identified in a specific embodiment that does not embody all embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] In order to more clearly illustrate the technical solution in this embodiment, the drawings required for use in the description of the embodiment will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0047] Figure 1 A flowchart of a multi-scale isogeometric topology optimization method for a complex design domain provided in an embodiment of the present application;

[0048] Figure 2 A schematic diagram of a multi-scale structure of an initialized complex design domain provided in an embodiment of the present application;

[0049] Figure 3 A schematic diagram of deep learning of microstructure equivalent elastic tensor of periodic microstructure in the macrostructure design domain provided in the embodiment of the present application;

[0050] Figure 4 A schematic diagram of three linearly independent unit test strain fields when the sample geometry provided in the embodiment of the present application is a 2D structure;

[0051] Figure 5 A schematic diagram of a material interpolation model for building blocks provided in an embodiment of the present application;

[0052] Figure 6 A schematic diagram of multi-scale structural optimization of a complex design domain to be optimized provided in an embodiment of the present application;

[0053] Figure 7 A schematic diagram of a complex design domain multi-scale isogeometric topology optimization device provided in an embodiment of the present application;

[0054] Figure 8 A schematic diagram of a computer system of an electronic device provided in an embodiment of the present application. DETAILED DESCRIPTION

[0055] In order to enable those skilled in the art to better understand the technical solution of the present application, the technical solution in the embodiments of the present application will be clearly and completely described below in conjunction with the accompanying drawings. The description in this section is only exemplary and explanatory and should not have any limiting effect on the protection scope of the present application. Specifically, the described embodiments are only embodiments of a part of the present application, not all embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in the field without making creative work should fall within the scope of protection of the present application.

[0056] It should be noted that similar reference numerals and letters represent similar items in the following figures, so once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions, for example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

[0057] In order to make the technical solution of the present application clearer and easier to understand, the geometric topology optimization method of complex design domain multi-scale provided in the embodiment of the present application is introduced below.

[0058] like Figure 1 As shown, the figure is a flow chart of a complex design domain multi-scale isogeometric topology optimization method provided in this embodiment, and the method includes the following steps:

[0059] S101. constructing a macrostructure design domain and a microstructure design domain of the multi-scale structure of the complex design domain to be optimized based on the optimization design parameter information of the multi-scale structure of the complex design domain to be optimized;

[0060] Specifically, the complex design domain multi-scale structure to be optimized is initialized, the optimization design parameter information of the complex design domain multi-scale structure to be optimized is obtained, and then based on the optimization design parameter information, the complex design domain multi-scale structure to be optimized is NURBS meshed to generate the macro-structure design domain, and based on the optimization design parameter information, the initial microstructure is constructed and discretized into NURBS meshes to generate the micro-structure design domain. Among them, the optimization design parameter information includes the CAD model file of the complex design domain multi-scale structure, the grid size and number, and the gridding direction, and of course, other parameter information can also be included, which can be set and adjusted according to the actual situation, and is not specifically limited here.

[0061] S102, obtaining a microstructure equivalent elastic tensor according to the microstructure density corresponding to the multi-scale structure of the complex design domain to be optimized and a preset equivalent elastic tensor prediction model;

[0062] Specifically, the microstructure density of multiple sample geometric structures and the microstructure equivalent elastic tensor of each sample geometric structure calculated by the energy homogenization algorithm are used as the input and output of the training model, and the fully connected neural network model is trained to obtain the preset equivalent elastic tensor prediction model, and then the microstructure density corresponding to the complex design domain multi-scale structure to be optimized is input into the preset equivalent elastic tensor prediction model to obtain the microstructure equivalent elastic tensor. The microstructure equivalent elastic tensor of the complex design domain multi-scale structure to be optimized is instantly predicted by the preset equivalent elastic tensor prediction model, which avoids the defect of excessive calculation of the equivalent elastic tensor of the fine grid microstructure solved by the traditional homogenization method, and effectively reduces the time cost.

[0063] S103, constructing a material interpolation model based on the microstructure equivalent elastic tensor; the material interpolation model includes a macro material interpolation sub-model and a micro material interpolation sub-model;

[0064] Specifically, based on the microstructure equivalent elastic tensor, a material interpolation scheme is defined according to the formula:

[0065]

[0066] Construct the macro material interpolation sub-model, where E M is the macrostructure elastic tensor, is the macroscopic isogeometric unit density, E hom is the microstructure equivalent elastic tensor, Δ is a constant, and p is a penalty parameter. According to the formula:

[0067]

[0068] Construct the microscopic material interpolation model; wherein, E m is the microstructure elastic tensor, is the density of microscopic isogeometric units, E0 is the constitutive elastic tensor of the material, Δ is a constant, and p is a penalty parameter. Based on the macroscopic material interpolation sub-model and the microscopic material interpolation sub-model, the material interpolation model is constructed.

[0069] S104, based on the macro-design variables corresponding to the macro-structure design domain, the micro-design variables corresponding to the micro-structure design domain, the micro-structure equivalent elastic tensor and the material interpolation model, taking the minimum force compliance as the optimization goal and the volume fraction of the material as the constraint, constructing a preset isogeometric topology optimization model of the multi-scale structure of the complex design domain to be optimized;

[0070] Specifically, according to the formula:

[0071]

[0072] Construct a preset isogeometric topology optimization model of the multi-scale structure of the complex design domain to be optimized; wherein, ρ M is the macro design variable, i.e., the density of macro structural control points; N is the number of isogeometric units included in the macro structural design domain; ρ m is the micro-design variable, i.e., the density of micro-structure control points; n is the number of iso-geometric units included in the micro-structure design domain; C(ρ M ,ρ m ) is the target value of the multi-scale structure in the complex design domain to be optimized, i.e., force compliance; C Mech (ρ M ,ρ m ) is the mechanical flexibility; K(ρ M ,ρ m ) is the stiffness matrix and thermal conductivity matrix of the global performance design domain, including the stiffness matrix and thermal conductivity matrix of the macrostructure design domain and the stiffness matrix and thermal conductivity matrix of the microstructure design domain; U M is the force load at the macrostructure control point, F is the displacement at the macrostructure control point, B M is the macrostructure strain displacement matrix, E M is the macrostructure elastic tensor, Ω M is the macrostructure design domain, Ω m is the microstructure design domain, V M is the specified structural volume of the macroscopic design variable, i.e., the maximum volume fraction of the macroscopic structure; V m is the prescribed structural volume of the micro-design variable, i.e., the maximum volume fraction of the microstructure; is the minimum value of the macro design variable, is the minimum value of the micro-design variable.

[0073] S105, calculating the macro sensitivity and micro sensitivity of the preset isogeometric topology optimization model, and updating the macro design variables and micro design variables of the preset isogeometric topology optimization model by using an optimization criterion method based on the macro sensitivity and micro sensitivity until a preset convergence condition is met, thereby obtaining target macro design variables and target micro design variables;

[0074] Specifically, according to the formula:

[0075]

[0076] Among them, C Mech (ρ M ,ρ m ) is the mechanical flexibility, ρ M is the macro design variable, i.e., the density of macro structure control points; S M is the macro design variable ρ M The set of cells affected by the corresponding control point, For S M The cell density of the i-th cell in , U M is the macrostructure control point force load, B M is the macrostructure strain displacement matrix, E hom is the microstructure equivalent elastic tensor; ρ m is the micro-design variable, i.e., the density of micro-structure control points; Δ is a constant, and p is a penalty parameter. Then, based on the macro-sensitivity and micro-sensitivity, the macro-design variables and micro-design variables of the preset equal geometric topology optimization model are updated by the optimization criterion method until the preset convergence conditions are met, and the target macro-design variables and target micro-design variables are obtained. Among them, the preset convergence condition package can be that the change in the macro-design variable (i.e., the density of macro-structure control points) and the micro-design variable (i.e., the relative density of micro-structure control points) is less than a preset threshold or the number of iterations reaches a preset number. For example, the preset threshold can be set to 0.002, and the preset number can be set to 100 times. The specific values ​​can be set and adjusted according to the actual situation, and are not specifically limited here.

[0077] S106. Based on the target macro-design variables and the target micro-design variables, a target macro-structure and a target micro-structure are generated respectively, the target micro-structure is filled into the target macro-structure to form a rough optimized multi-scale structure, and the rough optimized multi-scale structure is smoothed by using an isosurface extraction method to obtain a target complex design domain multi-scale structure model.

[0078] Specifically, according to the obtained target macro-design variables and target micro-design variables, a target macrostructure and a target microstructure are generated respectively, and the target microstructure is filled into the target macrostructure to form a rough optimized multi-scale structure. The rough optimized multi-size structure is smoothed using the isosurface extraction method to obtain a target complex design domain multi-scale structure model, and finally an STL format file is output, which lays the foundation for subsequent additive manufacturing and is more conducive to engineering applications.

[0079] On the basis of the above embodiment, further, the optimization design parameter information of the complex design domain multi-scale structure to be optimized is used to construct the macro-structure design domain and the micro-structure design domain of the complex design domain multi-scale structure to be optimized, including:

[0080] Obtaining optimization design parameter information of the multi-scale structure of the complex design domain to be optimized;

[0081] Based on the optimization design parameter information, the multi-scale structure of the complex design domain to be optimized is NURBS meshed to generate the macro-structure design domain;

[0082] Based on the optimization design parameter information, an initial microstructure is constructed and discretized into a NURBS grid to generate the microstructure design domain.

[0083] Specifically, the optimization design parameter information at least includes the CAD model file of the complex design domain multi-scale structure, the grid size and number, and the gridding direction; the CAD model file of the complex design domain multi-scale structure to be optimized is read, and the complex design domain multi-scale structure to be optimized is NURBS gridded on a macro scale according to the grid size and number and the gridding direction; the specific method is: using the function in the MATLAB toolbox Mesh voxelisation, reading the input optimization design parameter information, including the CAD model file, the grid size and number, and the gridding direction, and outputting the gridded data as a three-dimensional matrix, wherein 1 represents the solid area unit and 0 represents the blank area unit, and after visualizing the solid area unit, the initial structure diagram of the macro-structure design domain can be obtained. Figure 2 A schematic diagram of a multi-scale structure of a complex design domain for initialization provided in an embodiment of the present application is shown in FIG. Figure 2 As shown, for example, the complex design domain multi-scale structure to be optimized is a certain aircraft bearing bracket. After meshing, regular NURBS solid units with a given number of grids are generated, and the solid area units are visualized as a complex design domain model NURBS grid. The blank area is not shown in the diagram.

[0084] On the basis of the above embodiment, the method further includes:

[0085] Collecting microstructure densities of a plurality of sample geometric structures and calculating microstructure equivalent elastic tensors of each of the sample geometric structures using an energy homogenization algorithm;

[0086] The microstructure density of the sample geometric structure is used as the model input, and the microstructure equivalent elastic tensor of the sample geometric structure is used as the model output, and a fully connected neural network model is trained to obtain the preset equivalent elastic tensor prediction model.

[0087] Specifically, the energy homogenization algorithm is used to solve the microstructure equivalent elastic tensor of the sample geometry. Within the linear elastic range, the equivalent performance of the microstructure can be evaluated by the energy homogenization method. When the microstructure is periodically arranged in the macrostructure design domain, it can be regarded as a uniform material at the macro scale, and the corresponding equivalent elastic tensor can be obtained. Figure 3 The figure shows a schematic diagram of deep learning of the microstructure equivalent elastic tensor of the periodic microstructure in the macrostructure design domain provided by the embodiment of the present application. As shown in 3, the microstructure density of multiple sample geometric structures is collected, and according to the formula:

[0088]

[0089] The energy homogenization algorithm is used to calculate the microstructural equivalent elastic tensor of each sample geometry, where |Ω m | is the area or volume of the periodic unit, E ijpq is the locally varying elastic tensor, is the prescribed unit strain field, is the periodic characteristic strain, Ω m is the microstructure design domain. It should be noted that when the sample geometry is a 2D structure, |Ω m | is the area of ​​the periodic unit. When the sample geometry is a 3D structure, |Ω m | is the volume of the periodic unit; the local variation of the elastic tensor E ijpq In the solid area, the elastic matrix is ​​equal to the base material, and the blank area is approximated by the zero matrix. In energy homogenization, the unit test strain is directly applied to the boundary of the basic unit to produce a superimposed strain field. Right now If the microstructure under consideration is divided into n equal geometric units, the microstructure equivalent elastic tensor can be written as:

[0090]

[0091] in and For the corresponding The displacement of the unit control point, is the unit mutual energy, k e is the element stiffness matrix.

[0092] Then, the microstructure density of the sample geometric structure is used as the model input, and the microstructure equivalent elastic tensor of the sample geometric structure is used as the model output, and the fully connected neural network model is trained to obtain the preset equivalent elastic tensor prediction model, which can be used to replace the traditional energy homogenization method to instantly predict the microstructure equivalent elastic tensor of the multi-scale structure of the complex design domain to be optimized.

[0093] In addition, it should be noted that Figure 4 The schematic diagram of three linearly independent unit test strain fields when the sample geometry provided in the embodiment of the present application is a 2D structure is as follows: Figure 4 As shown, when the sample geometry is a 2D structure, there are three linearly independent unit test strain fields; and when the sample geometry is a 3D structure, there are six linearly independent unit test strain fields, corresponding to mn = 11, 22, 33, 12, 23, 13, respectively:

[0094] (0,1,0,0,0,0) T ,(0,0,1,0,0,0) T,(0,0,0,1,0,0) T ,(0,0,0,0,1,0) T , (0,0,0,0,0,1) T

[0095] On the basis of the above embodiment, further, constructing a material interpolation model based on the microstructure equivalent elastic tensor includes:

[0096] According to the formula:

[0097]

[0098] Construct the material interpolation model; wherein, E M is the macrostructure elastic tensor, is the macroscopic isogeometric unit density, E hom is the microstructure equivalent elastic tensor, E m is the microstructure elastic tensor, is the density of microscopic isogeometric units, E0 is the constitutive elastic tensor of the material, Δ is a constant, and p is the penalty parameter.

[0099] Specifically, Figure 5 A schematic diagram of a material interpolation model provided in an embodiment of the present application, such as Figure 5 As shown in FIG. 1 , material interpolation sub-models are established at the macroscopic and microscopic levels, namely, the macroscopic material interpolation sub-model and the microscopic material interpolation sub-model, to form the material interpolation model; it should be noted that Δ is a constant, and its value can be 1×10 -9 , which is used to avoid singularities in the stiffness matrix.

[0100] On the basis of the above embodiment, further, based on the macro-design variables corresponding to the macro-structure design domain, the micro-design variables corresponding to the micro-structure design domain, the micro-structure equivalent elastic tensor and the material interpolation model, the minimum force compliance is taken as the optimization goal, and the volume fraction of the material is taken as the constraint to construct a preset isogeometric topology optimization model of the multi-scale structure of the complex design domain to be optimized, including:

[0101] According to the formula:

[0102]

[0103] Construct a preset isogeometric topology optimization model of the multi-scale structure of the complex design domain to be optimized; wherein, ρ M is the macro design variable, i.e., the density of macro structural control points; N is the number of isogeometric units included in the macro structural design domain; ρ m is the micro-design variable, i.e., the density of micro-structure control points; n is the number of iso-geometric units included in the micro-structure design domain; C(ρM ,ρ m ) is the target value of the multi-scale structure in the complex design domain to be optimized, i.e., force compliance; C Mech (ρ M ,ρ m ) is the mechanical flexibility; K(ρ M ,ρ m ) is the stiffness matrix and thermal conductivity matrix of the global performance design domain, including the stiffness matrix and thermal conductivity matrix of the macrostructure design domain and the stiffness matrix and thermal conductivity matrix of the microstructure design domain; U M is the force load at the macrostructure control point, F is the displacement at the macrostructure control point, B M is the macrostructure strain displacement matrix, E M is the macrostructure elastic tensor, Ω M is the macrostructure design domain, Ω m is the microstructure design domain, V M is the specified structural volume of the macroscopic design variable, i.e., the maximum volume fraction of the macroscopic structure; V m is the prescribed structural volume of the micro-design variable, i.e., the maximum volume fraction of the microstructure; is the minimum value of the macro design variable, is the minimum value of the micro-design variable.

[0104] It should be noted that and are the minimum values ​​of the macro design variables and the micro design variables, respectively, which constrain the macro design variables and the micro design variables respectively to avoid numerical singularities in the optimization.

[0105] On the basis of the above embodiment, further, the calculating the macroscopic sensitivity and microscopic sensitivity of the preset isogeometric topology optimization model includes:

[0106] According to the formula:

[0107]

[0108] Among them, C Mech (ρ M ,ρ m ) is the mechanical flexibility, ρ M is the macro design variable, i.e., the density of macro structure control points; S M is the macro design variable ρ M The set of cells affected by the corresponding control point, For S M The cell density of the i-th cell in , U M is the macrostructure control point force load, B M is the macrostructure strain displacement matrix, Ehom is the microstructure equivalent elastic tensor; ρ m is the micro-design variable, i.e., the density of micro-structure control points; Δ is a constant, and p is the penalty parameter.

[0109] On the basis of the above embodiment, further, the updating of the macroscopic design variables and the microscopic design variables of the preset equal geometry topology optimization model by using the optimization criterion method based on the macroscopic sensitivity and the microscopic sensitivity includes:

[0110] According to the formula:

[0111]

[0112] The macroscopic design variables and microscopic design variables of the preset geometric topology optimization model are updated; wherein, ρ M is the macro design variable, i.e., the density of macro structure control points; k is the current iteration number, is the macro design variable at the k+1th iteration, is the macro design variable at the kth iteration, is the update factor of the macro design variables at the kth iteration; ρ m is the micro-design variable, i.e., the density of micro-structure control points; is the micro-design variable at the k+1th iteration, is the micro-design variable at the kth iteration, is the update factor of the micro-design variables at the kth iteration, μ is a constant, is the Lagrange multiplier of the macro design variable, V M is the prescribed structural volume of the macroscopic design variable, i.e., the maximum volume fraction of the macroscopic structure; is the Lagrange multiplier of the microscopic design variable, V m is the prescribed structural volume of the micro-design variable, i.e., the maximum volume fraction of the microstructure.

[0113] Specifically, Figure 6 The schematic diagram of multi-scale structure optimization of the complex design domain to be optimized provided in the embodiment of the present application is as follows: Figure 6 As shown in the figure, in the concurrent isogeometric topological design of the complex design domain multi-scale structure to be optimized, the optimization of macro and micro topologies is considered simultaneously, that is, the macro design variables and micro design variables are updated to obtain the final complex design domain multi-scale structure. It should be noted that μ is a constant and its value can be 1×10 -9 , the purpose is to avoid the denominator being 0; the Lagrange multiplier of the macro design variable and the Lagrange multipliers of the micro-design variables Both can be calculated by dichotomy; macro update factor and micro-update factor It contains both macro-design variables and micro-design variables, that is, it depends on the macro-design variables and micro-design variables

[0114] The complex design domain multi-scale equigeometric topology optimization method provided in the present application constructs a macrostructure design domain and a microstructure design domain of the complex design domain multi-scale structure to be optimized based on the optimization design parameter information of the complex design domain multi-scale structure to be optimized, and constructs a material interpolation model based on the microstructure density corresponding to the complex design domain multi-scale structure to be optimized and the microstructure equivalent elastic tensor obtained by the preset equivalent elastic tensor prediction model. Then, based on the macro-design variables and the micro-design variables and the microstructure equivalent elastic tensor, with the minimum force flexibility as the optimization goal and the volume fraction of the material as a constraint, a preset equigeometric topology optimization model is constructed, and based on the calculated macro-sensitivity and micro-sensitivity, the macro-design variables and the micro-design variables are updated by the optimization criterion method until the preset convergence conditions are met, and the target macro-design variables and the target micro-design variables are obtained, and the target macro-structure and the target micro-structure are generated respectively. The rough optimized multi-scale structure formed by filling the target micro-structure into the target macro-structure is smoothed to obtain the target complex design domain multi-scale structure model. Based on the gridded complex CAD surface model and the regular initial microstructure, a complex design domain multi-scale model for isogeometric concurrent topology optimization is constructed, breaking through the bottleneck that the existing isogeometric concurrent topology optimization is difficult to optimize complex multi-scale models; a fully connected neural network model is used to instantly predict the equivalent elastic tensor of the microstructure, avoiding the defect of excessive calculation of the equivalent elastic tensor of the microstructure by the traditional homogenization method, and reducing the time cost; by filling the microstructure into the macrostructure design domain and smoothing it using the isosurface extraction technology, a multi-scale structure model of the target complex design domain is obtained, which lays the foundation for subsequent additive manufacturing and is more conducive to engineering applications.

[0115] Combination of the above Figure 1-7 The complex design domain multi-scale and other geometric topology optimization method provided in the embodiment of the present application is introduced in detail. The complex design domain multi-scale and other geometric topology optimization device, electronic device and computer-readable storage medium provided in the embodiment of the present application will be introduced in conjunction with the accompanying drawings.

[0116] like Figure 7 As shown, the figure is a schematic diagram of a multi-scale isogeometric topology optimization device for a complex design domain provided by the present application, and the device includes:

[0117] The first construction module 201 is used to construct a macro-structure design domain and a micro-structure design domain of a complex design domain multi-scale structure to be optimized based on the optimization design parameter information of the complex design domain multi-scale structure to be optimized;

[0118] A first acquisition module 202 is used to acquire a microstructure equivalent elastic tensor according to the microstructure density corresponding to the multi-scale structure of the complex design domain to be optimized and a preset equivalent elastic tensor prediction model;

[0119] A second construction module 203 is used to construct a material interpolation model based on the microstructure equivalent elastic tensor; the material interpolation model includes a macro material interpolation sub-model and a micro material interpolation sub-model;

[0120] The third construction module 204 is used to construct a preset isogeometric topology optimization model of the multi-scale structure of the complex design domain to be optimized based on the macro-design variables corresponding to the macro-structure design domain, the micro-design variables corresponding to the micro-structure design domain, the micro-structure equivalent elastic tensor and the material interpolation model, with minimum force compliance as the optimization goal and the volume fraction of the material as the constraint;

[0121] A calculation and updating module 205 is used to calculate the macro sensitivity and micro sensitivity of the preset isogeometric topology optimization model, and update the macro design variables and micro design variables of the preset isogeometric topology optimization model using an optimization criterion method based on the macro sensitivity and micro sensitivity until a preset convergence condition is met, thereby obtaining target macro design variables and target micro design variables;

[0122] The second acquisition module 206 is used to generate a target macrostructure and a target microstructure based on the target macro-design variables and the target micro-design variables, respectively, fill the target microstructure into the target macrostructure to form a rough optimized multi-scale structure, and use an isosurface extraction method to smooth the rough optimized multi-scale structure to obtain a target complex design domain multi-scale structure model.

[0123] The complex design domain multi-scale isogeometric topology optimization device provided in the embodiment of the present application can correspond to executing the complex design domain multi-scale isogeometric topology optimization method described in the embodiment of the present application, and the above functions of each module of the device correspond to realizing Figure 1 For the sake of brevity, the corresponding process of the method shown will not be repeated here.

[0124] An embodiment of the present application also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the multi-scale geometric topology optimization method of the complex design domain as described in the above embodiment.

[0125] like Figure 8As shown, the computer system 300 of the electronic device includes a CPU 301, which can perform various appropriate actions and processes according to the program stored in the ROM 302 or the program loaded from the storage part 308 to the RAM 303. In the RAM 303, various programs and data required for system operation are also stored. The CPU 301, the ROM 302 and the RAM 303 are connected to each other through a bus 304. The I / O interface 305 is also connected to the bus 304. Among them, CPU 301 represents a central processing unit, ROM 302 represents a read-only memory, RAM 303 represents a random access memory, and I / O represents input / output.

[0126] The following components are connected to the I / O interface 305: an input section 306 including a keyboard, a mouse, etc.; an output section 307 including a cathode ray tube, a liquid crystal display, etc., and a speaker, etc.; a storage section 308 including a hard disk, etc.; and a communication section 309 including a network interface card such as a LAN card, a modem, etc. The communication section 309 performs communication processing via a network such as the Internet. A drive 310 is also connected to the I / O interface 305 as needed. A removable medium 311, such as a magnetic disk, an optical disk, a magneto-optical disk, a semiconductor memory, etc., is installed on the drive 310 as needed, so that a computer program read therefrom is installed into the storage section 308 as needed.

[0127] In particular, the process of the complex design domain multi-scale isogeometric topology optimization method described in the above embodiment can be implemented as a computer software program. For example, an embodiment of the present application includes a computer program product, which includes a computer program carried on a computer-readable storage medium, and the computer program contains program code for executing the complex design domain multi-scale isogeometric topology optimization method described in the above embodiment. In such an embodiment, the computer program can be downloaded and installed from the network through the communication part 309, and / or installed from the removable medium 311. When the computer program is executed by the CPU 301, the above functions defined in the present computer system 300 are executed.

[0128] An embodiment of the present application also provides a computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, the method for multi-scale geometric topology optimization of a complex design domain as described in the above embodiment is implemented.

[0129] Specifically, the computer-readable storage medium may be included in the electronic device described in the above embodiment; or it may exist independently without being assembled into the electronic device. The above computer-readable storage medium carries one or more programs, and when the above one or more programs are executed by an electronic device, the electronic device implements the geometric topology optimization method such as multi-scale of complex design domain as described in the above embodiment.

[0130] It should be noted that the computer-readable storage medium shown in the present application may be a computer-readable signal medium or a computer-readable storage medium or any combination of the above two. The computer-readable storage medium may be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, device or device, or any combination of the above. More specific examples of computer-readable storage media may include, but are not limited to: an electrical connection with one or more wires, a portable computer disk, a hard disk, a random access memory, a read-only memory, an erasable programmable read-only memory, an optical fiber, a portable compact disk read-only memory, an optical storage device, a magnetic storage device, or any suitable combination of the above. In the present application, a computer-readable storage medium may be any tangible medium containing or storing a program that can be used by or in combination with an instruction execution system, device or device. In the present application, a computer-readable signal medium may include a data signal propagated in a baseband or as part of a carrier wave, in which a computer-readable program code is carried. This propagated data signal may take a variety of forms, including but not limited to an electromagnetic signal, an optical signal, or any suitable combination of the above.

[0131] This article uses specific examples to illustrate the principles and implementation methods of this application. The description of the above embodiments is only used to help understand the method and its core ideas of this application. The above is only the preferred implementation method of this application. It should be pointed out that due to the limitations of textual expression and the objective existence of infinite specific structures, ordinary technicians in this technical field can make several improvements, modifications or changes without departing from the principles of the present invention, and can also combine the above technical features in an appropriate manner; these improvements, modifications, changes or combinations, or the direct application of the inventive concept and technical solution to other occasions without improvement, should be regarded as the scope of protection of this application.

Claims

1. A multi-scale isogeometric topology optimization method for a complex design domain, characterized in that: include: Based on the optimization design parameter information of the multi-scale structure of the complex design domain to be optimized, the macro-structure design domain and micro-structure design domain of the multi-scale structure of the complex design domain to be optimized are constructed; Obtaining a microstructure equivalent elastic tensor according to the microstructure density corresponding to the multi-scale structure of the complex design domain to be optimized and a preset equivalent elastic tensor prediction model; Based on the microstructure equivalent elastic tensor, a material interpolation model is constructed; the material interpolation model includes a macro material interpolation sub-model and a micro material interpolation sub-model; Based on the macro-design variables corresponding to the macro-structure design domain, the micro-design variables corresponding to the micro-structure design domain, the micro-structure equivalent elastic tensor and the material interpolation model, taking the minimum force compliance as the optimization goal and the volume fraction of the material as the constraint, a preset isogeometric topology optimization model of the multi-scale structure of the complex design domain to be optimized is constructed; Calculating the macro sensitivity and micro sensitivity of the preset isogeometric topology optimization model, and updating the macro design variables and micro design variables of the preset isogeometric topology optimization model by using an optimization criterion method based on the macro sensitivity and micro sensitivity until a preset convergence condition is met, thereby obtaining target macro design variables and target micro design variables; Based on the target macro-design variables and the target micro-design variables, a target macro-structure and a target micro-structure are generated respectively, the target micro-structure is filled into the target macro-structure to form a rough optimized multi-scale structure, and the rough optimized multi-scale structure is smoothed using an isosurface extraction method to obtain a target complex design domain multi-scale structure model.

2. The method according to claim 1, characterized in that The method of constructing a macrostructure design domain and a microstructure design domain of a multi-scale structure of a complex design domain to be optimized based on the optimization design parameter information of the multi-scale structure of the complex design domain to be optimized includes: Obtaining optimization design parameter information of the multi-scale structure of the complex design domain to be optimized; Based on the optimization design parameter information, the multi-scale structure of the complex design domain to be optimized is NURBS meshed to generate the macro-structure design domain; Based on the optimization design parameter information, an initial microstructure is constructed and discretized into a NURBS grid to generate the microstructure design domain.

3. The method according to claim 1, characterized in that The method further comprises: Collecting microstructure densities of a plurality of sample geometric structures and calculating microstructure equivalent elastic tensors of each of the sample geometric structures using an energy homogenization algorithm; The microstructure density of the sample geometric structure is used as the model input, and the microstructure equivalent elastic tensor of the sample geometric structure is used as the model output, and a fully connected neural network model is trained to obtain the preset equivalent elastic tensor prediction model.

4. The method according to claim 1, characterized in that: The material interpolation model is constructed based on the microstructure equivalent elastic tensor, including: According to the formula: Construct the material interpolation model; wherein, E M is the macrostructure elastic tensor, is the macroscopic isogeometric unit density, E hom is the microstructure equivalent elastic tensor, E m is the microstructure elastic tensor, is the density of microscopic isogeometric units, E0 is the constitutive elastic tensor of the material, Δ is a constant, and p is the penalty parameter.

5. The method according to claim 4, characterized in that The method is based on the macro-design variables corresponding to the macro-structure design domain, the micro-design variables corresponding to the micro-structure design domain, the micro-structure equivalent elastic tensor and the material interpolation model, takes the minimum force compliance as the optimization goal, takes the volume fraction of the material as the constraint, and constructs a preset isogeometric topology optimization model of the multi-scale structure of the complex design domain to be optimized, including: According to the formula: Construct a preset isogeometric topology optimization model of the multi-scale structure of the complex design domain to be optimized; wherein, ρ M is the macro design variable, i.e., the density of macro structural control points; N is the number of isogeometric units included in the macro structural design domain; ρ m is the micro-design variable, i.e., the density of micro-structure control points; n is the number of iso-geometric units included in the micro-structure design domain; C(ρ M ,ρ m ) is the target value of the multi-scale structure in the complex design domain to be optimized, i.e., force compliance; C Mech (ρ M ,ρ m ) is the mechanical flexibility; K(ρ M ,ρ m ) is the stiffness matrix and thermal conductivity matrix of the global performance design domain, including the stiffness matrix and thermal conductivity matrix of the macrostructure design domain and the stiffness matrix and thermal conductivity matrix of the microstructure design domain; U M is the force load at the macrostructure control point, F is the displacement at the macrostructure control point, B M is the macrostructure strain displacement matrix, E M is the macrostructure elastic tensor, Ω M is the macrostructure design domain, Ω m is the microstructure design domain, V M is the specified structural volume of the macroscopic design variable, i.e., the maximum volume fraction of the macroscopic structure; V m is the prescribed structural volume of the micro-design variable, i.e., the maximum volume fraction of the microstructure; is the minimum value of the macro design variable, is the minimum value of the micro-design variable.

6. The method according to claim 5, characterized in that The calculating of the macroscopic sensitivity and microscopic sensitivity of the preset isogeometric topology optimization model includes: According to the formula: Calculate the macroscopic sensitivity and microscopic sensitivity of the preset isogeometric topology optimization model, where C Mech (ρ M ,ρ m ) is the mechanical flexibility, ρ M is the macro design variable, i.e., the density of macro structure control points; S M is the macro design variable ρ M The set of cells affected by the corresponding control point, For S M The cell density of the i-th cell in , U M is the macrostructure control point force load, B M is the macrostructure strain displacement matrix, E hom is the microstructure equivalent elastic tensor; ρ m is the micro-design variable, i.e., the density of micro-structure control points; Δ is a constant, and p is the penalty parameter.

7. The method according to claim 6, characterized in that The updating of the macro-design variables and the micro-design variables of the preset equal geometry topology optimization model by using the optimization criterion method based on the macro-sensitivity and the micro-sensitivity includes: According to the formula: The macroscopic design variables and microscopic design variables of the preset geometric topology optimization model are updated; wherein, ρ M is the macro design variable, i.e., the density of macro structure control points; k is the current iteration number, is the macro design variable at the k+1th iteration, is the macro design variable at the kth iteration, is the update factor of the macro design variables at the kth iteration; ρ m is the micro-design variable, i.e., the density of micro-structure control points; is the micro-design variable at the k+1th iteration, is the micro-design variable at the kth iteration, is the update factor of the micro-design variables at the kth iteration, μ is a constant, is the Lagrange multiplier of the macro design variable, V M is the prescribed structural volume of the macroscopic design variable, i.e., the maximum volume fraction of the macroscopic structure; is the Lagrange multiplier of the microscopic design variable, V m is the prescribed structural volume of the micro-design variable, i.e., the maximum volume fraction of the microstructure.

8. A multi-scale isogeometric topology optimization device for a complex design domain, characterized in that: include: The first construction module is used to construct a macro-structure design domain and a micro-structure design domain of the multi-scale structure of the complex design domain to be optimized based on the optimization design parameter information of the multi-scale structure of the complex design domain to be optimized; A first acquisition module is used to acquire a microstructure equivalent elastic tensor according to the microstructure density corresponding to the multi-scale structure of the complex design domain to be optimized and a preset equivalent elastic tensor prediction model; A second construction module is used to construct a material interpolation model based on the microstructure equivalent elastic tensor; the material interpolation model includes a macro material interpolation sub-model and a micro material interpolation sub-model; A third construction module is used to construct a preset isogeometric topology optimization model of the multi-scale structure of the complex design domain to be optimized based on the macro-design variables corresponding to the macro-structure design domain, the micro-design variables corresponding to the micro-structure design domain, the micro-structure equivalent elastic tensor and the material interpolation model, with minimum force compliance as the optimization goal and the volume fraction of the material as the constraint; A calculation update module, used for calculating the macro sensitivity and micro sensitivity of the preset isogeometric topology optimization model, and updating the macro design variables and micro design variables of the preset isogeometric topology optimization model by using an optimization criterion method based on the macro sensitivity and micro sensitivity until a preset convergence condition is met, thereby obtaining target macro design variables and target micro design variables; The second acquisition module is used to generate a target macrostructure and a target microstructure based on the target macro-design variables and the target micro-design variables, respectively, fill the target microstructure into the target macrostructure to form a rough optimized multi-scale structure, and use the isosurface extraction method to smooth the rough optimized multi-size structure to obtain a target complex design domain multi-scale structure model.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the computer program, the method according to any one of claims 1 to 7 is implemented.

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

Images