A complex design domain multi-scale isometric topology optimization method, device, equipment and medium

Abstract

The application provides a complex design domain multi-scale isometric topology optimization method, device, equipment and medium, relates to the isometric topology optimization technical field, the method constructs macroscopic structure design domain and microscopic structure design domain based on optimization design parameter information, and constructs a material interpolation model based on the equivalent elastic tensor of the microscopic structure obtained according to the microscopic structure density and a preset equivalent elastic tensor prediction model, constructs a preset isometric topology optimization model, and updates the design variable based on the macroscopic sensitivity and the microscopic sensitivity obtained by calculation, obtains the target macroscopic design variable and the target microscopic design variable, generates the target macroscopic structure and the target microscopic structure respectively, carries out smoothing treatment on the rough optimization multi-scale structure formed by filling the target microscopic structure into the target macroscopic structure, and obtains a target complex design domain multi-scale structure model, which breaks through the bottleneck that the existing isometric concurrent topology optimization is difficult to optimize a complex multi-scale model.

Description

Technical Field

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

[0002] Multiscale structures possess excellent physical properties, such as lightweight and high stiffness, high ionic conductivity, and excellent heat dissipation and thermal insulation, making them suitable for a variety of complex engineering applications, including mechanics, aerospace, optoelectronics, and biomedicine. Multiscale concurrent topology optimization can design multiscale structures with improved mechanical and other properties. A research hotspot in structural optimization, topology optimization is a numerical iterative process that finds the optimal material distribution within a predefined design domain, following a specified objective function and constraints. This process offers significant advantages in material savings and improved structural performance.

[0003] In recent years, many scholars have conducted research on 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 other methods 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, which is the so-called isogeometric topology optimization. Although isogeometric topology optimization has been applied in many fields such as solids, fluids, electromagnetics, and heat since its proposal, 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 domains is needed. Summary of the Invention

[0005] The purpose of this application is to address the above problems and provide a method, system, device and medium for multi-scale equal geometric topology optimization of complex design domains, so as to solve the problem that existing concurrent equal geometric 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 geometric topology optimization of a complex design domain, comprising: 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 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-structural design domain, the micro-design variables corresponding to the micro-structural design domain, the micro-structural 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 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 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 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-scale structure is smoothed using the isosurface extraction method to obtain a target complex design domain multi-scale structure model.

[0012] According to the technical solution provided by this application, the optimization design parameter information of the complex design domain multi-scale structure to be optimized is used to construct the macrostructure design domain and microstructure 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 optimized 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 in this application, the method further includes:

[0017] collecting microstructural densities of a plurality of sample geometric structures and calculating the microstructural equivalent elastic tensor 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. A fully connected neural network model is trained to obtain the preset equivalent elastic tensor prediction model.

[0019] According to the technical solution provided in this 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 density of macroscopic isogeometric units, 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 a penalty parameter.

[0023] According to the technical solution provided by the present application, based on the macro-design variables corresponding to the macro-structural design domain, the micro-design variables corresponding to the micro-structural design domain, the micro-structural 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 preset isogeometric topology optimization model of the multi-scale structure of the complex design domain to be optimized is constructed, including:

[0024] According to the formula:

[0025]

[0026] Constructing a preset geometric 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 of the macrostructure control point, F is the displacement of 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 macro design variable, i.e., the maximum volume fraction of the macro 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 in this 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 geometric 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, 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 microstructure 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 isogeometric topology optimization model are updated using an optimization criterion method based on the macro sensitivity and micro sensitivity, including:

[0032] According to the formula:

[0033]

[0034] Update the macro-design variables and micro-design variables of the preset geometric topology optimization model; 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 microstructure 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 macro design variable, i.e., the maximum volume fraction of the macro structure; is the Lagrange multiplier of the microscopic design variable, V m is the prescribed structural volume of the micro-design variable, that is, the maximum volume fraction of the microstructure.

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

[0036] The first construction module is used to construct 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;

[0037] A first acquisition module is configured to acquire a microstructure equivalent elastic tensor according to a 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 configured to construct a preset isogeometric topology optimization model of the multi-scale structure in 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] The computing updating module is configured to calculate macroscopic sensitivity and microscopic sensitivity of the preset equal geometry topology optimization model, and update macroscopic design variables and microscopic design variables of the preset equal geometry topology optimization model based on the macroscopic sensitivity and the microscopic sensitivity by using an optimization criterion method until a preset convergence condition is met, so as to obtain target macroscopic design variables and target microscopic design variables.

[0041] The second obtaining module is configured to generate a target macroscopic structure and a target microscopic structure based on the target macroscopic design variables and the target microscopic design variables respectively, fill the target microscopic structure into the target macroscopic structure to form a rough optimization multi-scale structure, and perform smoothing processing on the rough optimization multi-scale structure by using an isosurface extraction method, so as to obtain a target complex design domain multi-scale structure model.

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

[0043] In a fourth aspect, the present application provides a computer readable storage medium, which stores a computer program, and the computer program is executable on a processor to implement the method as described above.

[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 isogeometric topology optimization of a complex design domain provided by the present application construct 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, and construct a material interpolation model based on the microstructure density corresponding to the multi-scale structure of the complex design domain 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 compliance as the optimization goal and the volume fraction of the material as the constraint, a preset isogeometric 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 using 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 macrostructure and the target microstructure are generated respectively. The rough optimized multi-scale structure formed by filling the target microstructure into the target macrostructure 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 computational complexity of the traditional homogenization method for solving the equivalent elastic tensor of the microstructure and reducing the time cost; by filling the microstructure into the macrostructure design domain and smoothing it using the isosurface extraction technology, a target complex design domain multi-scale structure model is obtained, laying the foundation for subsequent additive manufacturing and being 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 a feature or beneficial effect means that a specific technical feature, technical solution or beneficial effect is included in at least one embodiment. Therefore, the description of a technical feature, technical solution or beneficial effect 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 implemented 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 specific embodiments that do not embody all embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] In order to more clearly illustrate the technical solution in this embodiment, the following is a brief introduction to the drawings required for the description of the embodiment. 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 any 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 Schematic diagram of deep learning of microstructure equivalent elastic tensor of periodic microstructure within the macrostructure design domain provided in the embodiment of the present application;

[0050] Figure 4 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 provided in an embodiment of the present application;

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

[0053] Figure 7 A schematic diagram of a multi-scale isogeometric topology optimization device for a complex design domain 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 solutions of the present application, the technical solutions 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 scope of protection of the present application. Specifically, the embodiments described are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this 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. Therefore, once an item is defined in one figure, it does not need to be further defined or 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 apparatus that includes a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units that are not explicitly listed or inherent to these processes, methods, products or apparatuses.

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

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

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

[0060] Specifically, the multi-scale structure of the complex design domain to be optimized is initialized, and optimization design parameter information of the multi-scale structure of the complex design domain to be optimized is obtained. Then, 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. Moreover, based on the optimization design parameter information, an initial microstructure is constructed and discretized into a NURBS mesh to generate the micro-structure design domain. The optimization design parameter information includes the CAD model file of the multi-scale structure of the complex design domain, the mesh size and number, and the meshing direction. Of course, other parameter information may also be included, which can be set and adjusted according to actual conditions 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, a fully connected neural network model is trained using the microstructural density of multiple sample geometric structures and the microstructural equivalent elastic tensor of each sample geometric structure calculated using an energy homogenization algorithm as the input and output of the training model, respectively. This model then uses the microstructural density corresponding to the complex multi-scale structure to be optimized as input into the pre-set equivalent elastic tensor prediction model to obtain the microstructural equivalent elastic tensor. By using the pre-set equivalent elastic tensor prediction model to instantly predict the microstructural equivalent elastic tensor of the complex multi-scale structure to be optimized, the method avoids the drawback of the traditional homogenization method, which requires excessive computational effort to solve the equivalent elastic tensor of fine-grid microstructures, and effectively reduces time costs.

[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 density of macroscopic isogeometric units, 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. The material interpolation model is constructed based on the macroscopic material interpolation sub-model and the microscopic material interpolation sub-model.

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

[0070] Specifically, according to the formula:

[0071]

[0072] Constructing a preset geometric 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 of the macrostructure control point, F is the displacement of 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 macro design variable, i.e., the maximum volume fraction of the macro 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 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, S M unit density of the i-th unit, U M B is a macro-structure control point force load M E is a macro-structure strain displacement matrix hom C is a micro-structure equivalent elastic tensor; p m is a micro-design variable, i.e., a micro-structure control point density; Δ is a constant, and p is a penalty parameter. Then, macro-design variables and micro-design variables of the preset equal geometry topology optimization model are updated based on the macro-sensitivity and the micro-sensitivity by using an optimization criterion method until a preset convergence condition is met, to obtain target macro-design variables and target micro-design variables. The preset convergence condition can be that a variation of the macro-design variables (i.e., macro-structure control point density) and the micro-design variables (i.e., micro-structure control point relative density) is less than a preset threshold value or an iteration number reaches a preset number. For example, the preset threshold value 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 actual conditions, which are not 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 respectively generated, the target micro-structure is filled into the target macro-structure to form a rough optimization multi-scale structure, and an isosurface extraction method is used to smooth the rough optimization multi-scale structure to obtain a target complex design domain multi-scale structure model.

[0078] Specifically, based on the obtained target macro-design variables and target micro-design variables, a target macro-structure and a target micro-structure are respectively generated, the target micro-structure is filled into the target macro-structure to form a rough optimization multi-scale structure, an isosurface extraction method is used to smooth the rough optimization multi-scale structure to obtain a target complex design domain multi-scale structure model, and finally an STL format file is output, which lays a foundation for subsequent additive manufacturing and is more conducive to engineering application.

[0079] On the basis of the above embodiment, further, based on the optimization design parameter information of the to-be-optimized complex design domain multi-scale structure, a macro-structure design domain and a micro-structure design domain of the to-be-optimized complex design domain multi-scale structure are constructed, including:

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

[0081] Based on the optimization design parameter information, the to-be-optimized complex design domain multi-scale structure 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 a CAD model file of the complex design domain multi-scale structure, grid size and quantity, and grid 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 grid in the macro scale according to the grid size, quantity, and grid 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, grid size, quantity, and grid direction, and outputting the grid data in the form of a three-dimensional matrix, wherein 1 represents a solid area unit and 0 represents a blank area unit; the initial structure diagram of the macro structure design domain can be obtained after visualizing the solid area unit. Figure 2 The initial complex design domain multi-scale structure diagram provided by the embodiment of the application is shown in Figure 2 As shown in the figure, for example, the complex design domain multi-scale structure to be optimized is an aircraft bearing support, and after grid, a regular NURBS solid unit of a given grid quantity is generated, and the solid area unit is visualized as a complex design domain model NURBS grid, and the blank area is not shown in the figure.

[0084] On the basis of the above-mentioned embodiment, further, the method further comprises:

[0085] The microstructure density of the plurality of sample geometries is collected, and the energy homogenization algorithm is used to calculate the microstructure equivalent elastic tensor of each sample geometry;

[0086] The microstructure density of the sample geometry is taken as the model input, the microstructure equivalent elastic tensor of the sample geometry is taken as the model output, the full connection neural network model training is performed, and the preset equivalent elastic tensor prediction model is obtained.

[0087] Specifically, the energy homogenization algorithm is used to solve the microstructure equivalent elastic tensor of the sample geometry, and in the linear elasticity range, the equivalent performance of the microstructure can be evaluated by the energy homogenization method, when the microstructure is periodically arranged in the macro structure design domain, it can be regarded as a homogeneous material in the macro scale, and the corresponding equivalent elastic tensor can be obtained. As shown in Figure 3 As shown in the figure, the microstructure equivalent elastic tensor deep learning schematic diagram of the periodic microstructure in the macro structure design domain provided by the embodiment of the application is shown in 3, the microstructure density of the plurality of sample geometries 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 approximately equal to 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 To correspond to 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. A 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 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, as shown in FIG. Figure 4 As shown in the figure, when the sample geometry is a 2D structure, there are three linearly independent unit test strain fields; 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 density of macroscopic isogeometric units, 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 a penalty parameter.

[0099] Specifically, Figure 5 A schematic diagram of a material interpolation model provided in an embodiment of the present application is shown in FIG. Figure 5 As shown in FIG, 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, with 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, including:

[0101] According to the formula:

[0102]

[0103] Constructing a preset geometric 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 of the macrostructure control point, F is the displacement of 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 macro design variable, i.e., the maximum volume fraction of the macro 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 minimum values ​​of 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 of 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, 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 microstructure 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 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 the micro sensitivity includes:

[0110] According to the formula:

[0111]

[0112] Update the macro-design variables and micro-design variables of the preset geometric topology optimization model; 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 microstructure 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 macro design variable, i.e., the maximum volume fraction of the macro structure; is the Lagrange multiplier of the microscopic design variable, V m is the prescribed structural volume of the micro-design variable, that is, 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 this application is as follows: Figure 6 As shown in the figure, in the concurrent isogeometric topology 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 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 Contains both macro-design variables and micro-design variables, i.e. depends on the macro-design variables and micro-design variables

[0114] The complex design domain multi-scale isogeometric topology optimization method provided in the present application constructs the macrostructure design domain and 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 preset equivalent elastic tensor prediction model. Then, based on the macro-design variables and 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 the constraint, a preset isogeometric topology optimization model is constructed, and based on the calculated macro-sensitivity and micro-sensitivity, the macro-design variables and micro-design variables are updated using the optimization criterion method until the preset convergence conditions are met, and the target macro-design variables and target micro-design variables are obtained, and the target macrostructure and target microstructure are generated respectively. The rough optimized multi-scale structure formed by filling the target microstructure into the target macrostructure 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 computational complexity of the traditional homogenization method for solving the equivalent elastic tensor of the microstructure and reducing the time cost; by filling the microstructure into the macrostructure design domain and smoothing it using the isosurface extraction technology, a target complex design domain multi-scale structure model is obtained, laying the foundation for subsequent additive manufacturing and being more conducive to engineering applications.

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

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

[0117] The first construction module 201 is used to construct 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;

[0118] A first acquisition module 202 is configured 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 configured 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] A third construction module 204 is configured to construct a preset isogeometric topology optimization model of the multi-scale structure in the complex design domain to be optimized based on the macro-design variables corresponding to the macro-structural design domain, the micro-design variables corresponding to the micro-structural design domain, the micro-structural 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 configured 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 macrodesign variables and the target microdesign 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-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, the multi-scale geometric topology optimization method for the complex design domain as described in the above embodiment is implemented.

[0125] like Figure 8As shown, the computer system 300 of the electronic device includes a CPU 301 that can perform various appropriate actions and processes in accordance with a program stored in a ROM 302 or a program loaded into a RAM 303 from a storage section 308. 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. An I / O interface 305 is also connected to the bus 304. Among them, the CPU 301 denotes a central processing unit, the ROM 302 denotes a read only memory, the RAM 303 denotes a random access memory, and the I / O denotes an input / output.

[0126] Connected to the I / O interface 305 are an input section 306 including a keyboard, a mouse, and the like; an output section 307 including a display such as a cathode ray tube, a liquid crystal display, and the like, and a speaker and the like; a storage section 308 including a hard disk and the like; and a communication section 309 including a network interface card such as a LAN card, a modem, and the like. 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 necessary. A removable media 311 such as a magnetic disk, an optical disk, a magneto-optical disk, a semiconductor memory, and the like is mounted on the drive 310 as necessary, so that a computer program read therefrom is installed in the storage section 308 as necessary.

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

[0128] An embodiment of the present application also provides a computer readable storage medium having a computer program stored thereon, the computer program being executed by a processor to implement the complex design domain multi-scale isogeometric topology optimization method as described in the above embodiments.

[0129] Specifically, the computer-readable storage medium may be included in the electronic device described in the above embodiments, or may exist independently without being incorporated into the electronic device. The computer-readable storage medium carries one or more programs. When executed by the electronic device, the electronic device implements the complex design domain multi-scale isotropic geometric topology optimization method described in the above embodiments.

[0130] It should be noted that the computer-readable storage medium described in this application may be a computer-readable signal medium or a computer-readable storage medium, or any combination thereof. Computer-readable storage media may include, for example, but are not limited to, electrical, magnetic, optical, electromagnetic, infrared, or semiconductor systems, devices, or components, or any combination thereof. More specific examples of computer-readable storage media may include, but are not limited to, an electrical connection having one or more wires, a portable computer disk, a hard disk, random access memory, read-only memory, erasable programmable read-only memory, optical fiber, a portable compact disk read-only memory, an optical storage device, a magnetic storage device, or any suitable combination thereof. In this application, a computer-readable storage medium may be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, device, or component. Furthermore, in this application, a computer-readable signal medium may include a data signal propagated in baseband or as part of a carrier wave, carrying computer-readable program code. This propagated data signal may take a variety of forms, including, but not limited to, electromagnetic signals, optical signals, or any suitable combination thereof.

[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 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, there are objectively infinite specific structures. For ordinary technicians in this technical field, without departing from the principles of the present invention, they can also make several improvements, modifications or changes, 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 by: 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-structural design domain, the micro-design variables corresponding to the micro-structural design domain, the micro-structural 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 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 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 macrostructure and a target microstructure are generated respectively, the target microstructure is filled into the target macrostructure 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; The method comprises: constructing a preset isogeometric topology optimization model of the multi-scale structure in 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, including: According to the formula: Constructing a preset geometric 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 of the macrostructure control point, F is the displacement of 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 macro design variable, i.e., the maximum volume fraction of the macro 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; is the lth macro design variable, is the jth micro-design variable; The calculation 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 geometric topology optimization model, where C Mech (ρ M ,ρ m ) is the mechanical compliance, 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, 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 microstructure control points; Δ is a constant, and p is a penalty parameter; The updating of the macro-design variables and the micro-design variables of the preset isogeometric topology optimization model by using an optimization criterion method based on the macro-sensitivity and the micro-sensitivity includes: According to the formula: Update the macro-design variables and micro-design variables of the preset geometric topology optimization model; 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 microstructure 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 macro design variable, i.e., the maximum volume fraction of the macro structure; is the Lagrange multiplier of the microscopic design variable, V m is the prescribed structural volume of the micro-design variable, that is, the maximum volume fraction of the microstructure.

2. The method according to claim 1, characterized in that The method of constructing a macrostructure design domain and a microstructure design domain of the multiscale structure of the complex design domain to be optimized based on the optimization design parameter information of the multiscale 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 optimized 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 microstructural densities of a plurality of sample geometric structures and calculating the microstructural equivalent elastic tensor 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. A fully connected neural network model is trained to obtain the preset equivalent elastic tensor prediction model.

4. The method according to claim 1, wherein 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 density of macroscopic isogeometric units, E hom is the microstructure equivalent elastic tensor, E m is the microstructure elastic tensor, is the density of microscopic geometric units, E0 is the constitutive elastic tensor of the material, and Δ is a constant.

5. A device for executing the multi-scale isogeometric topology optimization method for a complex design domain according to any one of claims 1 to 4, characterized in that: include: The first construction module is used to construct 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; A first acquisition module is configured to acquire a microstructure equivalent elastic tensor according to a 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 configured to construct a preset isogeometric topology optimization model of the multi-scale structure in 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 and updating module, configured 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; The second acquisition module is used to generate a target macrostructure and a target microstructure based on the target macrodesign variables and the target microdesign 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-scale structure to obtain a target complex design domain multi-scale structure model.

6. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the computer program, the method according to any one of claims 1 to 4 is implemented.

7. 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 4 is implemented.

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