Macro-micro dual-scale structure topology optimization method and device capable of controlling minimum size of microstructure

Abstract

The invention belongs to the technical field related to structure optimization design, and discloses a macro-micro dual-scale structure topological optimization method and device capable of controlling the minimum size of a microstructure, and the method comprises the following steps: (1), carrying out the interpolation of an elastic matrix of an actual microstructure in an offline database and the corresponding density through employing radial basis function interpolation, and obtaining an elastic matrix of the actual microstructure; constructing a mapping model; (2) a flexibility minimization optimization model is constructed, design variables of the optimization model are cutting heights and topological variables of the two virtual microstructures in each unit, and constraint functions are volume fractions and topological variable constraints of the overall structure; (3) respectively calculating the sensitivity of the target function and the constraint function to the design variable, and further updating the design variable; (4) when the updated flexibility error of the dual-scale structure meets an optimization termination condition, completing optimization and obtaining the dual-scale structure meeting the requirement; otherwise, turning to the step (3). According to the method, the problems of low calculation efficiency and poor connectivity are solved.

Description

Technical Field

[0001] The present invention belongs to the technical field related to structural optimization design, and more specifically, relates to a macro-micro dual-scale structure topology optimization method and equipment capable of controlling the minimum size of a microstructure. Background Art

[0002] Bamboo and animal bones in nature are typical dual-scale structures. Through the observation of this type of dual-scale structure in nature, it is found that the unit cell morphology at the microscopic scale directly determines the performance of the material. Therefore, the dual-scale structural optimization can more reasonably distribute microstructures of various shapes in the most suitable structural position. The traditional M-VCUT dual-scale optimization method performs optimization analysis under the framework of the full scale. The full-scale finite element needs to be recalculated every time it is updated. In order to ensure the accuracy of the results, the mesh of the overall finite element becomes very large due to the existence of the microstructure in the structure, which increases the consumption of calculation time.

[0003] In order to improve computational efficiency, an offline data-driven method is used for dual-scale structural optimization. This method directly generates a large number of data samples as a database at one time, directly constructs a mapping model that meets the accuracy, and no longer updates the mapping model during the optimization process. Therefore, the dual-scale structural optimization under data-driven can greatly improve efficiency while ensuring accuracy. However, the results obtained contain many fine structures, and this type of structure does not meet the manufacturing constraints and 3D printing requirements. Therefore, the method of controlling the minimum size of the microstructure in the macro-micro dual-scale topology optimization is used to control the minimum size of the microstructure, thereby realizing structural manufacturing.

[0004] Research shows that by using a method to control the minimum size of the microstructure in macro-micro dual-scale topology optimization, the calculation efficiency can be accelerated on the basis of the traditional M-VCUT method to meet the minimum microstructure size requirements.

[0005] At present, there are still some design problems in the dual-scale structure optimization method: the dual-scale structure optimization performed by the scale separation method needs to solve the connectivity problem of the micro-scale structure; the dual-scale structure optimization performed by the scale association method usually has low computational efficiency. Summary of the invention

[0006] In view of the above defects or improvement needs of the prior art, the present invention provides a macro-micro dual-scale structure topology optimization method and equipment that can control the minimum size of the microstructure, which aims to solve the problems of low computational efficiency and poor connectivity of existing topology optimization methods.

[0007] To achieve the above object, according to one aspect of the present invention, a macro-micro dual-scale structure topology optimization method capable of controlling the minimum size of a microstructure is provided, the method comprising the following steps:

[0008] Step 1: interpolate the elastic matrix and corresponding density of the actual microstructure in the offline database using radial basis function interpolation, and then construct a mapping model of cutting height, topological variables, elastic parameters and density based on the interpolated data and the offline database; wherein the acquisition of the offline database includes the following steps:

[0009] S1, taking the cutting height and topological variables corresponding to each unit in the design domain of the dual-scale structure as design variables, and using the M-VCUT level set method to perform cutting operations on the level set function to obtain the virtual microstructure;

[0010] S2, multiplying the density of the two virtual microstructures obtained by their topological variables, and then obtaining the density of the actual microstructure of the unit by taking the max union, and using the homogenization method to calculate the elasticity matrix of each actual microstructure corresponding to the cutting height and topological variable at the predetermined interval, and the elasticity matrix of the actual microstructure obtained and the corresponding density form an offline database;

[0011] Step 2: Based on the mapping model, a dual-scale structure optimization design problem is defined to obtain a flexibility minimization optimization model, wherein the design variables of the flexibility minimization optimization model are the cutting heights and topological variables of the two virtual microstructures in each unit, the objective function is to minimize the flexibility of the dual-scale structure, and the constraint function is the volume fraction of the overall structure and the topological variable constraint;

[0012] Step 3, respectively calculating the sensitivity of the objective function and the constraint function to the design variables, and updating the design variables based on the obtained sensitivity results;

[0013] Step 4: When the flexibility error of the updated dual-scale structure meets the optimization termination condition, the optimization is completed and a dual-scale structure that meets the requirements is obtained; otherwise, go to step 3.

[0014] Furthermore, using the level set function and cutting function Represents the combined function obtained by a cutting operation

[0015]

[0016] Where D is the reference domain, Define the virtual microstructure according to the positive and negative relationship of the cutting results

[0017]

[0018] Each virtual microstructure Assigned a topology variable is the cutting height, and one cutting height is one cutting plane.

[0019] Furthermore, the density matrix of each virtual microstructure is obtained by calculation Thus, the density matrix of each virtual microstructure is obtained

[0020]

[0021] Afterwards, the density matrices of the virtual microstructures are combined to obtain the final density matrix of the actual microstructure:

[0022]

[0023] With the density of the actual microstructure, we get the actual microstructure:

[0024] Ω k ={x|ρ k (x)>0,x∈D k}

[0025] Finally, the actual microstructure is used to represent the dual-scale structure Ω:

[0026]

[0027] In the formula, is the joint symbol and the actual microstructure Ω at each position k The combination becomes the final overall dual-scale structure Ω.

[0028] Furthermore, according to the computational homogenization theory, the macroscopic equivalent elastic tensor of the periodic microstructure is expressed as:

[0029]

[0030] Where |V| represents the volume of the microstructure, E pqrs represents the local elastic tensor of the microstructure, is the known macroscopic strain field; Also expressed in matrix form:

[0031]

[0032] The elastic constant and volume fraction at any height are solved by using the multi-quadratic radial basis function interpolation formula and the offline database. Both types of design variables are uniformly expressed by σ I express:

[0033]

[0034] in and γ iThese are all expansion coefficients in MQ-RBF; It is the design variable information of the reference point stored in the offline database; is the Euclidean distance from the desired point to the reference point.

[0035] Furthermore, the cutting height and topological variables are used as design variables to solve the flexibility minimization optimization model under volume constraints and topological variable constraints:

[0036] min c=F T U

[0037] stKU=F

[0038]

[0039] g βi ≤μ

[0040] 0≤β i ≤1

[0041]

[0042] Where i represents the type of microstructure; g βi is the constraint that the topological variables need to satisfy; μ is a constant; U is the overall displacement of the dual-scale structure; V is the volume of the dual-scale structure; β i is a topological variable; is the unit cutting height; h is the minimum cutting height; The maximum cutting height.

[0043] Furthermore, the sensitivity of the objective function to the design variables is expressed as:

[0044]

[0045] at the same time:

[0046] K e =B T BYZGR e

[0047] Where B is the unit strain matrix, t is the unit thickness, A e is the unit area.

[0048] Furthermore, the sensitivity of the topological variable constraint function to the design variables is expressed as:

[0049]

[0050] In the formula, β I is a topological variable.

[0051] Furthermore, the optimization termination condition is set as:

[0052] or l≥l max ,

[0053] Among them, c err is the flexibility error, l is the current iteration number, ε is the lower limit of the flexibility error, l max is the upper limit of the number of iterations.

[0054] The present invention also provides a macro-micro dual-scale structure topology optimization system capable of controlling the minimum size of a microstructure. The system includes a memory and a processor. The memory stores a computer program. When the processor executes the computer program, it executes the macro-micro dual-scale structure topology optimization method capable of controlling the minimum size of a microstructure as described above.

[0055] The present invention also provides a computer-readable storage medium, which stores machine-executable instructions. When the machine-executable instructions are called and executed by a processor, the machine-executable instructions prompt the processor to implement the macro-micro dual-scale structure topology optimization method that can control the minimum size of the microstructure as described above.

[0056] In general, compared with the prior art, the above technical solution conceived by the present invention, the macro-micro dual-scale structure topology optimization method and device capable of controlling the minimum size of the microstructure provided by the present invention mainly have the following beneficial effects:

[0057] 1. The computational efficiency is improved by data-driven (offline database) means. At the same time, the microstructure obtained by using the M-VCUT level set cutting method also ensures the connectivity problem. Therefore, the present invention can ensure the connectivity of the microstructure in the overall structure, greatly improving the optimization efficiency. At the same time, all microstructures in the structure meet the minimum size requirements and are manufacturable.

[0058] 2. By introducing topological variables as design variables, a dual-scale structure with minimum microstructure size constraints can be obtained, and the obtained dual-scale structure can be used for direct 3D printing.

[0059] 3. The microstructure obtained by the M-VCUT level set method is finally used to obtain a dual-scale structure that meets the optimization requirements. The maximization of structural stiffness is taken as the design goal, and the constraints of the volume and topological variables of the overall structure are taken as constraints. The moving asymptote method is used to update the design variables until the optimization termination conditions are met to obtain the optimal dual-scale structure. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 It is a structural schematic diagram of a dual-scale structural optimization design of an MBB beam provided by an embodiment of the present invention;

[0061] Figure 2 (a) and (b) are the microstructure models of the two virtual microstructures in each unit of the dual-scale structure when the cutting height is 0 and the topological variable is 1;

[0062] Figure 3 is a method flow chart of a macro-micro dual-scale structure topology optimization method for controlling the minimum size of a microstructure provided by an embodiment of the present invention;

[0063] Figure 4 This is the initial design diagram for dual-scale structural optimization;

[0064] Figure 5 It is a schematic diagram of the optimization results of the dual-scale structure when the method provided by the present invention is adopted. DETAILED DESCRIPTION

[0065] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0066] The present invention provides a macro-micro dual-scale structure topology optimization method capable of controlling the minimum size of a microstructure, the method mainly comprising the following steps:

[0067] Step 1: interpolate the elastic matrix and corresponding density of the actual microstructure in the offline database using radial basis function interpolation, and then construct a mapping model of cutting height, topological variables, elastic parameters and density based on the interpolated data and the offline database; wherein the acquisition of the offline database includes the following steps:

[0068] S1, the cutting height and topological variables corresponding to each unit in the design domain of the dual-scale structure are taken as design variables, and the M-VCUT level set method is used to perform cutting operations on the level set function to obtain the virtual microstructure.

[0069] In this embodiment, the cutting height H of the two virtual microstructures used to form the actual microstructure of each unit is I and topological variables β I As the design variable, where I=1, 2, ..., 2N, N is the number of units;

[0070] Combined cutting height H I and topological variables β I Two types of design variables to obtain virtual microstructures in each unit The virtual microstructure The actual microstructure Ω is obtained by combining k ; The overall dual-scale structure Ω is obtained using the actual microstructure.

[0071] S2, multiply the density of the two virtual microstructures obtained by their topological variables, and then obtain the density of the actual microstructure of the unit by taking the max union, and use the homogenization method to calculate the elasticity matrix of each actual microstructure corresponding to the cutting height and topological variable at the predetermined interval, and the elasticity matrix of the actual microstructure and the corresponding density are formed into an offline database.

[0072] Using the level set function and cutting function Represents the combined function obtained by a cutting operation

[0073]

[0074] Where D is the reference domain, Define the virtual microstructure according to the positive and negative relationship of the cutting results

[0075]

[0076] Each virtual microstructure Assigned a topology variable Therefore, it is necessary to calculate the density matrix of each virtual microstructure Thus, the density matrix of each virtual microstructure is obtained

[0077]

[0078] Afterwards, the density matrices of the virtual microstructures are combined to obtain the final density matrix of the actual microstructure:

[0079]

[0080] With the density of the actual microstructure, we can get the actual microstructure:

[0081] Ω k ={x|ρ k (x)>0,x∈D k}

[0082] Finally, the actual microstructure is used to represent the dual-scale structure Ω:

[0083]

[0084] According to the computational homogenization theory, the macroscopic equivalent elastic tensor of the periodic microstructure can be expressed as:

[0085]

[0086] Where |V| represents the volume of the microstructure, E pqrs represents the local elastic tensor of the microstructure, is the known macroscopic strain field; It can also be expressed in matrix form:

[0087]

[0088] In this embodiment, the equidistant cutting height H is selected in each unit. I and the isometric topological variable β I , and the equivalent elastic matrix and corresponding density of the actual microstructures of M groups are obtained by homogenization formula to form an offline database. The elastic constant and volume fraction at any height are solved by using the multiple quadratic radial basis function (MQ-RBF) interpolation formula and offline database. Both types of design variables are uniformly expressed by σ I express:

[0089]

[0090] in and γ i These are all expansion coefficients in MQ-RBF; It is the design variable information of the reference point stored in the offline database; is the Euclidean distance from the desired point to the reference point.

[0091] In MQ-RBF:

[0092]

[0093] Where τ is the free shape parameter, which is taken as 0.05 here; p(σ) needs to satisfy:

[0094] p(σ)=p 0 +p 1 σ 1 +p 2 σ 2 +…+p M σ M

[0095] The stiffness matrix K of each unit is established using the equivalent elastic matrix of the actual microstructure e , the stiffness matrix K corresponding to each unit e Assembled into the overall stiffness matrix K.

[0096] The overall displacement vector u is solved using the formula Ku=f, where f is the external force vector, thereby completing the finite element analysis of the dual-scale structure.

[0097] Step two, based on the mapping model, define the dual-scale structure optimization design problem to obtain a flexibility minimization optimization model, wherein the design variables of the flexibility minimization optimization model are the cutting heights and topological variables of the two virtual microstructures in each unit, the objective function is to minimize the flexibility of the dual-scale structure, and the constraint function is the volume fraction of the overall structure and the topological variable constraints.

[0098] The flexibility minimization optimization model under volume constraints and topological variable constraints is solved with cutting height and topological variables as design variables:

[0099] min c=F T U

[0100] stKU=F

[0101]

[0102] g βi ≤μ

[0103] 0≤β i ≤1

[0104]

[0105] Where i represents the type of microstructure; are the constraints that the topological variables need to satisfy; μ is a constant.

[0106] Step three, calculate the sensitivity of the objective function and constraint function to the design variables respectively, and update the design variables based on the obtained sensitivity results.

[0107] The sensitivity of the objective function to the design variables can be expressed as:

[0108]

[0109] at the same time:

[0110] K e =B T BYZGR e

[0111] Where B is the element strain matrix, t is the element thickness, A e is the unit area.

[0112] It can be further expressed as:

[0113]

[0114] According to the interpolation formula mentioned above, we can It is expressed as:

[0115]

[0116] in:

[0117]

[0118] The volume constraint function in the constraint function is consistent with the above formula. The sensitivity of the topological variable constraint function to the design variable is expressed as:

[0119]

[0120] Step 4: When the flexibility error of the updated dual-scale structure meets the optimization termination condition, the optimization is completed and a dual-scale structure that meets the requirements is obtained; otherwise, go to step 3.

[0121] In one embodiment, the optimization termination condition is set to:

[0122] or l≥l max ,

[0123] Among them, c err is the flexibility error, l is the current iteration number, ε is the lower limit of the flexibility error, l max is the upper limit of the number of iterations.

[0124] The present invention also provides a macro-micro dual-scale structure topology optimization system capable of controlling the minimum size of a microstructure. The system includes a memory and a processor. The memory stores a computer program. When the processor executes the computer program, it executes the macro-micro dual-scale structure topology optimization method capable of controlling the minimum size of a microstructure as described above.

[0125] The present invention also provides a computer-readable storage medium, which stores machine-executable instructions. When the machine-executable instructions are called and executed by a processor, the machine-executable instructions prompt the processor to implement the macro-micro dual-scale structure topology optimization method that can control the minimum size of the microstructure as described above.

[0126] The present invention is further described in detail below with reference to specific embodiments.

[0127] See also Figure 1 In this embodiment, the present invention is explained by taking the optimization problem of minimizing the flexibility of a planar MBB beam structure subjected to a concentrated load as an example. An initial dual-scale structure is set in a given 3m×1m rectangular design domain D, the horizontal degree of freedom in the left area is fixed, the vertical degree of freedom in the lower right corner area is restricted, and a concentrated force f=1N is applied to the upper left corner area. The dual-scale structure is optimized to maximize the stiffness under the premise that the cutting height of the optimization result is above 0.1.

[0128] See also Figure 3 This embodiment provides a macro-micro dual-scale structure topology optimization method capable of controlling the minimum size of a microstructure, the method comprising the following steps:

[0129] S1: The cutting height and topological variables corresponding to each unit in the design domain of the dual-scale structure are taken as design variables, and the M-VCUT level set method is used to perform a cutting operation on the level set function to obtain a virtual microstructure;

[0130] Specifically, the given design domain Ω is divided into a certain number of square units, and the number of units N is 60×20.

[0131] S2: Multiply the density results of the two virtual microstructures by their respective topological variables and then take the max union to obtain the density of the actual microstructure of the unit, and use the homogenization method to calculate the elastic matrix of each actual microstructure under a certain cutting height spacing and topological variable spacing;

[0132] Specifically, two virtual microstructures such as Figure 2 As shown in the figure, the actual combined microstructure prototype Ω in each unit is obtained by Boolean operation, and 21 groups of virtual microstructure cutting heights with an interval of 0.05 from 0 to 1 and 26 groups of topological variables with an interval of 0.04 from 0 to 1 are obtained by homogenization method, which corresponds to a total of 21*21*26*26 data, where the offline database contains the equivalent elastic modulus D H and the equivalent volume fraction V H .

[0133] S3: Use the interpolation function to convert the elastic matrix and microstructure volume fraction in the offline database into the elastic matrix and microstructure volume at any height and any topological variable.

[0134] Specifically, according to the interpolation formula, select the n reference design variables closest to the unknown design variable a, where n is guaranteed to be greater than 1; interpolation calculation is performed to obtain the equivalent elastic modulus of the unknown design variable: And the corresponding equivalent volume fraction According to the finite element formula K e =B T BYZGR e Convert the equivalent elastic modulus to the element stiffness matrix Assemble the stiffness matrices corresponding to each unit into the overall stiffness matrix K;

[0135] The overall displacement vector u is solved using the formula Ku=f, where f is the external force vector, thereby completing the finite element analysis of the dual-scale structure.

[0136] S4: Define the dual-scale structure optimization design problem: the design variables are the cutting height and topological variables of the two virtual microstructures in each unit, the design goal is to minimize the flexibility of the dual-scale structure, and the design constraints are the volume fraction of the overall structure and the constraints on the topological variables;

[0137] Specifically, the cutting height and topological variables are used as design variables to solve the flexibility minimization optimization model under volume constraints:

[0138] min c=F T U

[0139] stKU=F

[0140]

[0141] g βi ≤μ

[0142] 0≤β i ≤1

[0143]

[0144] Where i represents the type of microstructure, which is equal to 2 here.

[0145] S5: Calculate the sensitivity of the objective function to the design variables, calculate the sensitivity of the constraint function to the design variables, and then update the design variables;

[0146] Specifically, the design variables H are updated according to the objective function, constraint functions and their sensitivity to the design variables, combined with the method of moving asymptotes (usually referred to as MMA). I and β I , MMA is an existing optimization algorithm, which will not be described here. Inew and β Inew The distribution of the actual microstructure of each unit is represented to obtain the overall dual-scale structure.

[0147] Repeat S5, each repetition is called an iteration, until the optimization termination condition is met and the optimal design of the dual-scale structure is obtained. The optimization termination condition is set as:

[0148] or l≥l max ,

[0149] where c err is the flexibility error, l is the current iteration number, ε is the lower limit of the flexibility error, which is 0.5% here, l max is the upper limit of the number of iterations, which is 500 here.

[0150] The optimization results of the preferred embodiment of the present invention are as follows:

[0151] The optimized dual-scale structure is as follows Figure 5 As shown, the flexibility value is 203.26. For comparison, the initial design of the dual-scale structure is as follows Figure 4 As shown in Figure 2, the compliance value is 806.16, which is reduced by about 74.79%. After optimization, the microstructure cutting heights in the dual-scale structure all meet h min >0.1, and the computational efficiency is improved, and the microstructures are well connected.

[0152] It will be easily understood by those skilled in the art that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A macro-micro dual-scale structure topology optimization method capable of controlling the minimum size of a microstructure, characterized in that: The method comprises the following steps: Step 1: interpolate the elastic matrix and corresponding density of the actual microstructure in the offline database using radial basis function interpolation, and then construct a mapping model of cutting height, topological variables, elastic parameters and density based on the interpolated data and the offline database; wherein the acquisition of the offline database includes the following steps: S1, taking the cutting height and topological variables corresponding to each unit in the design domain of the dual-scale structure as design variables, and using the M-VCUT level set method to perform cutting operations on the level set function to obtain the virtual microstructure; S2, multiplying the density of the two virtual microstructures obtained by their topological variables, and then obtaining the density of the actual microstructure of the unit by taking the max union, and using the homogenization method to calculate the elasticity matrix of each actual microstructure corresponding to the cutting height and topological variable at the predetermined interval, and the elasticity matrix of the actual microstructure obtained and the corresponding density form an offline database; Step 2: Based on the mapping model, a dual-scale structure optimization design problem is defined to obtain a flexibility minimization optimization model, wherein the design variables of the flexibility minimization optimization model are the cutting heights and topological variables of the two virtual microstructures in each unit, the objective function is to minimize the flexibility of the dual-scale structure, and the constraint function is the volume fraction of the overall structure and the topological variable constraint; Step 3, respectively calculating the sensitivity of the objective function and the constraint function to the design variables, and updating the design variables based on the obtained sensitivity results; Step 4: When the flexibility error of the updated dual-scale structure meets the optimization termination condition, the optimization is completed and a dual-scale structure that meets the requirements is obtained; otherwise, go to step 3.

2. The macro-micro dual-scale structure topology optimization method capable of controlling the minimum size of the microstructure as claimed in claim 1, characterized in that: Using the level set function and cutting function Represents the combined function obtained by a cutting operation Where D is the reference domain, Define the virtual microstructure according to the positive and negative relationship of the cutting results Each virtual microstructure Assigned a topology variable is the cutting height, and one cutting height is one cutting plane.

3. The macro-micro dual-scale structure topology optimization method capable of controlling the minimum size of the microstructure as claimed in claim 2, characterized in that: The density matrix of each virtual microstructure is obtained by calculation Thus, the density matrix of each virtual microstructure is obtained Afterwards, the density matrices of the virtual microstructures are combined to obtain the final density matrix of the actual microstructure: With the density of the actual microstructure, we get the actual microstructure: Qk={x|pk(x)>0,x∈Dk} Finally, the actual microstructure is used to represent the dual-scale structure Ω: In the formula, To combine the symbols and the actual microstructure Ωk at each position into the final overall dual-scale structure Ω.

4. The macro-micro dual-scale structure topology optimization method capable of controlling the minimum size of the microstructure as claimed in claim 1, characterized in that: According to the computational homogenization theory, the macroscopic equivalent elastic tensor of the periodic microstructure is expressed as: where |V| represents the volume of the microstructure, Epqrs represents the local elastic tensor of the microstructure, is the known macroscopic strain field; Also expressed in matrix form: The elastic constant and volume fraction at any height are solved by using the multi-quadratic radial basis function interpolation formula and the offline database. Both types of design variables are uniformly expressed by σ I express: in and γi are the expansion coefficients in MQ-RBF; It is the design variable information of the reference point stored in the offline database; is the Euclidean distance from the desired point to the reference point.

5. The macro-micro dual-scale structure topology optimization method capable of controlling the minimum size of the microstructure as claimed in claim 4, characterized in that: The flexibility minimization optimization model under volume constraints and topological variable constraints is solved with cutting height and topological variables as design variables: minc=FTU FWf 0≤β≤1 Where i represents the type of microstructure; is the constraint that the topological variable needs to satisfy; μ is a constant; U is the overall displacement of the dual-scale structure; V is the volume of the dual-scale structure; βi is the topological variable; is the unit cutting height; h is the minimum cutting height; The maximum cutting height.

6. The macro-micro dual-scale structure topology optimization method capable of controlling the minimum size of the microstructure as claimed in claim 5, characterized in that: The sensitivity of the objective function to the design variables is expressed as: at the same time: K=BTDBtA e Where B is the element strain matrix, t is the element thickness, A e is the unit area.

7. The macro-micro dual-scale structure topology optimization method capable of controlling the minimum size of the microstructure as claimed in claim 6, characterized in that: The sensitivity of the topological variable constraint function to the design variables is expressed as: In the formula, β I is a topological variable.

8. The macro-micro dual-scale structure topology optimization method capable of controlling the minimum size of the microstructure according to any one of claims 1 to 7, characterized in that: The optimization termination condition is set as: Among them, cer r is the flexibility error, l is the current iteration number, ε is the lower limit of the flexibility error, lma x is the upper limit of the number of iterations.

9. A macro-micro dual-scale structure topology optimization system capable of controlling the minimum size of a microstructure, characterized in that: The system includes a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, the macro-micro dual-scale structure topology optimization method capable of controlling the minimum size of the microstructure as described in any one of claims 1 to 8 is executed.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores machine executable instructions. When the machine executable instructions are called and executed by the processor, the machine executable instructions prompt the processor to implement the macro-micro dual-scale structure topology optimization method capable of controlling the minimum size of the microstructure as described in any one of claims 1-8.

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