A macro-micro double scale structure topology optimization method and device capable of controlling minimum size of microstructure

Abstract

The present application belongs to the technical field of structure optimization design, and discloses a macro-micro double-scale structure topology optimization method and equipment capable of controlling the minimum size of microstructure, comprising the following steps: (1) interpolating the elastic matrix and the corresponding density of the actual microstructure in the offline database by using radial basis function interpolation, and then constructing a mapping model; (2) constructing a compliance minimization optimization model, wherein the design variables of the optimization model are the cutting height of two virtual microstructures in each unit and the topology variable, and the constraint functions are the volume fraction of the overall structure and the topology variable constraint; (3) calculating the sensitivity of the objective function and the constraint function to the design variable, and then updating the design variable; (4) when the compliance error of the updated double-scale structure meets the optimization termination condition, the optimization is completed and the double-scale structure meeting the requirements is obtained; otherwise, go to step (3). The present application solves the problems of low calculation efficiency and poor connectivity.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of structural optimization design, and more particularly to a macro-micro double-scale structure topology optimization method and device capable of controlling the minimum size of microstructure. BACKGROUND

[0002] Bamboo and animal bones in nature are typical double-scale structures. Through observation of this kind of double-scale structure in nature, it is found that the morphology of the unit cell at the microscale directly determines the performance of the material. Therefore, the double-scale structure optimization can more reasonably distribute microstructures of different shapes at the most suitable structure positions. The traditional M-VCUT double-scale optimization method is to perform optimization analysis in the full-scale framework, and each time the whole finite element needs to be recalculated. In order to ensure the accuracy of the results, the overall finite element mesh becomes very large due to the existence of microstructures in the structure, thereby increasing the consumption of calculation time.

[0003] In order to improve the calculation efficiency, an offline data-driven method is used for double-scale structure 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 does not update the mapping model in the optimization process. Therefore, the double-scale structure optimization under data driving can greatly improve the efficiency under the condition of ensuring the accuracy. However, the results obtained have many fine structures, and this kind of structure does not meet the manufacturing constraints and 3D printing requirements. Therefore, the method for controlling the minimum size of microstructure in macro-micro double-scale topology optimization is used to control the minimum size of microstructure, so as to realize the structure manufacturing.

[0004] Research shows that by using the method for controlling the minimum size of microstructure in macro-micro double-scale topology optimization, the calculation efficiency can be accelerated on the basis of the traditional M-VCUT method, and the minimum microstructure size requirement can be met.

[0005] At present, the double-scale structure optimization method still has problems in design: the double-scale structure optimization by the scale separation method needs to solve the connectivity problem of the microscale structure; the double-scale structure optimization by the scale correlation method is usually low in calculation efficiency. SUMMARY

[0006] In view of the above defects or improvement needs of the prior art, the present application provides a macro-micro double-scale structure topology optimization method and device capable of controlling the minimum size of microstructure, which aims to solve the problems of low calculation efficiency and poor connectivity of the existing topology optimization method.

[0007] To achieve the above-mentioned purpose, according to one aspect of the present application, a macro-micro double-scale structure topology optimization method capable of controlling the minimum size of microstructure is provided, which comprises the following steps:

[0008] Step one, using radial basis function interpolation to interpolate the elastic matrix and corresponding density of actual microstructure in offline database, and then constructing a mapping model of cutting height, topological variable, elastic parameter and density based on the interpolated data and offline database; wherein the acquisition of the offline database comprises the following steps:

[0009] S1, taking the cutting height and topological variable of each unit in the design domain of the double-scale structure as the design variable, using M-VCUT level set method to cut the level set function to obtain the virtual microstructure;

[0010] S2, multiplying the density of the obtained two virtual microstructures with the topological variable, and then obtaining the density of the actual microstructure of the unit by max set, and calculating the elastic matrix of each actual microstructure under the predetermined interval of cutting height and topological variable by homogenization method, and then forming the offline database by the obtained elastic matrix and corresponding density of the actual microstructure;

[0011] Step two, defining the double-scale structure optimization design problem based on the mapping model to obtain the compliance minimization optimization model, wherein the design variable of the compliance minimization optimization model is the cutting height and topological variable of the two virtual microstructures in each unit, the objective function is the minimum compliance of the double-scale structure, and the constraint function is the volume fraction and topological variable constraint of the overall structure;

[0012] Step three, calculating the sensitivity of the objective function and the constraint function to the design variable respectively, and updating the design variable based on the obtained sensitivity result;

[0013] Step four, when the updated double-scale structure compliance error meets the optimization termination condition, the optimization is completed and the required double-scale structure is obtained; otherwise, go to step three.

[0014] Further, the level set function and the cutting function are used to represent the combined function

[0015]

[0016] Wherein D is the reference domain, The cutting result is defined as virtual microstructure according to the positive and negative relationship

[0017]

[0018] Each virtual microstructure is assigned a topological variable A cut height is a cut plane.

[0019] Further, the density matrix of each virtual microstructure is calculated Thus the density matrix of each virtual microstructure is obtained

[0020]

[0021] Then, the density matrix of the final actual microstructure is obtained by combining the density matrix of the virtual microstructure:

[0022]

[0023] After obtaining the density of the actual microstructure, the actual microstructure is obtained:

[0024] Ω k = {x | p k (x) > 0, x ∈ D k}

[0025] Finally, the double-scale structure Ω is represented by the actual microstructure:

[0026]

[0027] In the formula, is a joint symbol, and the actual microstructure Ω k at each position is combined into the final overall double-scale structure Ω.

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

[0029]

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

[0031]

[0032] The elastic constant and volume fraction at any height are solved by using the multiple quadratic surface radial basis function interpolation formula and the offline database, and both types of design variables are uniformly represented by σ I :

[0033]

[0034] Where and γ iare the expansion coefficients in MQ-RBF; are the design variable information of the reference points stored in the offline database; are the Euclidean distances from the sought point to the reference points.

[0035] Further, the minimum compliance optimization model under the volume constraint and the topological variable constraint is solved with the cutting height and the topological variable as the design variables:

[0036] min c=F T U

[0037] s.t.KU=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 variable needs to satisfy; μ is a constant; U is the total displacement of the bimodal structure; V is the volume of the bimodal structure; β i is the topological variable; is the unit cutting height; h is the minimum value of the cutting height; is the maximum value of the cutting height.

[0043] Further, the sensitivity of the objective function to the design variable is expressed as:

[0044]

[0045] Meanwhile:

[0046] K e =B T DBtA e

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

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

[0049]

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

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

[0052] or l>l max ,

[0053] wherein c err is the compliance error, l is the current iteration number, epsilon is the lower limit value of the compliance error, l max is the upper limit value of the iteration number.

[0054] The application further provides a macro-micro double-scale structure topology optimization system capable of controlling the minimum size of microstructures, which comprises a memory and a processor, the memory stores a computer program, and the processor executes the computer program to execute the macro-micro double-scale structure topology optimization method capable of controlling the minimum size of microstructures.

[0055] The application further provides a computer readable storage medium, which stores machine executable instructions, and the machine executable instructions, when called and executed by a processor, cause the processor to implement the macro-micro double-scale structure topology optimization method capable of controlling the minimum size of microstructures.

[0056] Overall, compared with the prior art, the macro-micro double-scale structure topology optimization method and device capable of controlling the minimum size of microstructures provided by the application mainly have the following beneficial effects:

[0057] 1. The calculation efficiency is improved through data driving (offline database), and the microstructures obtained by using the M-VCUT level set cutting method also guarantee the connectivity problem, so that the application can guarantee the connectivity of the microstructures in the overall structure, greatly improve the optimization efficiency, and all the microstructures in the structure meet the minimum size requirement and have the manufacturability.

[0058] 2. The topology variable is introduced as a design variable, so that the double-scale structure with the minimum microstructure size constraint can be obtained, and the double-scale structure obtained can be used for direct 3D printing.

[0059] 3. The microstructure obtained by using the M-VCUT level set method is finally used to obtain the double-scale structure meeting the optimization requirement, the maximum structural stiffness is taken as the design target, the volume of the overall structure and the topology variable constraint are taken as the constraint condition, the design variable is updated by using the moving asymptote method until the optimization termination condition is met, and the optimal double-scale structure is obtained. BRIEF DESCRIPTION OF DRAWINGS

[0060] Figure 1 is a structure schematic diagram of the MBB beam double-scale structure optimization design provided by the embodiment of the application;

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

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

[0063] Figure 4 is an initial design drawing about double-scale structure optimization;

[0064] Figure 5 is an optimization result schematic drawing about double-scale structure when the method provided by the present application is adopted. DETAILED DESCRIPTION

[0065] In order to make the objectives, technical solutions and advantages of the present application clearer, the present application is further described in detail below with reference to the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and do not limit the present application. In addition, the technical features involved in each embodiment of the present application described below can be combined with each other as long as they do not conflict with each other.

[0066] The present application provides a macro-micro double-scale structure topological optimization method capable of controlling the minimum size of the microstructure, which mainly comprises the following steps:

[0067] Step 1: interpolating the elastic matrix and the corresponding density of the actual microstructure in the offline database by using the radial basis function interpolation, and then constructing a mapping model of the cutting height, the topological variable, the elastic parameter and the density based on the data obtained by interpolation and the offline database; wherein the acquisition of the offline database comprises the following steps:

[0068] S1: taking the cutting height and the topological variable of each unit in the design domain of the double-scale structure as the design variables, and using the M-VCUT level set method to perform cutting operation on the level set function to obtain the virtual microstructure.

[0069] In the embodiment, the cutting height H I and the topological variable β I of the two kinds of virtual microstructures used for composing the actual microstructure of each unit are taken as the design variables, wherein I = 1, 2,..., 2N, and N is the number of units;

[0070] The cutting height H I and the topological variable β I are combined to obtain the virtual microstructure in each unit, and the obtained virtual microstructure Combination of the two virtual microstructures k ; and obtaining the overall double-scale structure Ω using the actual microstructure.

[0071] S2, multiplying the densities of the two virtual microstructures obtained by their topological variables, and then obtaining the density of the actual microstructure of the unit by max set, and using the homogenization method to calculate the elastic matrix of each actual microstructure corresponding to the cutting height and topological variable of the predetermined interval, and the elastic matrix of the actual microstructure obtained and the corresponding density constitute an offline database.

[0072] The combination function obtained by one cutting operation is represented by a level set function and a cutting function

[0073]

[0074] where D is the reference domain, The cutting result is defined as a virtual microstructure according to the positive and negative relationship

[0075]

[0076] Each virtual microstructure is assigned a topological variable Therefore, the density matrix of each virtual microstructure needs to be obtained by calculation Thus, the density matrix of each virtual microstructure is obtained

[0077]

[0078] Then, the density matrix of the final actual microstructure is obtained by combining the density matrix of the virtual microstructure:

[0079]

[0080] With the density of the actual microstructure, the actual microstructure can be obtained:

[0081] Ω k = {x | ρ k (x) > 0, x ∈ D k}

[0082] Finally, the double-scale structure Ω is represented by the actual microstructure:

[0083]

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

[0085]

[0086] Where |V| represents the microstructure volume, E pqrs The local elastic tensor representing the microstructure, The known macroscopic strain field; at the same time It can also be represented in matrix form:

[0087]

[0088] In this embodiment, equidistant cutting heights H are selected in each unit. I and equidistant topological variables β I An offline database was created by using the homogenization formula to obtain the equivalent elasticity matrix and corresponding density of the M groups of actual microstructures. The elastic constants and volume fractions at any height were then solved using the multiple quadratic surface radial basis function (MQ-RBF) interpolation formula and the offline database. Both types of design variables were uniformly represented 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 reference points stored in an offline database; It is the Euclidean distance from the point in question 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)=p0+p1σ1+p2σ2+…+p M σ M

[0095] The stiffness matrix K of each element is established using the equivalent elastic matrix of the actual microstructure. e The stiffness matrix K corresponding to each of the aforementioned units e It is assembled into an overall stiffness matrix K.

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

[0097] Step two, define a bi-scale structure optimization design problem based on the mapping model to obtain a compliance minimization optimization model, the design variables of the compliance minimization optimization model are the cutting height and topology variable of each unit, the objective function is the compliance minimization of the bi-scale structure, and the constraint function is the volume fraction and topology variable constraint of the overall structure.

[0098] Solve the compliance minimization optimization model under the volume constraint and topology variable constraint with the cutting height and topology variable as the design variable:

[0099] min c=F T U

[0100] s.t.KU=F

[0101]

[0102] g βi ≤μ

[0103] 0≤β i ≤1

[0104]

[0105] Where i represents the type of microstructure; is the constraint that the topology variable needs to meet; μ is a constant.

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

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

[0108]

[0109] At the same time:

[0110] K e =B T DBtA e

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

[0112] It can be further expressed as:

[0113]

[0114] According to the interpolation formula mentioned above, it can be expressed as:

[0115] ​

[0116] wherein:

[0117]

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

[0119]

[0120] Step four, when the updated double-scale structure flexibility error meets the optimization termination condition, the optimization is completed and the double-scale structure meeting the requirements is obtained; otherwise, go to step three.

[0121] In one of the embodiments, the optimization termination condition is set as:

[0122] or l≥l max ,

[0123] wherein c err is the flexibility error, l is the current iteration number, ε is the lower limit value of the flexibility error, and l max is the upper limit value of the iteration number.

[0124] The application further provides a macro-micro double-scale structure topological optimization system capable of controlling the minimum size of microstructure, which comprises a memory and a processor, the memory stores a computer program, and the processor executes the computer program to execute the macro-micro double-scale structure topological optimization method capable of controlling the minimum size of microstructure as described above.

[0125] The application further provides a computer readable storage medium, which stores machine executable instructions, the machine executable instructions, when called and executed by a processor, cause the processor to implement the macro-micro double-scale structure topological optimization method capable of controlling the minimum size of microstructure as described above.

[0126] The application will be further described in detail below with specific embodiments.

[0127] Please refer to Figure 1 , the optimization problem of minimizing the flexibility of the plane MBB beam structure under the action of concentrated load is taken as an example to explain the application. An initialized double-scale structure is arranged in a given 3m*1m rectangular design domain D, the horizontal degree of freedom of the left side region is fixed, the vertical degree of freedom of the lower right corner region is limited, and a concentrated force f=1N is applied to the upper left corner region. The double-scale structure is optimized to maximize the stiffness under the premise that the cutting height of the optimization result is all above 0.1.

[0128] Please refer toFigure 3 The embodiment provides a macro-micro double-scale structure topology optimization method capable of controlling the minimum size of a microstructure, and the method comprises the following steps:

[0129] S1: taking the cutting height and the topology variable corresponding to each unit in the design domain of the double-scale structure as design variables, performing a cutting operation on a level set function by using an M-VCUT level set method to obtain a virtual microstructure;

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

[0131] S2: multiplying the density results of the two virtual microstructures and the respective topology variables, obtaining the density of the actual microstructure of the unit by taking the max set, and calculating the elastic matrix of each actual microstructure under a certain cutting height interval and topology variable interval by using a homogenization method;

[0132] Specifically, the two virtual microstructures are as shown in Figure 2 The actual combined microstructure prototype Ω in each unit is obtained by using a Boolean operation, and 21 groups of data from 0 to 1 with a cutting height interval of 0.05 and 26 groups of data from 0 to 1 with a topology variable interval of 0.04 corresponding to each virtual microstructure are obtained by using a homogenization method, wherein the offline database contains the equivalent elastic modulus D H and the equivalent volume fraction V H .

[0133] S3: converting the elastic matrix and the microstructure volume fraction in the offline database into the elastic matrix and the microstructure volume under any height and any topology variable by using an interpolation function.

[0134] Specifically, according to the interpolation formula, the nearest n reference design variables of the unknown design variable a are selected, and n is ensured to be greater than 1; the equivalent elastic modulus and the corresponding equivalent volume fraction of the unknown design variable are obtained by interpolation calculation. According to the finite element formula K e =B T DBtA e , the equivalent elastic modulus is converted into a unit stiffness matrix The stiffness matrix corresponding to each unit is assembled into a whole stiffness matrix K.

[0135] The whole displacement vector u is solved by using the formula Ku=f, and f is an external force vector, so that the finite element analysis of the double-scale structure is completed.

[0136] S4: define the bi-scale structure optimization design problem: the design variables are the cutting height of the two virtual microstructures in each unit and the topological variable, the design objective is the minimum flexibility of the bi-scale structure, and the design constraints are the volume fraction of the overall structure and the constraint on the topological variable;

[0137] Specifically, the minimum flexibility optimization model under the volume constraint is solved by taking the cutting height and the topological variable as the design variables:

[0138] min c=F T U

[0139] s.t.KU=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 variable, calculate the sensitivity of the constraint function to the design variable, and then update the design variable;

[0146] Specifically, according to the objective function, the constraint function and their sensitivity to the design variable, the design variables H I and β I are updated by combining the Method of Moving Asymptotes (usually referred to as MMA), which is an existing optimization algorithm and will not be described here. The updated H Inew and β Inew indicate the distribution of the actual microstructure of each unit, thereby obtaining the overall bi-scale structure.

[0147] Repeat S5, each repetition is called an iteration, until the optimization termination condition is met, and the optimal design of the bi-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 value of the flexibility error, which is 0.5% here, l max is the upper limit value of the iteration number, which is 500 here.

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

[0151] The optimized double-scale structure is shown in Figure 5 , and the flexibility value is 203.26. For comparison, the initial design of the double-scale structure is shown in Figure 4 , and the flexibility value is 806.16, which is reduced by about 74.79%. The microstructure cutting height in the optimized double-scale structure all satisfies h min >0.1, and the calculation efficiency is improved, and the microstructures are well connected.

[0152] Those skilled in the art will easily understand that the above description is only a preferred embodiment of the present application, and is not intended to limit the present application. Any modification, equivalent replacement and improvement made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A macro-micro bi-scale structure topology optimization method capable of controlling the minimum size of microstructure, characterized in that: The method comprises the following steps: Step one, using radial basis function interpolation to interpolate the elastic matrix and the corresponding density of the actual microstructure in the offline database, and then constructing a mapping model of cutting height, topological variable, elastic parameter and density based on the interpolated data and the offline database; wherein, the acquisition of the offline database comprises the following steps: S1, taking the cutting height and topological variable of each unit in the design domain of the double-scale structure as the design variable, using the M-VCUT level set method to cut the level set function to obtain the virtual microstructure; S2, multiplying the density of the obtained two virtual microstructures with the topological variable, and then obtaining the density of the actual microstructure of the unit by max set, and calculating the elastic matrix of each actual microstructure under the predetermined interval of cutting height and topological variable by using the homogenization method, and then the obtained elastic matrix and the corresponding density of the actual microstructure constitute the offline database; Step two, defining a double-scale structure optimization design problem based on the mapping model to obtain a compliance minimization optimization model, wherein the design variable of the compliance minimization optimization model is the cutting height and topological variable of the two virtual microstructures in each unit, the objective function is the minimum compliance of the double-scale structure, and the constraint function is the volume fraction and topological variable constraint of the overall structure; Step three, calculating the sensitivity of the objective function and the constraint function to the design variable, and updating the design variable based on the obtained sensitivity result; Step four, when the updated double-scale structure compliance error meets the optimization termination condition, the optimization is completed and the required double-scale structure is obtained; otherwise, go to step three.

2. The macro-micro bi-scale structure topology optimization method capable of controlling the minimum size of micro structure according to claim 1, wherein: with a level set function and a cut function representing the combined function resulting from a cut operation : where D is a reference domain, ; define the virtual microstructure according to the positive and negative relationship of the cutting result : Each virtual microstructure A topology variable is assigned ; For the cutting height, a cutting height is a cutting plane.

3. The macro-micro bi-scale structure topology optimization method capable of controlling the minimum size of micro structure according to claim 2, wherein: The density matrix of each virtual microstructure is obtained by calculation The density matrix of each virtual microstructure is obtained by calculation : Then, the density matrix of the final actual microstructure is obtained by combining the density matrix of the virtual microstructure: After obtaining the density of the actual microstructure, the actual microstructure is obtained: Ultimately, the actual microstructure is used to represent the bi-scale structure : wherein are the combined symbols and the actual microstructure at each position are combined into the final overall bi-scale structure .

4. The macro-micro bi-scale structure topology optimization method capable of controlling the minimum size of micro structure according to claim 1, wherein: According to the calculation homogenization theory, the macroscopic equivalent elastic tensor of the periodic microstructure is expressed as: wherein denotes the microstructure volume, denotes the local elastic tensor of the microstructure, is the known macroscopic strain field; while is also denoted in matrix form: The elastic constants and volume fraction at any height are solved by using the multiple quadratic surface radial basis function interpolation formula and off-line database. Both types of design variables are unified as represent: wherein and are the expansion coefficients in the MQ-RBF; is the design variable information of the reference points stored in the offline database; is the Euclidean distance from the sought point to the reference points.

5. The macro-micro bi-scale structure topology optimization method capable of controlling the minimum size of micro structure according to claim 4, characterized in that: The cutting height and topological variable are taken as the design variable to solve the compliance minimization optimization model under the volume constraint and topological variable constraint: wherein i represents the kind of microstructure; is a constraint that needs to be satisfied by the topological variable; is a constant; is the total displacement of the bi-scale structure; is the volume of the bi-scale structure; is the topological variable; is the unit cut height; is the minimum cut height; is the maximum cut height.

6. The macro-micro bi-scale structure topology optimization method capable of controlling the minimum size of micro structure according to claim 5, characterized in that: The sensitivity of the objective function to the design variable is expressed as: At the same time: where B is the element strain matrix, t is the element thickness, is the element area.

7. The macro-micro bi-scale structure topology optimization method capable of controlling the minimum size of micro structure according to claim 6, wherein: The sensitivity of the topological variable constraint function to the design variable is expressed as: In the formula, is a topological variable.

8. The macro-micro bi-scale structure topology optimization method capable of controlling the minimum size of micro structure according to any one of claims 1-7, characterized in that: The optimization termination condition is set as: wherein, is the compliance error, l is the current iteration number, is a lower limit value for the compliance error, is an upper limit value for the iteration number.

9. A macro-micro bi-scale structure topology optimization system capable of controlling the minimum size of microstructure, characterized in that: The system comprises a memory and a processor, the memory stores a computer program, and the processor executes the computer program to execute the macro-micro double-scale structure topology optimization method capable of controlling the minimum size of the microstructure according to any one of claims 1-8.

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

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