A periodic microstructure and its optimization design method

Abstract

The present invention provides a periodic microstructure and an optimization design method thereof, belonging to the technical field of aerospace structure design. The present invention adopts a linear material interpolation model to perform topological optimization of the microstructure, avoiding the convergence difficulties and local optimal problems caused by the high penalty factor in the traditional topological optimization method, thereby greatly improving the convergence and global optimization ability of the algorithm; the energy-based homogenization method provides fast and high-precision calculation support for the prediction of the equivalent macroscopic performance of the microstructure, and combines the periodic boundary conditions to achieve excellent connectivity at the macro and micro scales; the implicit 0 / 1 constraint function is applied through the floating projection technology, so that the optimization result presents a clear binary characteristic, can be accurately post-processed, has clear boundaries and has the characteristics of being directly used for additive manufacturing, greatly improving the feasibility and efficiency from design to manufacturing.

Description

Technical Field

[0001] The invention belongs to the technical field of aerospace structure design, and in particular relates to a periodic microstructure and an optimization design method thereof. Background Art

[0002] A porous structure is a microstructure with a periodic or non-periodic arrangement. Its unique geometric properties give it many advantages: (1) It has extremely high specific strength and specific stiffness, which enables it to significantly reduce weight while meeting strength requirements. This is the key to achieving lightweight design in the aerospace field. (2) The porous structure also has excellent thermal and acoustic properties, and can provide outstanding performance in heat exchangers or noise reduction devices in aerospace equipment.

[0003] In the related technology, the design of periodic microstructures in the aerospace field mainly adopts the method of topology optimization. Topology optimization is an inverse design method based on mathematical optimization. It automatically generates the optimal material distribution through algorithms and calculations, greatly improving the design efficiency. When facing microstructure design problems, most of the existing unit-based topology optimization methods are SIMP methods with material penalties, which ignore the 0 / 1 nature of the design variables. The use of material penalties can easily produce approximate solutions that meet the conditions. When facing microstructure design problems, due to the particularity of the problem, a higher material penalty factor p=5 is usually selected in order to obtain a solution closer to 0 / 1 and make the structure clearer. However, a high material penalty factor will bring difficulties to the convergence of the algorithm. At the same time, it increases the nonlinearity of the optimization problem, making the algorithm more likely to fall into a local optimal solution.

[0004] Therefore, it is necessary to provide a periodic microstructure and an optimization design method thereof to solve the above problems. Summary of the invention

[0005] The present invention provides a periodic microstructure and an optimization design method thereof, which adopts a linear material interpolation model to perform topological optimization of the microstructure, avoiding the convergence difficulty and local optimal problem caused by the high penalty factor in the traditional topological optimization method, thereby greatly improving the convergence and global optimization ability of the algorithm, and can effectively solve at least one technical problem involved in the background technology.

[0006] In order to solve the above-mentioned technical problems, the present invention is achieved as follows:

[0007] An optimization design method for a periodic microstructure comprises the following steps:

[0008] Step S1, creating an initial design domain of a non-uniform microstructure, dividing the initial design domain into a plurality of units, and selecting a constraint function and an objective function required for optimization according to the needs of engineering applications;

[0009] Step S2, performing finite element analysis by an energy-based homogenization method to calculate the equivalent elastic matrix of the periodic microstructure;

[0010] Step S3, applying linear material without material penalty to each unit based on the linear interpolation model, and calculating the sensitivity of the constraint function and the objective function to the design variables;

[0011] Step S4, updating the design variables according to the sensitivity of the objective function and the constraint function, and applying an implicit 0 / 1 constraint function to the design variables by means of floating projection;

[0012] Step S5, determining whether the convergence condition is met, if so, executing step S6; otherwise, returning to step S2;

[0013] Step S6, performing post-processing design on the structure, and obtaining an explicit structural boundary based on the design variable distribution combined with the level set function;

[0014] Step S7, using the energy-based homogenization method to solve the objective function of the smoothed structure, calculate the relative error of the post-processing design on the objective function, and determine whether the relative error is less than 1%. If so, end the optimization and perform periodic array to complete the design process. If not, use a stricter 0 / 1 constraint function and return to step S2.

[0015] As a preferred improvement, the objective function is expressed as:

[0016] ;

[0017] In the formula, represents the objective function; represents the design variable; Represents the weight factor, with a value range of 0-1. The larger the value, the higher the proportion in the objective function; represents the macroscopic equivalent elastic tensor; i , j , k , l represents the direction in the Cartesian coordinate system. When the microstructure is a two-dimensional structure, i , j , k , l The values ​​are 1 and 2, corresponding to x , y direction; when the microstructure is a three-dimensional structure, i , j , k , l The values ​​are 1, 2, and 3, corresponding to x , y , z direction.

[0018] As a preferred improvement, the optimization target is selected as maximizing the bulk modulus or maximizing the shear modulus; the constraint function is selected as the volume constraint function;

[0019] When the microstructure is a two-dimensional structure:

[0020] The objective function of maximizing the bulk modulus is expressed as:

[0021] ;

[0022] The objective function of maximizing the shear modulus is expressed as: ;

[0023] When the microstructure is a three-dimensional structure:

[0024] The objective function of maximizing the bulk modulus is expressed as:

[0025] ;

[0026] The objective function of maximizing the shear modulus is expressed as:

[0027] .

[0028] As a preferred improvement, based on the energy homogenization method, the displacement field of the macrostructure is expanded as follows:

[0029] ;

[0030] In the formula, x and y denote global macro variables and local micro variables respectively; represents the coupling coefficient; represents the displacement field of the macrostructure; represents the displacement of the macrostructure; represents the first-order disturbance term; represents the second-order disturbance term;

[0031] In the linear elastic stage, only the first-order expansion is considered, and the macroscopic equivalent elastic tensor is It is expressed as:

[0032] ;

[0033] in, represents the elastic modulus of the matrix material; p , q , r , s represents the direction in the Cartesian coordinate system. When the microstructure is a two-dimensional structure, p , q ,r , s The values ​​are 1 and 2, corresponding to x , y direction; when the microstructure is a three-dimensional structure, p , q , r , s The values ​​are 1, 2, and 3, corresponding to x , y , z direction; Represents the design domain, which represents the area in a two-dimensional structure and the volume in a three-dimensional structure; , represents the test strain field; , represents the periodic fluctuating strain field under the test strain field conditions;

[0034] Macroscopic equivalent elasticity tensor Solve it by the following formula:

[0035] ;

[0036] In the formula, represents the virtual displacement field; express j The basic unit size of the direction;

[0037] The energy-based method applies the unit test strain field directly to the boundary. According to the basic mutual energy principle, the macroscopic equivalent elastic tensor Rephrased as:

[0038] ;

[0039] In the formula, , represents the superimposed strain field;

[0040] Written in finite element form as follows:

[0041] ;

[0042] In the formula, Indicates the serial number of the finite element unit; N represents the total number of finite element elements; , represents the unit displacement vector; T represents the matrix transpose; represents the element stiffness matrix;

[0043] When the microstructure is a two-dimensional structure, the elastic tensor is expanded as follows:

[0044] ;

[0045] When the microstructure is a three-dimensional structure, the elastic tensor is expanded as follows:

[0046] .

[0047] As a preferred improvement, in step S3, the linear interpolation model is expressed as:

[0048] ;

[0049] In the formula, Representation unit e Young's modulus; represents the Young's modulus of the initial material;

[0050] According to the adjoint method, the sensitivity of the objective function to the design variables is as follows:

[0051] ;

[0052] In the formula, represents the element stiffness matrix with unit Young's modulus;

[0053] The sensitivity of the volume constraint function to the design variables is as follows:

[0054] ;

[0055] In the formula, A volume constraint function representing the optimization problem; Represents the volume of the unit.

[0056] As a preferred improvement, in step S4, the design variables are updated by an optimality criterion method, a moving asymptote method or a sequential linear programming method.

[0057] As a preferred improvement, the design variables are updated by the optimality criterion method, and the update strategy is as follows:

[0058] ;

[0059] In the formula, Indicates k +1 design variables during the iteration; Indicates k The design variables in the iteration process; C represents the abbreviated form of the objective function; V Represents the abbreviated form of the volume constraint function; represents the Lagrange multiplier, solved using the bisection method.

[0060] As a preferred improvement, in step S4, the floating projection process is expressed as follows:

[0061] ;

[0062] In the formula, represents the density after projection; th Represents the projection threshold, which is determined using the binary method to ensure that the volume of the structure remains unchanged before and after projection. th When , the density of the unit is projected toward 0, otherwise, the density of the unit is projected toward 1; β Represents the control parameter, which is used to control the design variable The strictness with which the 0 / 1 constraint function is enforced, β The larger the value, the stricter the execution of the 0 / 1 constraint function; Represents the filter weight factor.

[0063] As a preferred improvement, in step S6, the level set function established is , the design variables are truncated by the threshold to obtain different level set function values, and different values ​​represent different areas:

[0064] .

[0065] A periodic microstructure is designed by using the above-mentioned optimization design method for periodic microstructure.

[0066] The beneficial effects of the present invention are:

[0067] (1) The linear material interpolation model is used for topology optimization of microstructures, which avoids the convergence difficulties and local optimal problems caused by high penalty factors in traditional topology optimization methods, thereby greatly improving the convergence and global optimization capabilities of the algorithm;

[0068] (2) The energy-based homogenization method provides fast and high-precision computational support for the prediction of the equivalent macroscopic performance of microstructures, and combines periodic boundary conditions to achieve excellent connectivity at the macro and micro scales;

[0069] (3) By applying an implicit 0 / 1 constraint function through floating projection technology, the optimization results present clear binary characteristics, can be accurately post-processed, have clear boundaries and have the characteristics of being directly used in additive manufacturing, greatly improving the feasibility and efficiency from design to manufacturing;

[0070] (4) The method demonstrates the ability to precisely control target performance in the optimization design and can be widely used in high-performance structural design in the fields of aerospace, heat conduction, acoustic absorption, etc. The experimental results show that the performance of the microstructure designed by the present invention is close to the theoretical limit. Compared with the traditional SIMP-based method, the performance level and manufacturing adaptability of the optimization results are significantly improved, showing great industrialization potential and scientific value. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for describing the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative work, among which:

[0072] Figure 1 A flow chart showing an optimization design method for a periodic microstructure provided by the present invention;

[0073] Figure 2 The figure shows the design domain and the optimization design result in Example 1;

[0074] Figure 3 A comparison diagram showing the optimized design results in Example 1 and the prior art;

[0075] Figure 4 The figure shows the design domain and the optimization design result in Example 2;

[0076] Figure 5 The figure shows the design domain and the optimization design result in Example 3. DETAILED DESCRIPTION

[0077] The following will be combined with the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0078] like Figure 1-Figure 5 As shown, this embodiment provides an optimization design method for a periodic microstructure, comprising the following steps:

[0079] Step S1, creating an initial design domain of a non-uniform microstructure, dividing the initial design domain into multiple units, and selecting constraint functions and objective functions required for optimization according to the needs of engineering applications.

[0080] In this embodiment, the initial design domain is a square area with holes arranged inside, the hole shape is circular or square, and the number of holes is arbitrary. When the number of holes is one, it is arranged at the center of the initial design domain; when the number of holes is two or more, they are evenly distributed along the initial design domain. For example, when the number of holes is two, they are symmetrically distributed along the center of the initial design domain; when the number of holes is three or four, they are distributed in a ring array along the center of the initial design domain; when the number of holes is five, one of the holes is arranged at the center of the initial design domain, and the other four are distributed in a ring array along the center of the initial design domain.

[0081] The objective function is expressed as:

[0082] ;

[0083] In the formula, represents the objective function; represents the design variable; Represents the weight factor, with a value range of 0-1. The larger the value, the higher the proportion in the objective function; represents the macroscopic equivalent elastic tensor; i , j , k , l represents the direction in the Cartesian coordinate system. When the microstructure is a two-dimensional structure, i , j , k , l The values ​​are 1 and 2, corresponding to x , y direction; when the microstructure is a three-dimensional structure, i , j , k , l The values ​​are 1, 2, and 3, corresponding to x , y , z direction.

[0084] In the application scenarios of aerospace, the optimization objective is generally selected as maximizing the bulk modulus or maximizing the shear modulus, and the constraint function is selected as the volume constraint function.

[0085] When the microstructure is a two-dimensional structure:

[0086] The objective function of maximizing the bulk modulus is expressed as:

[0087] ;

[0088] The objective function of maximizing the shear modulus is expressed as: ;

[0089] When the microstructure is a three-dimensional structure:

[0090] The objective function of maximizing the bulk modulus is expressed as:

[0091] ;

[0092] The objective function of maximizing the shear modulus is expressed as:

[0093] .

[0094] Step S2, performing finite element analysis by an energy-based homogenization method to calculate the equivalent elastic matrix of the periodic microstructure.

[0095] Based on the energy homogenization method, the displacement field of the macrostructure is expanded as follows:

[0096] ;

[0097] In the formula, x and y denote global macro variables and local micro variables respectively; represents the coupling coefficient; represents the displacement field of the macrostructure; represents the displacement of the macrostructure; represents the first-order disturbance term; represents the second-order disturbance term;

[0098] In the linear elastic stage, only the first-order expansion is considered, and the macroscopic equivalent elastic tensor is It is expressed as:

[0099] ;

[0100] in, represents the elastic modulus of the matrix material; p , q , r , s represents the direction in the Cartesian coordinate system. When the microstructure is a two-dimensional structure, p , q , r , s The values ​​are 1 and 2, corresponding to x , y direction; when the microstructure is a three-dimensional structure, p , q , r , s The values ​​are 1, 2, and 3, corresponding to x , y , z direction; Represents the design domain, which represents the area in a two-dimensional structure and the volume in a three-dimensional structure; , represents the test strain field; , represents the periodic fluctuating strain field under the test strain field conditions;

[0101] Macroscopic equivalent elasticity tensor Solve it by the following formula:

[0102] ;

[0103] In the formula, represents the virtual displacement field; express j The basic unit size of the direction;

[0104] The energy-based method applies the unit test strain field directly to the boundary. According to the basic mutual energy principle, the macroscopic equivalent elastic tensor Rephrased as:

[0105] ;

[0106] In the formula, , represents the superimposed strain field;

[0107] Written in finite element form as follows:

[0108] ;

[0109] In the formula, Indicates the serial number of the finite element unit; N represents the total number of finite element elements; , represents the unit displacement vector; T represents the matrix transpose; represents the element stiffness matrix;

[0110] When the microstructure is a two-dimensional structure, the elastic tensor is expanded as follows:

[0111] ;

[0112] When the microstructure is a three-dimensional structure, the elastic tensor is expanded as follows:

[0113] .

[0114] Step S3, applying linear material without material penalty to each unit based on the linear interpolation model, and calculating the sensitivity of the constraint function and the objective function to the design variables.

[0115] The linear interpolation model is expressed as:

[0116] ;

[0117] In the formula, Representation unit e Young's modulus; represents the Young's modulus of the initial material;

[0118] According to the adjoint method, the sensitivity of the objective function to the design variables is as follows:

[0119] ;

[0120] In the formula, represents the element stiffness matrix with unit Young's modulus;

[0121] The sensitivity of the volume constraint function to the design variables is as follows:

[0122] ;

[0123] In the formula, A volume constraint function representing the optimization problem; Represents the volume of the unit.

[0124] Step S4, updating the design variables according to the sensitivity of the objective function and the constraint function, and applying an implicit 0 / 1 constraint function to the design variables by means of floating projection.

[0125] The design variables are updated by the optimality criterion method, the moving asymptote method or the sequential linear programming method. In this embodiment, the design variables are updated by the optimality criterion method, and the update strategy is as follows:

[0126] ;

[0127] In the formula, represents the design variable in the k+1th iteration process; Indicates k The design variables in the iteration process; C represents the abbreviated form of the objective function; V represents the abbreviated form of the volume constraint function; represents the Lagrange multiplier, solved using the bisection method.

[0128] In topology optimization, when global design variables are used, most methods use material penalties to obtain approximate solutions, which can solve the optimization problem well. However, there are the following problems: Even when material penalties are used, there are still a certain number of intermediate units in the optimization results. In order to obtain a clearer structure, a larger penalty will be used in the microstructure design, which will affect the convergence and optimization ability of the algorithm. For some problems such as displacement minimization, material penalties cannot be imposed, but linear material interpolation cannot obtain a clear topological solution. There is a lack of corresponding technical means to solve such problems. Therefore, in order to reduce the number of intermediate units and obtain a clear optimized configuration, a clear optimized configuration is obtained through floating projection. The process of floating projection is expressed as:

[0129] ;

[0130] In the formula, represents the density after projection; th Represents the projection threshold, which is determined using the binary method to ensure that the volume of the structure remains unchanged before and after projection. th When , the density of the unit is projected toward 0, otherwise, the density of the unit is projected toward 1; β Represents the control parameter, which is used to control the design variable The strictness with which the 0 / 1 constraint function is enforced, β The larger the value, the stricter the execution of the 0 / 1 constraint function; Represents the filter weight factor.

[0131] Step S5, determine whether the convergence condition is met, if so, execute step S6; otherwise, return to step S2.

[0132] The convergence condition is that the maximum change of the design variable is less than 0.001.

[0133] Step S6, performing post-processing design on the structure, and obtaining an explicit structural boundary based on the design variable distribution combined with the level set function.

[0134] The established level set function is , the design variables are truncated by the threshold to obtain different level set function values, and different values ​​represent different areas:

[0135] .

[0136] Step S7, using the energy-based homogenization method to solve the objective function of the smoothed structure, calculate the relative error of the post-processing design on the objective function, and determine whether the relative error is less than 1%. If so, end the optimization and perform periodic array to complete the design process. If not, use a stricter 0 / 1 constraint function and return to step S2.

[0137] A stricter 0 / 1 constraint function selects the larger one in the floating projection β The method adopted in this implementation is to increase the original β value by 0.5.

[0138] This embodiment also provides a periodic microstructure, which is designed using the above-mentioned optimization design method for periodic microstructure.

[0139] Example 1

[0140] like Figure 2 As shown, in this embodiment, the design domain of the non-uniform periodic microstructure is a square area, a circular hole with a radius of 0.3 times the side length is set at its center, and topological optimization is performed with the goal of maximizing the bulk modulus. The optimization goal is expressed as:

[0141] ;

[0142] Input optimization parameters, the number of grids is 100×100, the filter radius is 3, the β value in the floating projection is 1, and the volume constraint function is set to 0.25, 0.3, 0.4, and 0.5 respectively. By applying periodic boundary conditions, the good connectivity of the structure is guaranteed, and at the same time, the requirements of the energy-based homogenization method for the periodic arrangement of the structure are strictly ensured, and the optimization design method provided by the present invention is used for optimization design.

[0143] Figure 2 The optimized structure is also shown in the figure, including the microstructure unit cell, periodic array and effective elastic tensor. The bulk modulus of the final structure is 1.68, and the optimized structure has a clear display boundary, which can be used for the next step of optimization or processing. The output result can be a periodic array structure. Taking the 5×3 periodic array in the figure as an example, any periodic arrangement can be output in a format that can be used for additive manufacturing.

[0144] Figure 3 The property curves of the structural properties obtained by the method of the present invention and the HS theoretical upper limit, as well as the microstructure optimized by the traditional SIMP method. As can be seen from the figure, the bulk modulus of the structure designed by the microstructure design method proposed in the present invention is very close to the limit bulk modulus obtained by theoretical calculation. At the same time, compared with the traditional SIMP method, the design method obtains a larger bulk modulus, which shows that the algorithm has a stronger optimization ability and obtains a better structure.

[0145] Example 2

[0146] In this embodiment, the initial design domain is replaced on the basis of embodiment 1, and the optimization steps are consistent with embodiment 1. The initial design domain and the optimized results are shown in FIG. Figure 4 shown.

[0147] Example 3

[0148] This embodiment changes the optimization target based on the embodiment 2, and the initial design domain and the optimization steps are consistent with the embodiment 2. The initial design domain and the optimized results are shown in Figure 5 shown.

[0149] In this embodiment, the maximization of shear modulus is taken as the optimization goal, and the objective function is expressed as:

[0150] .

[0151] The embodiments of the present invention are described above in conjunction with the accompanying drawings, but the present invention is not limited to the above-mentioned specific implementation modes, which are merely illustrative rather than restrictive. Under the guidance of the present invention, ordinary technicians in this field can also make many forms without departing from the scope of protection of the present invention and the claims, all of which are within the protection of the present invention.

Claims

1. A method for optimizing the design of a periodic microstructure, characterized in that: The steps include: Step S1, creating an initial design domain of a non-uniform microstructure, dividing the initial design domain into a plurality of units, and selecting a constraint function and an objective function required for optimization according to the needs of engineering applications; Step S2, performing finite element analysis by an energy-based homogenization method to calculate the equivalent elastic matrix of the periodic microstructure; Step S3, applying linear material without material penalty to each unit based on the linear interpolation model, and calculating the sensitivity of the constraint function and the objective function to the design variables; Step S4, updating the design variables according to the sensitivity of the objective function and the constraint function, and applying an implicit 0 / 1 constraint function to the design variables by means of floating projection; Step S5, determining whether the convergence condition is met, if so, executing step S6; otherwise, returning to step S2; Step S6, performing post-processing design on the structure, and obtaining an explicit structural boundary based on the design variable distribution combined with the level set function; Step S7, using the energy-based homogenization method to solve the objective function of the smoothed structure, calculate the relative error of the post-processing design on the objective function, and determine whether the relative error is less than 1%. If so, end the optimization and perform periodic array to complete the design process. If not, use a stricter 0 / 1 constraint function and return to step S2; The objective function is expressed as: ； In the formula, represents the objective function; represents the design variable; Represents the weight factor, with a value range of 0-1. The larger the value, the higher the proportion in the objective function; represents the macroscopic equivalent elastic tensor; i , j , k , l represents the direction in the Cartesian coordinate system. When the microstructure is a two-dimensional structure, i , j , k , l The values ​​are 1 and 2, corresponding to x , y direction; when the microstructure is a three-dimensional structure, i , j , k , l The values ​​are 1, 2, and 3, corresponding to x , y , z direction; The optimization objective is selected as maximizing the bulk modulus or maximizing the shear modulus; the constraint function is selected as the volume constraint function; When the microstructure is a two-dimensional structure: The objective function of maximizing the bulk modulus is expressed as: ； The objective function of maximizing the shear modulus is expressed as: ; When the microstructure is a three-dimensional structure: The objective function of maximizing the bulk modulus is expressed as: ； The objective function of maximizing the shear modulus is expressed as: 。 2. The optimization design method of periodic microstructure according to claim 1, characterized in that: Based on the energy homogenization method, the displacement field of the macrostructure is expanded as follows: ； In the formula, x and y denote global macro variables and local micro variables respectively; represents the coupling coefficient; represents the displacement field of the macrostructure; represents the displacement of the macrostructure; represents the first-order disturbance term; represents the second-order disturbance term; In the linear elastic stage, only the first-order expansion is considered, and the macroscopic equivalent elastic tensor is It is expressed as: ； in, represents the elastic modulus of the matrix material; p , q , r , s represents the direction in the Cartesian coordinate system. When the microstructure is a two-dimensional structure, p , q , r , s The values ​​are 1 and 2, corresponding to x , y direction; when the microstructure is a three-dimensional structure, p , q , r , s The values ​​are 1, 2, and 3, corresponding to x , y , z direction; Represents the design domain, which represents the area in a two-dimensional structure and the volume in a three-dimensional structure; , represents the test strain field; , represents the periodic fluctuating strain field under the test strain field conditions; Macroscopic equivalent elasticity tensor Solve it by the following formula: ； In the formula, represents the virtual displacement field; express j The basic unit size of the direction; The energy-based method applies the unit test strain field directly to the boundary. According to the basic mutual energy principle, the macroscopic equivalent elastic tensor Rephrased as: ； In the formula, , represents the superimposed strain field; Written in finite element form as follows: ； In the formula, Indicates the serial number of the finite element unit; N represents the total number of finite element elements; , represents the unit displacement vector; T represents the matrix transpose; represents the element stiffness matrix; When the microstructure is a two-dimensional structure, the elastic tensor is expanded as follows: ； When the microstructure is a three-dimensional structure, the elastic tensor is expanded as follows: 。 3. The optimization design method of periodic microstructure according to claim 2, characterized in that: In step S3, the linear interpolation model is expressed as: ； In the formula, Representation unit e Young's modulus; represents the Young's modulus of the initial material; According to the adjoint method, the sensitivity of the objective function to the design variables is as follows: ； In the formula, represents the element stiffness matrix with unit Young's modulus; The sensitivity of the volume constraint function to the design variables is as follows: ； In the formula, A volume constraint function representing the optimization problem; Represents the volume of the unit.

4. The optimization design method of periodic microstructure according to claim 3, characterized in that: In step S4, the design variables are updated by an optimality criterion method, a moving asymptote method or a sequential linear programming method.

5. The optimization design method of periodic microstructure according to claim 4, characterized in that: The design variables are updated using the optimality criterion method, and the update strategy is as follows: ； In the formula, Indicates k +1 design variables during the iteration; Indicates k The design variables in the iteration process; C represents the abbreviated form of the objective function; V Represents the abbreviated form of the volume constraint function; represents the Lagrange multiplier, solved using the bisection method.

6. The optimization design method of periodic microstructure according to claim 5, characterized in that: In step S4, the process of floating projection is expressed as: ； In the formula, represents the density after projection; th Represents the projection threshold, which is determined by the binary method to ensure that the volume of the structure remains unchanged before and after projection. th When , the density of the unit is projected toward 0, otherwise, the density of the unit is projected toward 1; β Represents the control parameter, which is used to control the design variable The strictness with which the 0 / 1 constraint function is enforced, β The larger the value, the stricter the execution of the 0 / 1 constraint function; Represents the filter weight factor.

7. The optimization design method of periodic microstructure according to claim 6, characterized in that: In step S6, the level set function established is , the design variables are truncated by the threshold to obtain different level set function values, and different values ​​represent different areas: 。 8. A periodic microstructure, characterized in that The periodic microstructure is designed by using the optimization design method of any one of claims 1 to 7.

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