Quasi-periodic hierarchical topology optimization method based on corrosion-diffusion operator

Abstract

The application discloses a quasi-periodic hierarchical structure topology optimization method based on an erosion-diffusion operator, and comprises the following steps: establishing a structure model; performing erosion-diffusion operation on a microstructure to obtain a quasi-periodic microstructure library; predicting the equivalent elastic tensor of the microstructure in the quasi-periodic microstructure library by using an asymptotic homogenization method; based on the obtained elastic modulus of the microstructure database, an explicit function relationship between the microstructure elastic modulus and the volume fraction is established by using a B-spline function fitting, and an optimization model is established; according to the optimization model, the sensitivity of the compliance function of the structure with respect to the two types of design variables, i.e., the macroscopic topological variable and the microscopic topological variable, is calculated; according to the obtained sensitivity information, the design variables are iteratively updated, and the collaborative optimization design of the microscopic unit density and the macroscopic unit density is completed; and the geometric model of the entire heterogeneous structure is obtained by reconstructing the macroscopic and microscopic optimization results of the optimization model.

Description

Technical Field

[0001] This invention belongs to the field of structural topology optimization technology, and particularly relates to a quasi-periodic hierarchical structure topology optimization method based on erosion-diffusion operators. Background Technology

[0002] The statements in this section are merely background information relating to this disclosure and do not necessarily constitute prior art.

[0003] Biological structures in nature, such as animal skeletons and plant stems, are mostly hierarchical structures. Their geometric characteristics exhibit configurations at multiple scales, including macroscopic, sub-macroscopic, and microscopic, demonstrating high specific stiffness, defect resistance, and multifunctionality. Inspired by this, many artificial hierarchical structures, such as sandwich panels and lattice materials, are widely used in aerospace, biomedical, and other fields. In recent years, the rapid development of advanced manufacturing technologies, especially additive manufacturing, has provided powerful tools for the fabrication of hierarchical structures with complex geometries, while also placing higher demands on the design methods of hierarchical structures.

[0004] Topology optimization is an advanced and intelligent structural design method that designs optimal structural configurations that meet specific performance / material constraints by finding the optimal distribution of materials. Designing hierarchical structures using topology optimization has become a research hotspot in this field. The earliest known application can be traced back to reference 1 (“Rodrigues, H., Guedes, JM, and Bendsoe, MP (2002). Hierarchical optimization of material and structure. Structural and Multidisciplinary Optimization 24, 1-10”), which discloses a nested, heterogeneous hierarchical structure topology optimization solution strategy. This strategy can obtain the optimal material property distribution and obtain the corresponding microstructure configuration through an inverse homogenization method. However, such methods involve huge computational costs and are difficult to solve multi-constraint, multi-physics optimization problems, limiting their application scope.

[0005] Reference 2 (“Liu, L., Yan, J., and Cheng, G. (2008). Optimum structure with homogeneous optimum truss-like material. Computers & Structures 86, 1417-1425”) proposes a topology optimization method for periodic hierarchical structures. This method is a single-layer optimization model, which has the advantages of fewer design variables, lower computational cost, and better versatility. Furthermore, the obtained periodic hierarchical structure does not exhibit interface discontinuities between microstructures. However, since the periodic hierarchical structure contains only one type of microstructure configuration at the macroscopic scale, the design space is relatively small, and the improvement in structural performance is limited.

[0006] Reference 3 (“Zhang, P.; Toman, J.; Yu, Y.; Biyikli, E.; Kirca, M.; Chmielus, M.; To, AC (2015) Efficient Design-Optimization of Variable-Density Hexagonal Cellular Structure by Additive Manufacturing: Theory and Validation. Journal of Manufacturing Science & Engineering, 137”) proposes an optimization method for quasi-periodic hierarchical structures. By optimizing the macroscopic distribution of pore diameters within a single cell, the structural performance can be effectively improved, and additive manufacturing technology is used for fabrication. However, this method does not optimize the microstructure topology.

[0007] Reference 4 (“Wang,Y.;Chen,F.;Wang,MY (2017) Concurrent design with connectable graded microstructures. Computer Methods in Applied Mechanics and Engineering, 317, 84-101.”) discloses a quasi-periodic hierarchical structure topology optimization method based on the level set framework, but it cannot be directly applied to the most widely used variable density method topology optimization framework.

[0008] In summary, the hierarchical topology optimization methods disclosed in the prior art have irreconcilable contradictions in terms of computational efficiency, scope of application, and structural performance. Summary of the Invention

[0009] To overcome the shortcomings of the prior art, this invention provides a quasi-periodic hierarchical structure topology optimization method based on the corrosion-diffusion operator. By optimizing the topology configuration at both the macroscopic and microscopic scales, the method can improve structural performance while reducing computational load and expanding the scope of application.

[0010] To achieve the above objectives, one or more embodiments of the present invention provide the following technical solutions:

[0011] Quasi-periodic hierarchical topology optimization methods based on erosion-diffusion operators include:

[0012] Establish a structural model and mesh it with finite element mesh; define the micro-design domain for topology optimization and mesh it with micro-mesh.

[0013] A library of quasi-periodic microstructures was obtained by performing corrosion-diffusion operations on the microstructures.

[0014] The equivalent elastic tensor of microstructures in the quasi-periodic microstructure library is predicted using an asymptotic homogenization method.

[0015] Based on the elastic modulus obtained from the microstructure database, an explicit functional relationship between the elastic modulus of the microstructure and the volume fraction ratio is established by fitting B-spline functions, and an optimization model is established.

[0016] Based on the optimization model, the sensitivity of the structure's compliance function to macroscopic and microscopic design variables was calculated.

[0017] Based on the obtained sensitivity information, the design variables are iteratively updated to complete the collaborative optimization design of micro density and macro density;

[0018] The geometric model of the entire heterogeneous structure is obtained by reconstructing the macroscopic and microscopic optimization results obtained from the optimization model.

[0019] A further technical solution involves selecting a square or cubic structure for the micro-design domain and dividing it into quadrilateral or hexahedral meshes.

[0020] A further technical solution defines the micro-unit density as a first-class design variable and the macro-unit density as a second-class design variable.

[0021] A further technical solution involves substituting the obtained microstructure elastic modulus into the finite element method formula to calculate the element stiffness matrix, and then performing finite element analysis to obtain the macroscopic displacement field. In the corresponding topology optimization problem, the objective function is defined as minimizing the compliance of the structure, with the constraint that the amount of micromaterial used is less than the volumetric material. and the amount of macroscopic material used is less than the volume Establish an optimization model.

[0022] A further technical solution is that the method for reconstructing the geometric model is to use a boundary recognition program to identify the geometric boundaries of the microstructure obtained from the optimized model.

[0023] A further technical solution involves importing the boundary into geometry software to reconstruct the unit cell geometric model: using the optimization results and the created unit cell geometric model, the entire heterogeneous bi-level model obtained through optimization is reconstructed.

[0024] This invention discloses the application of the above-mentioned quasi-periodic hierarchical structure topology optimization method based on erosion-diffusion operators in the fields of 3D printing, aerospace structures and biomedicine.

[0025] Quasi-periodic hierarchical topology optimization system based on erosion-diffusion operators includes:

[0026] The structural model building module builds the structural model and meshes it with finite element meshes; it also defines the micro-design domain for topology optimization and meshes it with micro-meshes.

[0027] The model building module is optimized to perform corrosion-diffusion operations on microstructures to obtain a library of quasi-periodic microstructures;

[0028] The equivalent elastic tensor of microstructures in the quasi-periodic microstructure library is predicted using an asymptotic homogenization method.

[0029] Based on the elastic modulus obtained from the microstructure database, an explicit functional relationship between the elastic modulus of the microstructure and the volume fraction ratio is established by fitting B-spline functions, and an optimization model is established.

[0030] The geometric model reconstruction module calculates the sensitivity of the structure's compliance function to two types of design variables: macroscopic design variables and micro-unit cell size variables, based on the optimization model.

[0031] Based on the obtained sensitivity information, the design variables are iteratively updated to complete the collaborative optimization design of micro density, macro density and size variables;

[0032] The geometric model of the entire heterogeneous structure is obtained by reconstructing the macroscopic and microscopic optimization results obtained from the optimization model.

[0033] A computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that the processor performs the following steps when executing the program:

[0034] Establish a structural model and mesh it with finite element mesh; define the micro-design domain for topology optimization and mesh it with micro-mesh.

[0035] A library of quasi-periodic microstructures was obtained by performing corrosion-diffusion operations on the microstructures.

[0036] The equivalent elastic tensor of microstructures in the quasi-periodic microstructure library is predicted using an asymptotic homogenization method.

[0037] Based on the elastic modulus obtained from the microstructure database, an explicit functional relationship between the elastic modulus of the microstructure and the volume fraction ratio is established by fitting B-spline functions, and an optimization model is established.

[0038] Based on the optimization model, the sensitivity of the structure's compliance function to two types of design variables—macro-design variables and micro-unit cell size variables—was calculated.

[0039] Based on the obtained sensitivity information, the design variables are iteratively updated to complete the collaborative optimization design of micro density, macro density and size variables;

[0040] The geometric model of the entire heterogeneous structure is obtained by reconstructing the macroscopic and microscopic optimization results obtained from the optimization model.

[0041] A computer-readable storage medium having a computer program stored thereon, characterized in that the program, when executed by a processor, performs the following steps:

[0042] Establish a structural model and mesh it with finite element mesh; define the micro-design domain for topology optimization and mesh it with micro-mesh.

[0043] A library of quasi-periodic microstructures was obtained by performing corrosion-diffusion operations on the microstructures.

[0044] The equivalent elastic tensor of microstructures in the quasi-periodic microstructure library is predicted using an asymptotic homogenization method.

[0045] Based on the elastic modulus obtained from the microstructure database, an explicit functional relationship between the elastic modulus of the microstructure and the volume fraction ratio is established by fitting B-spline functions, and an optimization model is established.

[0046] Based on the optimization model, the sensitivity of the structure's compliance function to two types of design variables—macro-design variables and micro-unit cell size variables—was calculated.

[0047] Based on the obtained sensitivity information, the design variables are iteratively updated to complete the collaborative optimization design of micro density, macro density and size variables;

[0048] The geometric model of the entire heterogeneous structure is obtained by reconstructing the macroscopic and microscopic optimization results obtained from the optimization model.

[0049] The above one or more technical solutions have the following beneficial effects:

[0050] (1) This invention establishes a quasi-periodic hierarchical structure topology description method under the variable density method framework through the corrosion-diffusion operator. This description method is applicable to any microstructure topology configuration and has the characteristics of wide applicability and simple mathematical derivation. It can effectively solve the problem that the single cell in the prior art limits the performance potential of the microstructure. The method of this invention can realize the spatial transformation of material properties by adjusting the spatial distribution of the quasi-periodic cell.

[0051] (2) Compared with traditional periodic macro-micro structure topology optimization design, the optimization method proposed in this invention can improve the stiffness of 3D printed structures by more than 200%, further unleash the performance potential of microstructures, and significantly improve the performance of 3D printed structures. At the same time, the optimization model format in the optimization method proposed in this invention is simple and convenient for considering multi-constraint and multi-physics problems. Attached Figure Description

[0052] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0053] Figure 1 This is a schematic diagram of the two types of design variables (micro-unit density and macro-unit density) in Example 1;

[0054] Figure 2 This is a schematic diagram of the boundary conditions, dimensions, and loads of the design domain model in Example 1;

[0055] Figure 3 This refers to the quasi-periodic single-cell library generated based on the corrosion-diffusion operator in Example 1;

[0056] Figure 4 The equivalent elasticity matrix fitting curve of the quasi-periodic unit cell library in Example 1;

[0057] Figures 5(a)-5(b) Figure 5(a) shows the topology optimization design diagrams for Example 1 and Comparative Example 1; where Figure 5(b) is Comparative Example 1 and Figure 5(a) is Example 1.

[0058] Figures 6(a)-6(b) Figure 6(a) shows the effect diagrams of the 3D printed parts of the topology optimization design results in Example 1 and Comparative Example 1; wherein, Figure 6(b) is Comparative Example 1 and Figure 6(a) is Example 1. Detailed Implementation

[0059] It should be noted that the following detailed descriptions are exemplary and intended to provide further illustration of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0060] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the scope of exemplary embodiments according to the invention. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0061] Where there is no conflict, the embodiments and features in the embodiments of the present invention can be combined with each other.

[0062] The overall concept proposed in this invention is as follows:

[0063] By implementing quasi-periodic unit cell topology description under the variable density method framework through corrosion-diffusion operators, the bottleneck of existing technologies being unable to perform quasi-periodic transformations on arbitrary unit cells can be effectively addressed. Furthermore, by co-optimizing the unit cell topology and its spatial distribution, the spatial distribution optimization of material properties can be achieved, further enhancing structural performance.

[0064] Example 1

[0065] This application discloses a quasi-periodic hierarchical structure topology optimization method based on corrosion-diffusion operators. Step 1: For the design case, establish a structural model and divide it into finite element meshes; define the micro-design domain for topology optimization and divide it into micro-meshes;

[0066] Preferably, the micro-design domain is typically selected as a square or cubic structure and divided into quadrilateral or hexahedral meshes;

[0067] Divide the finite element mesh: This facilitates finite element analysis and the definition of design variables in step 2.

[0068] Step 2: Define the element density in the micro-design domain For the first type of design variable, the element density in the macroscopic design domain For the second type of design variables, N mi N represents the number of grids in the micro-design domain. ma The number of grids in the macroscopic design domain;

[0069] The two types of design variables are updated in step 9, and then the final design result is generated in step 10.

[0070] Step 3: Set the convergence criterion as: max||x i+1 -x i ||>Δx max with i≤i max Where i is the iteration step, i max x is the maximum number of iterations. i Design variable values ​​for step i (including and (Two types), Δx max The maximum allowable change value for the variable;

[0071] Step 4: Each microgrid has a cell density, which is used to describe the microstructure. An erosion-diffusion operation is performed on the micro-design domain to obtain a library of quasi-periodic microstructures. The calculation formula for the erosion-diffusion operator is shown below:

[0072]

[0073] in, and v i These are the element density and element volume in the micro-design domain, respectively, w(x) i ) = r min -||x i -x e || is the weight function, x i N represents the coordinates of the unit center point. e ={i|||x i -x e ||≤r min} represents the filter design domain, r min The filter radius is [value].

[0074]

[0075] Where β and η are calculation parameters.

[0076] Step 5: Predict the equivalent elastic tensor D of the microstructures in the quasi-periodic microstructure library using the asymptotic homogenization method. H The D H The calculation formula is as follows:

[0077]

[0078] Where y represents the position coordinates of any point in the microscopic domain, D(y) is the material elasticity matrix, and ε y Let φ be the strain vector and φ be the characteristic displacement vector. The calculation formula is as follows:

[0079]

[0080] Where v is the virtual displacement.

[0081] Step 6: Based on the elastic tensor of the microstructure database obtained in the previous step, use B-spline function fitting to establish the relationship between the microstructure elastic modulus and volume fraction. Explicit functional relationship between them;

[0082]

[0083] The purpose of obtaining explicit functional relationships is to reduce the amount of computation and facilitate the sensitivity analysis in step 8.

[0084] Step 7: Convert the elastic tensor obtained in Step 6 Substituting the values ​​into the finite element solution formula, the element stiffness matrix K is calculated. e Finite element analysis is performed to obtain the macroscopic displacement field U, which is used when calculating the structural stiffness (i.e., the compliance objective). In the corresponding topology optimization problem, the objective function is defined as minimizing the structural compliance, with the constraint that the amount of micromaterial used is less than the lower limit of the volumetric material usage. And the amount of macroscopic materials used is less than the upper limit of volumetric materials used. Establish the optimization model as shown in the following equation:

[0085]

[0086] min c = F T U = U T KU

[0087]

[0088]

[0089]

[0090]

[0091] Where, N mi =2500, N ma =300,

[0092] Step 8: Based on the finite element analysis results from Step 7 and the established optimization model, calculate the structural compliance function (objective function) for the macroscopic design variables. and micro design variables Sensitivity of these two types of design variables:

[0093]

[0094]

[0095] Step 9: Based on the sensitivity information obtained in Step 8, use the MMA algorithm to iteratively update the two types of design variables to complete the collaborative optimization design of micro density and macro density;

[0096] Step 10: Reconstruct the geometric model of the entire heterogeneous structure by solving the macroscopic and microscopic optimization results obtained in Step 7.

[0097] In step 3, i max Choose 160, Δx max The value is set to 0.001; the penalty coefficient is 2-5.

[0098] The parameters β and η are selected in step 4 as shown in the table below:

[0099]

[0100]

[0101] In step 6, the penalty coefficient is set to:

[0102]

[0103] In step 7, the finite element solution formula is: KU = F, where K is the overall stiffness matrix, F is the load vector, and U is the structural displacement vector.

[0104] In step 10, the method for geometric model reconstruction is as follows: the geometric boundaries of the microstructure obtained from the optimized model in step 5 are identified using a boundary recognition program, and the boundaries are imported into the geometric software to reconstruct the unit cell geometric model.

[0105] Geometry software includes HyperMesh, etc. In HyperMesh, a program is written using the Tcl scripting language, and the optimization results obtained in step 7 are used to quickly and accurately reconstruct the entire heterogeneous two-level model.

[0106] Furthermore, this invention discloses the application of the above-mentioned quasi-periodic hierarchical structure topology optimization method based on erosion-diffusion operators in fields such as 3D printing, aerospace structures, and biomedicine.

[0107] Example 2

[0108] The purpose of this embodiment is to provide a computing device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the specific steps in the first embodiment.

[0109] Example 3

[0110] The purpose of this embodiment is to provide a computer-readable storage medium.

[0111] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, performs the specific steps in Example 1.

[0112] Example 4

[0113] The purpose of this embodiment is to provide a quasi-periodic hierarchical topology optimization system based on the erosion-diffusion operator, including:

[0114] The structural model building module builds the structural model and meshes it with finite element meshes; it also defines the micro-design domain for topology optimization and meshes it with micro-meshes.

[0115] The model building module is optimized to perform corrosion-diffusion operations on microstructures to obtain a library of quasi-periodic microstructures;

[0116] The equivalent elastic tensor of microstructures in the quasi-periodic microstructure library is predicted using an asymptotic homogenization method.

[0117] Based on the elastic modulus obtained from the microstructure database, an explicit functional relationship between the elastic modulus of the microstructure and the volume fraction ratio is established by fitting B-spline functions, and an optimization model is established.

[0118] The geometric model reconstruction module calculates the sensitivity of the structure's compliance function relative to both macroscopic and microscopic topological variables, based on the optimization model.

[0119] Based on the obtained sensitivity information, the design variables are iteratively updated to complete the collaborative optimization design of micro density and macro density;

[0120] The geometric model of the entire heterogeneous structure is obtained by reconstructing the macroscopic and microscopic optimization results obtained from the optimization model.

[0121] The steps and methods involved in the apparatuses of Embodiments 2, 3, and 4 above correspond to those in Embodiment 1. For specific implementation details, please refer to the relevant description section of Embodiment 1. The term "computer-readable storage medium" should be understood as a single medium or multiple media including one or more instruction sets; it should also be understood as including any medium capable of storing, encoding, or carrying an instruction set for execution by a processor and enabling the processor to perform any of the methods in this invention.

[0122] Experimental Example 1

[0123] Step 1: Define the micro-design domain for topology optimization as a 1x1 square with a mesh size of 50x50, and the macro-design domain as a 20x15 rectangle with a mesh size of 20x15 (e.g., ...). Figure 2 ).

[0124] Step 2: Define the density of micro-units For microscopic design variables; macroscopic unit density Design variables for macroscopic purposes, such as Figure 1 As shown;

[0125] Step 3: Set the convergence criterion as: max||x i+1 -xi ||>Δx max with i≤i max i max 160, Δx max It is 0.001;

[0126] Step 4: Perform an etching-diffusion operation on the microstructure to obtain a quasi-periodic microstructure library (e.g., Figure 3 (As shown). The calculation formula for the corrosion-diffusion operator is as follows:

[0127]

[0128]

[0129] Where, N e ={i|||x i -x e ||≤r min} represents the filter design domain, and the parameters β and η are selected as shown in the table below:

[0130]

[0131] Step 5: Predict the equivalent elastic tensor D of the microstructures in the quasi-periodic microstructure library using the asymptotic homogenization method. H The D H The calculation formula is as follows:

[0132]

[0133] Where φ is the characteristic displacement vector, calculated as follows:

[0134]

[0135] Through steps 4 and 5 above, the method of the present invention can achieve spatial transformation of material properties by adjusting the spatial distribution of quasi-periodic unit cells.

[0136] Step 6: Based on the elastic modulus of the microstructure database calculated in the previous step, use B-spline function fitting to establish the relationship between the microstructure elastic modulus and the volume fraction. The explicit functional relationship between them, the fitted curve is as follows Figure 4 As shown;

[0137]

[0138] Step 7: Convert the elastic tensor obtained in Step 6 Substituting the values ​​into the finite element solution formula, the element stiffness matrix K is calculated. eFinite element analysis was performed to obtain the macroscopic displacement field U; in the corresponding topology optimization problem, the objective function was defined as minimizing the compliance of the structure, and the constraint was that the amount of micromaterial used was less than the volume. and the amount of macroscopic material used is less than the volume Establish the optimization model as shown in the following equation:

[0139]

[0140] min c = F T U = U T KU

[0141]

[0142]

[0143]

[0144]

[0145] Where, N mi =2500, N ma =300,

[0146] Step 8: Based on the finite element analysis results from Step 7 and the established optimization model, calculate the compliance function of the structure relative to the macroscopic topological variables. and micro-topological variables Sensitivity of these two types of design variables:

[0147]

[0148]

[0149] Step 9: Based on the sensitivity information obtained in Step 8, use the MMA algorithm to iteratively update the two types of design variables to complete the collaborative optimization design of micro-unit density and macro-unit density;

[0150] Step 10: Import the macroscopic and microscopic optimization results obtained from the optimization model in Step 7 into HyperMesh software. Use the Tcl scripting language to write a program to reconstruct the geometric model of the entire heterogeneous structure. Performance testing is performed using a fine finite element mesh with a minimum mesh size of 0.02. The equivalent stiffnesses of this embodiment and Comparative Example 1 are 39.48 and 18.93, respectively, representing a performance improvement of more than double.

[0151] Step 11: The design results were fabricated using a photopolymer 3D printer. The material was photosensitive resin with an elastic modulus of 181 MPa, a Poisson's ratio of 0.44, and a manufacturing precision of 0.01 mm. Figures 6(a) and 6(b) show the 3D printed parts of the topology optimization design results in this embodiment and Comparative Example 1, respectively.

[0152] Comparative Example 1

[0153] The topology optimization design method for a periodic hierarchical structure (periodic arrangement of single microstructures) proposed in Reference 2 of the background art of this invention was used for experiments, as a comparison with the optimization method proposed in this invention. The results are as follows: Figures 5(a)-5(b) As shown.

[0154] Those skilled in the art will understand that the modules or steps of the present invention described above can be implemented using general-purpose computer devices. Optionally, they can be implemented using computer-executable program code, thereby allowing them to be stored in a storage device for execution by a computer device, or they can be fabricated as separate integrated circuit modules, or multiple modules or steps can be fabricated as a single integrated circuit module. The present invention is not limited to any particular combination of hardware and software.

[0155] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

[0156] While the specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A quasi-periodic hierarchical topology optimization method based on corrosion-diffusion operator, characterized in that, The method comprises the following steps: establishing a structure model and dividing a finite element grid for a macro-structure design domain and a micro-structure design domain; defining a micro-structure design domain for topology optimization and dividing a micro-grid, defining a micro-unit density as a first type of design variable and a macro-unit density as a second type of design variable; performing corrosion-diffusion operation on the micro-structure to obtain a quasi-periodic micro-structure library, and the calculation formula is: and wherein, and v i are the cell density and cell volume in the micro-design domain, respectively, w(x i ) = r min -||x i -x e || as a weight function, x i is the unit center point coordinate, N e = {i || x i -x e ||≤r min} is the filter design domain, r min is the filter radius; β and η are calculation parameters; predicting the equivalent elastic tensor of the micro-structure in the quasi-periodic micro-structure library by using an asymptotic homogenization method; Based on the obtained elastic tensor of the microstructure database, an explicit function relationship between the microstructure elastic modulus and the volume fraction is established by using B-spline function fitting, and an optimization model is established; the volume fraction expression is The explicit function relationship is: Elasticity modulus, Macro design variable, Micro design variable, q is a penalty coefficient; the optimization model is: min c=F T U=U T KU where N mi is the number of grid points in the micro design domain, N ma is the number of grid points in the macro design domain, is the lower limit of volume material usage, is the upper limit of volume material usage, N mi = 2500, N ma = 300, calculating the sensitivity of the compliance function of the macro-structure and the micro-structure with respect to the two types of design variables, i.e., the macro-topology variable and the micro-topology variable, according to the optimization model, and the sensitivity calculation formula is: wherein is a macroscopic topological variable, is a microscopic topological variable; iteratively updating the design variables according to the obtained sensitivity information to complete the collaborative optimization design of the micro-unit density and the macro-unit density; reconstructing the macro-structure and the micro-structure obtained by the optimization model to obtain a geometric model of the entire heterogeneous structure.

2. The quasi-periodic hierarchical topology optimization method based on the corrosion-diffusion operator according to claim 1, characterized in that, The micro-structure design domain is selected as a square or a cube structure and is divided into a quadrilateral or a hexahedral grid.

3. The quasi-periodic hierarchical topology optimization method based on the corrosion-diffusion operator according to claim 1, characterized in that, The micro-unit density is defined as the first type of design variable, and the macro-unit density is defined as the second type of design variable.

4. The quasi-periodic hierarchical topology optimization method based on the corrosion-diffusion operator according to claim 1, characterized in that, The obtained elastic modulus is brought into the finite element solving formula, the unit stiffness matrix is calculated, the macroscopic displacement field is obtained by finite element analysis; in the corresponding topological optimization problem, the objective function is defined as the minimum flexibility of the structure, the constraint condition is that the micro material consumption is less than the volume and the macro material consumption is less than the volume The optimization model is established.

5. The quasi-periodic hierarchical topology optimization method based on the corrosion-diffusion operator according to claim 1, characterized in that, The method for reconstructing the geometric model is: identifying the geometric boundary of the micro-structure obtained by the optimization model by using a boundary identification program, and importing the boundary into a geometric software to reconstruct the geometric model of the unit cell.

6. The quasi-periodic hierarchical topology optimization method based on the corrosion-diffusion operator according to claim 5, characterized in that, The method for reconstructing the geometric model of the unit cell by importing the boundary into the geometric software is: reconstructing the entire heterogeneous double-level model obtained by the optimization by using the optimization result information and the created geometric model of the unit cell.

7. An application, characterized in that The application of the quasi-periodic hierarchical structure topology optimization method based on the corrosion-diffusion algorithm in any one of claims 1-6 in the fields of 3D printing, aviation structure and biomedical engineering.

8. A quasi-periodic hierarchical topology optimization system based on a corrosion-diffusion operator, characterized in that, The method comprises the following steps: a structure model establishing module for establishing a structure model and dividing a finite element grid; defining a micro-structure design domain for topology optimization and dividing a micro-grid, defining a micro-unit density as a first type of design variable and a macro-unit density as a second type of design variable; an optimization model establishing module for performing corrosion-diffusion operation on the micro-structure to obtain a quasi-periodic micro-structure library; the calculation formula is: performing corrosion-diffusion operation on the micro-structure to obtain a quasi-periodic micro-structure library, and the calculation formula is: and wherein and v i are the cell density and cell volume in the micro-design domain, respectively, w(x i ) = r min -||x i -x e || as a weight function, x i is the unit center point coordinate, N e = {i || x i -x e || ≤ r min} is the filter design domain, r min is the filter radius; β and η are calculation parameters; predicting the equivalent elastic tensor of the micro-structure in the quasi-periodic micro-structure library by using an asymptotic homogenization method; Based on the obtained elastic tensor of the microstructure database, an explicit function relationship between the microstructure elastic modulus and the volume fraction is established by using B-spline function fitting, and an optimization model is established; the volume fraction expression is The explicit function relationship is: E is the elastic modulus, is a macro design variable, is a micro design variable, q is a penalty coefficient; the optimization model is: min c=F T U=U T KU where N mi is the number of grid points in the micro design domain, N ma is the number of grid points in the macro design domain, is the lower bound of the volume material usage, is the upper bound of the volume material usage, N mi = 2500, N ma = 300, a geometric model reconstructing module for calculating the sensitivity of the compliance function of the macro-structure and the micro-structure with respect to the two types of design variables, i.e., the macro-topology variable and the micro-topology variable, according to the optimization model, and the sensitivity calculation formula is: wherein is a macroscopic topological variable, is a microscopic topological variable; iteratively updating the design variables according to the obtained sensitivity information to complete the collaborative optimization design of the micro-unit density and the macro-unit density; reconstructing the macro-structure and the micro-structure obtained by the optimization model to obtain a geometric model of the entire heterogeneous structure.

9. A computer device comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, The processor implements the steps of the quasi-periodic hierarchical structure topology optimization method based on the corrosion-diffusion algorithm when executing the program.

10. A computer-readable storage medium having stored thereon a computer program, characterized in that, The program, when executed by the processor, implements the steps of the quasi-periodic hierarchical topology optimization method based on the corrosion-diffusion operator as claimed in claim 1.

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