A multi-scale topology optimization method for gradient multi-configuration lattice structures

Abstract

The present invention belongs to the technical field related to structural optimization, and discloses a multi-scale topology optimization method for a gradient multi-configuration lattice structure, comprising the following steps: (1) obtaining a prototype level set function of a lattice unit cell of each configuration; (2) performing shape interpolation based on each prototype level set function to obtain M types of sample lattice units with equivalent density values ​​in an arithmetic progression, and calculating their equivalent elastic tensors, thereby constructing M Kriging prediction models; (3) constructing a Kriging model-assisted uniform multiphase material interpolation model, and then constructing a multi-scale topology optimization model for the gradient multi-configuration lattice structure, thereby optimizing the distribution of lattice units of different configurations within the design domain and their equivalent densities; (4) selecting a prototype level set function, interpolating to obtain the gradient multi-configuration lattice unit cells and backfilling, and then completing the optimization. The present invention achieves the simultaneous optimization of the distribution of lattice units of different configurations within the structural design area and their equivalent density values.

Description

Technical Field

[0001] The present invention belongs to the technical field related to structural optimization, and more specifically, relates to a multi-scale topology optimization method for a gradient multi-configuration lattice structure. Background Art

[0002] Gradient multi-configuration lattice structures are formed by the periodic arrangement of several gradient lattice cells with different configurations. They have the characteristics of ultra-lightweight, high specific bending stiffness / strength, efficient impact energy absorption, and excellent biocompatibility, and are widely used in aerospace, biomedical engineering and other fields. The multiphase material topology optimization method is an efficient optimization design method for optimizing the distribution of different materials in the design domain. It is suitable for optimizing and solving the optimal distribution of different materials in the design domain. The multi-scale topology optimization design method of lattice structures filled with lattice cells with multiple configurations and gradient equivalent density values ​​can fully explore the design potential of lattice cell configuration changes and lattice cell equivalent density changes, and achieve a significant improvement in structural performance with less material usage.

[0003] Regarding the multi-scale topology optimization of gradient multi-configuration lattice structures, relevant technicians in this field have conducted some research. For example, Reference 1: "Wang C, Zhu JH, Zhang WH, et al. Concurrent topology optimization design of structures and non-uniform parameterized lattice microstructures [J]. Structural and Multidisciplinary Optimization, 2018, 58(1): 35-50." discloses a design method for gradient multi-configuration lattice structures. The designed lattice structure contains gradient lattice unit cells of different configurations, which can better adapt to the boundary load conditions of the structure. This method only considers lattice structures containing three configurations. For example, Reference 2, "Wu Z, Xia L, Wang S, et al. Topology optimization of hierarchical lattice structures with substructuring [J]. Computer Methods in Applied Mechanics and Engineering, 2019, 345: 602-617," published a substructuring-based gradient multi-configuration lattice structure design method for minimizing the flexibility of gradient multi-configuration lattice structures. However, the core of this method is the substructuring method, which describes the geometry of lattice cells. This method is only applicable to truss-type lattice cells and has very limited applicability to other types of lattice cells.

[0004] Therefore, with a lower computational cost, the distribution optimization of more than ten configuration gradient lattice unit cells and the multi-scale topological optimization method of gradient multi-configuration lattice structures that optimize the equivalent density value of lattice unit cells in the design domain can be considered simultaneously. Designing a lattice structure with gradient multi-configuration lattice unit cells to fully explore the design space of the lattice structure and maximize the mechanical properties of the structure is a hot issue that needs to be solved urgently. Summary of the Invention

[0005] In response to the above-mentioned defects or improvement needs of the prior art, the present invention provides a multi-scale topology optimization method for a gradient multi-configuration lattice structure. Combining the characteristics of the gradient multi-configuration lattice structure itself, the method simultaneously optimizes the distribution of lattice cells of different configurations in the design domain and their equivalent density values, and fully explores the multi-scale design space of the lattice structure at a low computational cost, while ensuring the connectivity between the gradient lattice cells within the lattice structure, thereby fully realizing the material potential, improving the mechanical properties of the lattice structure, and realizing multi-scale topology optimization design.

[0006] To achieve the above objectives, according to one aspect of the present invention, a multi-scale topology optimization method for a gradient multi-configuration lattice structure is provided, which mainly comprises the following steps:

[0007] (1) Select M configurations of lattice unit cells as candidate lattice unit cells, and use level set functions to geometrically describe each configuration of lattice unit cells to obtain M prototype level set functions; where M is a positive integer greater than 2;

[0008] (2) Shape interpolation is used to interpolate each prototype level set function in turn to obtain M types of sample lattice cells with equivalent density values ​​in an arithmetic progression, and the equivalent elastic tensor of the sample lattice cells is calculated using the homogenization method. Kriging prediction models are constructed based on the elastic tensor data of the sample lattice cells of various configurations, thereby obtaining M Kriging prediction models;

[0009] (3) constructing a Kriging model-assisted homogeneous multiphase material interpolation model based on M Kriging prediction models, using the Kriging model-assisted homogeneous multiphase material interpolation model to obtain the elastic tensor of the finite element unit, and then constructing a multi-scale topology optimization model of a gradient multi-configuration lattice structure, optimizing the distribution of lattice unit cells of different configurations in the design domain and their equivalent density based on the multi-scale topology optimization model, and obtaining the optimized configuration of the lattice unit cells in the design domain and their equivalent density value;

[0010] (4) Based on the configuration of the lattice unit cell in the optimized design domain and its equivalent density value, the prototype level set function corresponding to the lattice unit cell is selected, and then the optimized lattice unit cell is obtained by shape interpolation based on the equivalent density value of the optimized lattice unit cell. The optimized lattice unit cell is backfilled to the corresponding position to obtain the optimized gradient multi-configuration lattice structure.

[0011] Furthermore, the calculation formula for the equivalent density value of the lattice unit cell is:

[0012]

[0013] Among them, φ mn (x) represents the level set function of the lattice unit cell, H represents the Heaviside function, D represents the design domain where a unit cell is located, and x represents the coordinate point in the design domain.

[0014] Furthermore, the mathematical expression of the Kriging model-assisted homogeneous multiphase material interpolation model is:

[0015]

[0016] in, is the elastic tensor of the interpolated finite element, m = 1, 2, ..., M, M is the total number of prototype level set functions, n = 1, 2, ..., N, N is the total number of finite element elements in the design domain, represents the elastic tensor of the lattice unit cell, i, j, k, l = 1, 2, ..., d, d is the spatial dimension, is the continuous design variable ρ mn The value after density filtering, ρ mn is a continuous design variable representing the equivalent density of the lattice unit cell, and δ is a positive number much smaller than 1 to avoid matrix singularity. is a discrete design variable representing the lattice unit cell configuration and satisfies p represents the penalty parameter.

[0017] Furthermore, the mathematical expression of the multi-scale topology optimization model is:

[0018] Find:s mn ,ρ mn

[0019] Minimize:C(s mn ,ρ mn )=F T U

[0020]

[0021] F=K(s mn ,ρ mn )U,

[0022]

[0023] 0≤s mn ≤1,(m=1,2,...,M; n=1,2,...,N)

[0024] ρ min ≤ρ mn ≤ρ max ,(m=1,2,...,M; n=1,2,...,N)

[0025]

[0026] Among them, C(s mn ,ρ mn ) is the structural flexibility of the gradient multi-configuration lattice structure, and the continuous design variable s mn is composed of discrete design variables The relaxation is obtained, F represents the force vector acting on the design domain, U represents the node displacement vector, G(s mn ,ρ mn) represents the material volume rate constraint in the entire design domain, v n is the area or volume of a finite element unit in the design domain, V max is the maximum area or volume of the solid structure allowed in the design domain, K(s mn ,ρ mn ) represents the overall stiffness matrix of the structure, B represents the strain displacement matrix, Ω n represents the structural domain of a finite element unit, ρ max and ρ min They represent the upper and lower limits of the design variable values, β is a positive number much larger than 1, and η is the value that determines the discrete design variable. With continuous setting variable s mn The threshold of the conversion relationship between them.

[0027] Furthermore, based on the equivalent density value of the optimized lattice unit cell, the algorithm used to obtain the optimized lattice unit cell by shape interpolation is a bisection method.

[0028] Furthermore, M is 15.

[0029] Furthermore, in step (4), the number of prototype level set functions selected is 1.

[0030] Furthermore, the equivalent density refers to the percentage of the area or volume of the solid structure part in the design domain to the area or volume of the entire design domain, and its value range is between (0, 1].

[0031] Furthermore, the number of sample lattice cells is 100, and the equivalent density value of the sample lattice cells is uniformly sampled in the interval [0.1, 1].

[0032] Furthermore, the formula corresponding to shape interpolation is:

[0033]

[0034] in is the prototype level set function, is the interpolation coefficient, φ mn (x) is the level set function of the lattice unit cell after shape interpolation.

[0035] In general, compared with the prior art, the multi-scale topology optimization method of the gradient multi-configuration lattice structure provided by the present invention has the following beneficial effects:

[0036] 1. The present invention achieves simultaneous optimization of the distribution of lattice unit cells of different configurations within the structural design area and their equivalent density values, maximizes the potential of the material, and fully improves the mechanical properties of the lattice structure.

[0037] 2. The present invention adopts the level set function to geometrically describe the lattice unit cells of different configurations, and then interpolates the level set function of the lattice unit cells through the shape interpolation technology, thereby obtaining the lattice unit cells with gradient equivalent density values, ensuring good connectivity between the lattice unit cells inside the gradient lattice structure.

[0038] 3. Since the present invention adopts the Kriging model to predict the equivalent elastic tensor of the lattice unit cell, the computational cost of using the homogenization method to evaluate the elastic tensor of the lattice unit cell during the optimization iteration process is reduced, and the computational cost of the multi-scale topology optimization design of the gradient multi-configuration lattice structure is reduced.

[0039] 4. The present invention constructs a homogenized multiphase material interpolation model assisted by the Kriging model to obtain the elastic tensor of the finite element unit, thereby avoiding the disadvantage of the small number of configurations of lattice unit cells in the existing technology. It can achieve distribution optimization of more than ten different configurations of lattice unit cells, greatly expanding the design freedom.

[0040] 5. The present invention achieves the simultaneous optimization of the distribution of lattice cells of different configurations and their equivalent density values ​​within the structural design area, while ensuring that all gradient lattice cells have good connectivity. The elastic tensor of the lattice cells is evaluated during the iterative optimization process, consuming less computational resources. Compared with the traditional multi-scale topological optimization method of gradient multi-configuration lattice structures, the present invention not only greatly reduces the computational cost, but also greatly expands the optimization design space, and can effectively improve the mechanical properties of the lattice structure. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 This is a flow chart of a multi-scale topology optimization method for a gradient multi-configuration lattice structure constructed by the present invention;

[0042] Figure 2 a~p in the figure are schematic diagrams of 15 candidate lattice unit cells with different configurations constructed by the present invention;

[0043] Figure 3 It is a schematic diagram of the gradient lattice unit cell obtained by adopting shape interpolation technology based on the prototype level set function constructed by the present invention;

[0044] Figure 4 is a schematic diagram of the design domain, loads and boundary conditions of the lattice structure constructed by the present invention;

[0045] Figure 5 yes Figure 4 Schematic diagram of the distribution of lattice unit cells of different configurations after optimization within the design domain of the mid-lattice structure;

[0046] Figure 6 yes Figure 4Schematic diagram of the distribution of equivalent density values ​​of the lattice unit cell after optimization in the design domain of the mid-lattice structure;

[0047] Figure 7 yes Figure 4 Schematic diagram of the multi-scale structure of the optimized gradient multi-configuration lattice structure in the middle lattice structure. DETAILED DESCRIPTION

[0048] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely for the purpose of explaining the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.

[0049] The present invention provides a multi-scale topology optimization method for a gradient multi-configuration lattice structure, which mainly includes the following steps:

[0050] S1, select M configurations of lattice unit cells as candidate lattice unit cells, and use level set functions to geometrically describe the lattice unit cells of each configuration to obtain M prototype level set functions.

[0051] In this embodiment, the number of prototype level set functions is 15.

[0052] S2, shape interpolation technology is used to interpolate each prototype level set function in turn to obtain M types of sample lattice unit cells with equivalent density values ​​in an arithmetic progression, the equivalent elastic tensor of the sample lattice unit cell is calculated using the homogenization method, and Kriging prediction models are constructed based on the elastic tensor data of the sample lattice unit cells of various configuration lattices, thereby obtaining M Kriging prediction models.

[0053] The equivalent density values ​​obtained by interpolation of a prototype level set function are in an arithmetic progression of sample lattice cells. The number of sample lattice cells is 100, and the equivalent density values ​​of the sample lattice cells are uniformly sampled in the interval [0.1,1].

[0054] The calculation formula of the equivalent density value of the lattice unit cell is:

[0055]

[0056] Among them, φ mn (x) represents the level set function of the lattice unit cell, H represents the Heaviside function, D represents the design domain where a unit cell is located, and x represents the coordinate point in the design domain.

[0057] S3. The M Kriging prediction models obtained are used to construct a Kriging model-assisted uniform multiphase material interpolation model, and the elastic tensor of the finite element unit is obtained based on the Kriging model-assisted uniform multiphase material interpolation model. Then, a multi-scale topology optimization model of a gradient multi-configuration lattice structure is constructed, and the distribution of lattice unit cells with different configurations and their equivalent densities in the design domain are optimized based on the multi-scale topology optimization model to obtain the configuration of the lattice unit cells in the optimized design domain and their equivalent density values.

[0058] The mathematical expression of the homogeneous multiphase material interpolation model assisted by the Kriging model is:

[0059]

[0060] in, is the elastic tensor of the interpolated finite element, m = 1, 2, ..., M, M is the total number of prototype level set functions, n = 1, 2, ..., N, N is the total number of finite element elements in the design domain, represents the elastic tensor of the lattice unit cell, i, j, k, l = 1, 2, ..., d, d is the spatial dimension, is the continuous design variable ρ mn The value after density filtering, ρ mn is a continuous design variable representing the equivalent density of the lattice unit cell, and δ is a positive number much smaller than 1 to avoid matrix singularity. is a discrete design variable representing the lattice unit cell configuration and satisfies p represents the penalty parameter.

[0061] The mathematical expression of the multi-scale topology optimization model is:

[0062] Find:s mn ,ρ mn

[0063] Minimize:C(s mn ,ρ mn )=F T U

[0064]

[0065] F=K(s mn ,ρ mn )U,

[0066]

[0067] 0≤s mn ≤1,(m=1,2,...,M; n=1,2,...,N)

[0068] ρmin ≤ρ mn ≤ρ max ,(m=1,2,...,M; n=1,2,...,N)

[0069]

[0070] Among them, C(s mn ,ρ mn ) is the structural flexibility of the gradient multi-configuration lattice structure, and the continuous design variable s mn is composed of discrete design variables The relaxation is obtained, F represents the force vector acting on the design domain, U represents the node displacement vector, G(s mn ,ρ mn ) represents the material volume rate constraint in the entire design domain, v n is the area or volume of a finite element unit in the design domain, V max is the maximum area or volume of the solid structure allowed in the design domain, K(s mn ,ρ mn ) represents the overall stiffness matrix of the structure, B represents the strain displacement matrix, Ω n represents the structural domain of a finite element unit, ρ max and ρ min They represent the upper and lower limits of the design variable values, β is a positive number much larger than 1, and η is the value that determines the discrete design variable. With continuous setting variable s mn The threshold of the conversion relationship between them.

[0071] Among them, the finite element unit is obtained by discretizing the design domain.

[0072] S4, based on the configuration of the lattice unit cell in the optimized design domain and its equivalent density value, the prototype level set function corresponding to the lattice unit cell is selected, and then the optimized lattice unit cell is obtained by shape interpolation based on the equivalent density value of the optimized lattice unit cell, and the optimized lattice unit cell is backfilled to the corresponding position to obtain the optimized gradient multi-configuration lattice structure.

[0073] According to the equivalent density value of the optimized lattice unit cell, the algorithm used to obtain the optimized lattice unit cell using the shape interpolation technique is the bisection method. According to the configuration of the lattice unit cell, the corresponding prototype level set function is selected, and the number of selected prototype level set functions is 1.

[0074] The lattice structure to be optimized in this embodiment has the following design domain, load and boundary conditions: Figure 4As shown, its left side is fixed and the midpoint of the right side is subjected to a downward force. The equivalent density in this embodiment refers to the percentage of the area or volume of the solid structure part in the design domain to the area or volume of the entire design domain. Its value range is between (0, 1]. Without loss of generality, all physical quantities used in this embodiment are assumed to be dimensionless.

[0075] The present invention is further described in detail below with reference to specific embodiments.

[0076] like Figure 1 As shown, the multi-scale topology optimization method of a gradient multi-configuration lattice structure provided by the present invention includes the following steps:

[0077] Step 1: Select 15 configurations of lattice cells as candidate lattice cells, use level set function to describe the geometry of each configuration of lattice cells, and obtain 15 prototype level set functions. Figure 2 shown.

[0078] Step 2: Take the 15 prototype level set functions obtained in step 1 in turn, use the shape interpolation technique to interpolate each prototype level set function, obtain M types of sample lattice cells with equivalent density values ​​in an arithmetic progression, use the homogenization method to calculate the equivalent elastic tensor of the sample lattice cell, and use the elastic tensor data to construct the Kriging prediction model, thereby obtaining 15 Kriging prediction models, which specifically includes the following sub-steps:

[0079] (2.1) Take the prototype level set function obtained in step 1, uniformly sample one hundred points in the density interval [0.1, 1] as the equivalent density value of the sample lattice, and use the shape interpolation technique to obtain the level set function of the sample lattice. The formula corresponding to the shape interpolation is:

[0080]

[0081] in is the prototype level set function, is the interpolation coefficient, φ mn (x) is the level set function of the lattice cell after shape interpolation. The interpolation coefficient of the lattice cell with a specific equivalent density value is determined by bisection. The formula for determining the equivalent density value of the lattice cell from the level set function of the lattice cell is:

[0082]

[0083] Where H represents the Heaviside function, D represents the design domain where a lattice unit cell is located, and x represents the coordinate point in the design domain.

[0084] (2.2) The equivalent elastic tensor of the sample lattice unit cell is calculated using the homogenization method. The calculation formula of the homogenization method is:

[0085]

[0086] in is the equivalent elastic tensor of the lattice unit cell, Ω n and |Ω n |represent the design domain and volume of the lattice unit cell, respectively. represents the microscopic strain field of local variation, represents a given macroscopic test strain field, i, j, k, l = 1, 2, ..., d, d is the spatial dimension, D pqrs represents the elastic tensor of the base material, H represents the Heaviside function, is with The corresponding displacement field, It can be calculated by the following formula:

[0087]

[0088] in represents the virtual displacement field, represents the statically allowed displacement field under periodic boundary conditions.

[0089] (2.3) Construct a Kriging prediction model based on the calculated elastic tensor of the sample lattice unit cell.

[0090] (2.4) Repeat steps (2.1) to (2.3) until the Kriging prediction model corresponding to 15 configuration gradient lattice unit cells is completed.

[0091] Step 3: Use the 15 Kriging prediction models obtained in Step 2 to construct a Kriging model-assisted homogeneous multiphase material interpolation model to obtain the elastic tensor of the finite element unit. Then, construct a multi-scale topology optimization model of the gradient multi-configuration lattice structure. Simultaneously optimize the configuration and equivalent density of the lattice unit cell in the design domain to obtain the distribution of optimized lattice unit cells with different configurations and their equivalent density values. This specifically includes the following sub-steps:

[0092] (3.1) Based on the 15 Kriging prediction models obtained in step 2, the Kriging model-assisted homogeneous multiphase material interpolation model is constructed as follows:

[0093]

[0094] in, is the elastic tensor of the interpolated finite element, m = 1, 2, ..., M, M is the total number of prototype level set functions, n = 1, 2, ..., N, N is the total number of finite element elements in the design domain, represents the elastic tensor of the lattice unit cell, i, j, k, l = 1, 2, ..., d, d is the spatial dimension, is the continuous design variable ρ mn The value after density filtering, ρ mn is a continuous design variable representing the equivalent density of the lattice unit cell, and δ is a positive number much smaller than 1 to avoid matrix singularity. is a discrete design variable representing the lattice unit cell configuration and satisfies p represents the penalty parameter.

[0095] (3.2) The lattice structure to be optimized is set as the initial lattice structure. The finite element method is used to discretize the design domain of the lattice structure into 80 × 50 = 4000 four-node macro units. The Young's modulus E0 of the base material is set to 1, and the Poisson's ratio μ is set to 0.38. With the goal of minimizing the structural flexibility of the lattice structure, combined with the pre-given maximum material usage, i.e., the volume rate constraint, a multi-scale topology optimization model for the gradient multi-configuration lattice structure is constructed as follows:

[0096] Find:s mn ,ρ mn

[0097] Minimize:C(s mn ,ρ mn )=F T U

[0098]

[0099] F=K(s mn ,ρ mn )U,

[0100]

[0101] 0≤s mn ≤1,(m=1,2,...,M; n=1,2,...,N)

[0102] ρ min ≤ρ mn ≤ρ max ,(m=1,2,...,M; n=1,2,...,N)

[0103]

[0104] Among them, C(s mn ,ρ mn) is the structural flexibility of the gradient multi-configuration lattice structure, and the continuous design variable s mn is composed of discrete design variables The relaxation is obtained, F represents the force vector acting on the design domain, U represents the node displacement vector, G(s mn ,ρ mn ) represents the material volume rate constraint in the entire design domain, v n is the volume of a finite element unit in the design domain, V max is the maximum volume of the solid structure allowed in the design domain, K(s mn ,ρ mn ) represents the overall stiffness matrix of the structure, B represents the strain displacement matrix, Ω n represents the structural domain of a finite element unit, ρ max and ρ min They represent the upper and lower limits of the design variable values, β is a positive number much larger than 1, and η is the value that determines the discrete design variable. With continuous setting variable s mn In order to ensure the stability of the iterative convergence process, the value of η is set to 0.5.

[0105] (3.3) Calculate the objective function for the design variable s mn The sensitivity information of is used to update the design variables using a gradient-based optimization algorithm. The sensitivity is calculated as follows:

[0106]

[0107]

[0108]

[0109]

[0110]

[0111] Among them H ne , H ei and N e Is the indicator matrix in density filtering. Calculate the objective function for the design variable ρ mn The sensitivity information of the sensitivity calculation formula is as follows:

[0112]

[0113]

[0114]

[0115] Calculate the constraint function for the design variable s mnand ρ mn The sensitivity information of the sensitivity calculation formula is as follows:

[0116]

[0117]

[0118] The design variables are updated using a gradient-based optimization algorithm. When calculating the sensitivity information, the sensitivity information of the current macro unit is filtered using the sensitivity information of the neighboring macro units to avoid numerical instability such as checkerboard and grid dependence. At the same time, the distribution areas of the lattice cells of different configurations within the current lattice structure are clearly separable. Based on the optimization results, it is determined whether the objective function meets the set threshold, that is, the convergence condition. If the convergence condition is met, the distribution of the lattice cells of different configurations in the current design domain and their equivalent density values ​​are output. Otherwise, continue to execute (3.3) and update the design variable s. mn and ρ mn .

[0119] Step 4: Based on the distribution of optimized lattice cells of different configurations and their equivalent density values ​​obtained in step 3, select the corresponding prototype level set function in step 1 according to the configuration of the lattice cell, and then use the shape interpolation technology based on the equivalent density value of the optimized lattice cell to obtain the optimized lattice cell, assemble and backfill each lattice cell to its corresponding position, and obtain the optimized gradient multi-configuration lattice structure.

[0120] See also Figures 2 to 7 , the following is a further explanation of the present invention using the design of a cantilever beam structure. To avoid loss of generality, all physical quantities used in this embodiment are assumed to be dimensionless. Figure 2 As shown in the figure, 15 different configurations of lattice cells are used as candidate lattice cells. The level set function is used to describe the geometry of each cell to obtain 15 prototype level set functions. The schematic diagram of obtaining the gradient lattice cell by shape interpolation technology based on the prototype level set function is shown in the figure. Figure 3 The cantilever beam design domain is shown in Figure 4 As shown, the cantilever beam design domain dimensions are L = 400 mm and W = 250 mm. A concentrated load F of magnitude F = 5 is applied at the right midpoint of the cantilever beam. The left side of the cantilever beam is fixed. The cantilever beam is meshed using 80 × 50 = 4000 quadrilateral macroelements. The base material properties used are elastic modulus E0 = 1 and Poisson's ratio μ = 0.38. The optimization objective is to minimize the flexibility of the cantilever beam structure, with a material usage limit of 35%.

[0121] since Figure 6It can be seen that the lattice unit cells with high equivalent density are mainly distributed near the main force transmission path inside the cantilever beam, and the lattice unit cells with low density are mainly distributed near the secondary force transmission path inside the cantilever beam. This distribution method helps to enhance the overall structural stiffness of the cantilever beam and reduce the structural flexibility of the cantilever beam under stress conditions.

[0122] since Figure 7 It can be seen that the lattice cells with strong axial tensile strength are mainly distributed in the upper and lower positions of the cantilever beam, and the lattice cells with strong shear strength are mainly distributed inside the cantilever beam. This is very meaningful for the cantilever beam structure, because when the cantilever beam structure is subjected to force, its upper and lower parts are mainly subjected to axial tension / compression, and the inside of the cantilever beam is mainly subjected to shear force. This distribution of gradient lattice cells with different configurations helps the cantilever beam structure to better resist lateral tensile deformation and shear deformation, and improve the mechanical properties of the structure. In addition, it can be seen that all gradient lattice cells have good connectivity.

[0123] In summary, the multi-scale topology optimization method of a gradient multi-configuration lattice structure provided by the present invention realizes the simultaneous optimization of the distribution of lattice cells of different configurations and their equivalent density values ​​within the structural design area compared with the existing technology, while ensuring that all gradient lattice cells have good connectivity. The elastic tensor of the lattice cell is evaluated during the iterative optimization process, which consumes less computing resources. Compared with the traditional multi-scale topology optimization method of the gradient multi-configuration lattice structure, the present invention not only greatly reduces the computing cost, but also greatly expands the optimization design space, and can effectively improve the mechanical properties of the lattice structure.

[0124] It will be easily understood by those skilled in the art that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A multi-scale topology optimization method for gradient multi-configuration lattice structures, characterized in that: The method comprises the following steps: (1) Select M configurations of lattice unit cells as candidate lattice unit cells, and use level set functions to geometrically describe each configuration of lattice unit cells to obtain M prototype level set functions; where M is a positive integer greater than 2; (2) Shape interpolation is used to interpolate each prototype level set function in turn to obtain M types of sample lattice cells with equivalent density values ​​in an arithmetic progression. The equivalent elastic tensor of the sample lattice cells is calculated using the homogenization method. Kriging prediction models are constructed based on the elastic tensor data of the sample lattice cells of various configurations, thereby obtaining M Kriging prediction models. (3) Based on M Kriging prediction models, a Kriging model-assisted uniform multiphase material interpolation model is constructed. The elastic tensor of the finite element unit is obtained using the Kriging model-assisted uniform multiphase material interpolation model. Then, a multiscale topology optimization model of a gradient multi-configuration lattice structure is constructed. Based on the multiscale topology optimization model, the distribution of lattice unit cells with different configurations in the design domain and their equivalent density are optimized to obtain the optimized configuration of the lattice unit cells in the design domain and their equivalent density values. (4) Based on the configuration of the lattice unit cell in the optimized design domain and its equivalent density value, the prototype level set function corresponding to the lattice unit cell is selected, and then the optimized lattice unit cell is obtained by shape interpolation based on the equivalent density value of the optimized lattice unit cell. The optimized lattice unit cell is backfilled to the corresponding position to obtain the optimized gradient multi-configuration lattice structure; The mathematical expression of the Kriging model-assisted homogeneous multiphase material interpolation model is: in, is the elastic tensor of the interpolated finite element, m =1, 2, …, M, where M is the total number of prototype level set functions, n =1, 2, ..., N, where N is the total number of finite element elements in the design domain, represents the elasticity tensor of the lattice unit cell, i , j , k , l =1, 2, ..., d, d is the spatial dimension, is a continuous design variable After density filtering, is the continuous design variable of the equivalent density of the lattice unit cell, is a positive number much smaller than 1 to avoid matrix singularity. is a discrete design variable of the lattice unit cell configuration and satisfies , represents the penalty parameter.

2. The multi-scale topology optimization method for a gradient multi-configuration lattice structure according to claim 1, characterized in that: The calculation formula of the equivalent density value of the lattice unit cell is: in, represents the level set function of the lattice unit cell, represents the Heaviside function, D represents the design domain where a unit cell is located, Represents the coordinate points within the design domain.

3. The multi-scale topology optimization method for a gradient multi-configuration lattice structure according to claim 1, characterized in that: The mathematical expression of the multi-scale topology optimization model is: in, is the structural flexibility of the gradient multi-configuration lattice structure, and the continuous design variable is composed of discrete design variables Relaxation obtained, represents the force vector acting on the design domain, represents the node displacement vector, represents the material volume fraction constraint within the entire design domain, is the area or volume of a finite element in the design domain, is the maximum area or volume of the solid structure allowed in the design domain, represents the overall stiffness matrix of the structure, represents the strain-displacement matrix, represents the domain of a finite element unit, and represent the upper and lower limits of the design variable values, respectively. is a positive number greater than 1, Is to determine the discrete design variables With continuous setting variables The threshold of the conversion relationship between them.

4. The multi-scale topology optimization method for a gradient multi-configuration lattice structure according to any one of claims 1 to 3, characterized in that: Based on the equivalent density value of the optimized lattice unit cell, the algorithm used to obtain the optimized lattice unit cell by shape interpolation is the bisection method.

5. The multi-scale topology optimization method for a gradient multi-configuration lattice structure according to any one of claims 1 to 3, characterized in that: M is 15.

6. The multi-scale topology optimization method for a gradient multi-configuration lattice structure according to any one of claims 1 to 3, characterized in that: In step (4), the number of prototype level set functions selected is 1.

7. The multi-scale topology optimization method for a gradient multi-configuration lattice structure according to any one of claims 1 to 3, characterized in that: Equivalent density refers to the percentage of the area or volume of the solid structure in the design domain to the area or volume of the entire design domain, and its value range is between (0, 1].

8. The multi-scale topology optimization method for a gradient multi-configuration lattice structure according to claim 7, characterized in that: The number of sample lattice cells is 100, and the equivalent density value of the sample lattice cells is uniformly sampled in the interval [0.1, 1].

9. The multi-scale topology optimization method for a gradient multi-configuration lattice structure according to any one of claims 1 to 3, characterized in that: The formula corresponding to shape interpolation is: in is the prototype level set function, is the interpolation coefficient, is the level set function of the lattice unit cell after shape interpolation.

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