A lattice structure multi-scale design method considering multi-type lattice configuration and topological distribution thereof

Abstract

This invention discloses a multi-scale design method for lattice structures considering multiple lattice configurations and their topological distributions. Addressing the shortcomings of existing technologies, this invention, based on the synergistic optimization of the microscopic configuration and macroscopic topological distribution of lattice unit cells, simultaneously considers multiple types of lattice unit cells and proposes a multi-scale design method for lattice structures. At the microscopic scale, an approximate model-assisted particle swarm optimization algorithm (ESPSO) is used to optimize the microscopic configuration of multiple types of lattice unit cells; at the macroscopic scale, a multi-material topology optimization algorithm is used to optimize the macroscopic topological distribution of multiple types of lattice unit cells. By achieving synergistic optimization of the microscopic configuration and macroscopic topological distribution of multiple types of lattice unit cells, this invention fully explores the coupling effect between the microscopic and macroscopic scales, while leveraging the configurational diversity of multiple types of lattice unit cells, greatly expanding the design space of lattice structures, and maximizing the improvement of the mechanical performance and reducing the weight of lattice structures.

Description

Technical Field

[0001] This invention relates to a method for designing lattice structures, and in particular to a multi-scale design method for lattice structures that considers multiple types of lattice configurations and their topological distributions. Background Technology

[0002] A lattice structure is a periodic porous structure composed of regular lattice unit cells arranged repeatedly in a design space. It has excellent mechanical properties such as light weight, high specific stiffness / specific strength, and high vibration reduction and energy absorption efficiency. It has important application value in many engineering fields such as aerospace, automobile, shipbuilding, and biomedicine. Its design rationality and innovation directly determine the service performance and material utilization efficiency of the structure. Current optimization designs for lattice structures are primarily based on a single type of lattice unit cell, typically optimizing only the microstructure or macroscopic distribution of the unit cell. This approach fails to achieve synergistic optimization of both microstructure and macroscopic distribution, neglecting the coupling effect between the micro and macro scales. Consequently, the design space of lattice structures is not fully explored, hindering further improvements in their mechanical properties. A few designs incorporating multiple types of lattice unit cells only consider the macroscopic distribution optimization, neglecting the microstructure optimization of each type. This ignores the design freedom of the microstructure, failing to leverage the diverse configuration advantages of different unit cell types and making it difficult to meet the structural performance requirements under complex working conditions. Multi-scale design methods are advanced structural design approaches that achieve synergistic optimization of microscopic lattice configuration and macroscopic lattice distribution. They fully consider the coupling effect between the micro and macro scales, making them highly suitable for lattice structure designs considering multiple lattice configurations and their topological distributions. These methods can achieve optimal mechanical performance design of lattice structures with minimal material usage.

[0003] Research has been conducted by those skilled in the art on the optimization design of lattice structures. Regarding the optimization of the microstructure of lattice units, an existing lattice structure design method based on deep learning and genetic algorithms has obtained lattice structures with excellent buckling resistance by optimizing the topological configuration of lattice units. However, this method does not further optimize the macroscopic topological distribution of lattice units, neglecting the coupling effect between the macro and micro scales, and thus failing to fully improve the mechanical performance of the structure. Regarding the optimization of the macroscopic topological distribution of lattice units, some existing methods employ topology optimization to improve the macroscopic topological distribution of lattice units, achieving improvements in the mechanical performance of the lattice structure. However, this method does not further optimize the microstructure of lattice units, making it difficult to fully explore the design space of the lattice structure and realize the potential of the material. In the design of lattice structures incorporating multiple types of lattice units, for example, an existing multi-type lattice structure design method based on a digital unit library improves the mechanical performance of the lattice structure by establishing a digital library containing multiple types of lattice units and optimizing their macroscopic topological distribution. In this method, the microstructures of various lattice unit cells are generated based on a preset library, without further optimization of the microstructure design of the lattice unit cells to fully expand the design space of the lattice structure and improve its mechanical properties. Summary of the Invention

[0004] This invention addresses the shortcomings of existing technologies by proposing a multi-scale design method for lattice structures. This method considers the synergistic optimization of the microstructure and macroscopic topological distribution of lattice units, and takes into account multiple types of lattice units. At the microscale, an approximate model-assisted particle swarm optimization (ESPSO) algorithm is used to optimize the microstructure of various types of lattice units. At the macroscale, a multi-material topology optimization algorithm is used to optimize the macroscopic topological distribution of various types of lattice units, fully exploiting the coupling effect between the micro and macroscales to maximize the mechanical performance and reduce the weight of the lattice structure.

[0005] The present invention adopts the following technical solution:

[0006] A multi-scale design method for lattice structures considering multiple lattice configurations and their topological distributions includes the following steps:

[0007] Step 1: Establish the initial design of the macroscopic topological distribution of multiple types of lattice unit cells, determine the number N of lattice unit cell types within the macroscopic design domain. Each type of lattice unit cell consists of preset nodes in three-dimensional space and rods connecting these preset nodes. The number and distribution of rods differ in different lattice unit cells. Each lattice rod consists of a cylinder and two spheres at its two ends. The geometry of the cylinder and spheres is described using explicit topological functions based on level sets, thus achieving an explicit description of the geometry of the lattice rod. The rods are used to connect the predefined nodes to form the initial design of the lattice unit cell.

[0008] Step 2: Calculate the macroscopic equivalent elastic tensor of each type of lattice unit cell in Step 1 using a numerical homogenization method. Based on this, calculate the element stiffness matrix of each lattice unit cell in the macroscopic design domain. At the macroscopic scale, different types of lattice unit cells are considered as different material phases. On this basis, the macroscopic distribution parameters of different lattice material phases, i.e., the level set function in the DS-MMLS model, are used as design variables. The objective function is to minimize the overall compliance of the lattice structure under complex service conditions. The macroscopic volume fraction corresponding to each lattice material is used as a constraint condition to establish a macroscopic topology optimization model for multiple types of lattice materials. Then, using the alternating active phase algorithm, the multi-material distribution optimization problem containing N+1 phases (i.e., N types of lattice unit cells and 1 type of porous phase) is decomposed into N(N+1) / 2 two-phase material distribution optimization sub-problems. Finally, in each two-phase material distribution optimization sub-problem, the optimization criterion method is used to iteratively optimize the two-phase material distribution. By traversing all two-phase material distribution optimization sub-problems, the macroscopic topology distribution of each type of lattice unit cell in the macroscopic design domain is obtained.

[0009] Step 3: Based on the macroscopic topological distribution of each type of lattice unit cell obtained in the previous step, optimize the configuration of each type of lattice unit cell. Using the rod diameter of each lattice unit cell as the design variable and the given material volume ratio of each lattice unit cell as the constraint, and taking the minimization of the overall flexibility of the lattice structure under complex service conditions as the optimization objective, establish a mathematical model for the microscopic configuration optimization of each type of lattice unit cell. Finally, use the improved ESPSO algorithm to efficiently solve the optimization model and obtain the optimized and updated rod diameter parameters of each lattice unit cell.

[0010] Step 4: Extract the rod diameter parameters of each lattice unit cell after optimization and updating in Step 3, and generate a new microscopic topological configuration. Recalculate the equivalent elastic tensor corresponding to each lattice unit cell using the numerical homogenization method. Calculate the overall flexibility of the lattice structure based on this. Determine whether convergence has occurred. If it has, proceed to the next step; otherwise, return to Step 2. After updating the configuration of each type of lattice unit cell, perform the next round of macroscopic topological distribution optimization. This establishes an iterative optimization mechanism that alternates between macroscopic and microscopic levels, allowing Step 2 and Step 3 to be executed alternately.

[0011] Step 5: Output the various lattice unit cell configurations obtained in the last iteration and their distribution in the macroscopic design domain, and fill each type of lattice unit cell configuration into its corresponding macroscopic distribution region to obtain the optimized lattice structure.

[0012] Furthermore, step 2 specifically includes the following steps:

[0013] Step 2.1: Treat different lattice unit cells as different material phases. Using the calculated macroscopic equivalent elastic tensors of each lattice unit cell, establish a DS-MMLS multi-material level set topological description model based on difference sets. In this model, N level set functions are used to represent the multi-material structure containing N types of lattice material phases and 1 type of porous phase, as shown in the following equation:

[0014] in, Describes the function of the nth level set. express The physical area, Represents entity region The boundary, It is a fixed Euler reference space. In space The coordinates of the points within the level plane, where t is the time variable describing the motion of the zero level plane of the level set function at any given moment. To represent the union, such as Describe the union of m level set functions. To represent the intersection, such as This represents the intersection of m-1 level set functions. To represent the difference set, such as Represents entity region Boundary of physical region The difference set;

[0015] Step 2.2: Based on the DS-MMLS multi-material level set topological description model, the equivalent elastic tensor of the macroscopic finite element is calculated using the following interpolation model:

[0016]

[0017] In the formula, i, j, k, l = 1, 2, 3, …d, where d is the spatial dimension of the design space. Let be the macroscopic equivalent elastic tensor of the nth lattice unit cell. The equivalent elastic tensor of the porous phase; It is the Heaviside function, used to identify level set functions. Characterizes different parts of a structural region;

[0018] Step 2.3: Optimize the macroscopic topological distribution of multiple lattice unit cells using a topology optimization method based on parameterized level sets. The original N+1 phase multi-material distribution optimization problem is decomposed into N(N+1) / 2 sub-problems for two-phase material distribution optimization using the alternating active phase method. Multiple iterations are performed on each two-phase material distribution optimization sub-problem, obtaining the macroscopic topological distribution of N types of lattice unit cells in each iteration until convergence. The iteration stops, and the final macroscopic topological distribution of N types of lattice unit cells is output. Assuming N is 3, the macroscopic design domain contains 4 material phases: 3 types of lattice unit cells and 1 type of porous phase, namely lattice unit cells a, b, and c, and porous phase d. The 4 material phases are divided into 6 groups: (a, b), (a, c), (a, d), (b, c), (b, d), and (c, d). The optimization model of the two-phase material distribution optimization sub-problem is used to optimize the distribution of the 6 groups of two-phase phases sequentially.

[0019] For the macroscopic topological distribution of lattice unit cell a: First, when optimizing the (a, b) group within the macroscopic distribution regions of lattice units a and b, the topological distributions of lattice units a and b are randomly initialized, and the topological distribution result of lattice unit cell a is extracted; then, based on the extracted topological distribution result of lattice unit cell a, the (a, c) group is optimized within the macroscopic distribution regions of lattice units a and c to update the topological distribution of lattice unit cell a; then, the (a, d) group is optimized within the macroscopic distribution regions of lattice units a and d, and the topological distribution of lattice unit cell a is updated again; after iterating through the optimization of the three groups of two-phase material distributions (a, b), (a, c), and (a, d) in sequence, the macroscopic topological distribution of lattice unit cell a is finally determined;

[0020] For the macroscopic topological distribution of lattice unit cell b: Firstly, optimization is performed on group (b, c) within the macroscopic distribution regions of lattice units b and c to extract the topological distribution result of lattice unit cell b. Subsequently, based on the extracted topological distribution result of lattice unit cell b, optimization is performed on group (b, d) within the macroscopic distribution regions of lattice units b and d to update the topological distribution of lattice unit cell b. This process is repeated for both groups (b, c) and (b, d) to optimize the distribution of the two-phase materials, ultimately determining the macroscopic topological distribution of lattice unit cell b.

[0021] For the macroscopic topological distribution of lattice unit cell c: Optimize the (c, d) group within the macroscopic distribution region of lattice unit cells c and d to obtain the topological distribution of lattice unit cells c and d; Thus, after iterating through the six groups of two-phase material distribution optimization problems (a, b), (a, c), (a, d), (b, c), (b, d), (c, d) in sequence, the macroscopic topological distribution of lattice unit cells a, b, c and porous phase d can be obtained;

[0022] In the next iteration, the distribution of the six groups of biphase materials is optimized in the same order. When optimizing the (a, b) group, the topological distribution of lattice unit cells a and b is updated to the result obtained in the previous iteration. After optimizing the six groups of biphase materials in sequence, the topological distribution results of the three types of lattice unit cells and the one type of porous phase in this iteration are finally obtained.

[0023] Furthermore, in step 2.3, the optimization model for the two-phase material distribution optimization subproblem is as follows:

[0024]

[0025] Where a and b represent lattice cell a and lattice cell b in the distribution optimization subproblem of the two types of lattice cells, respectively. These are design variables, representing the expansion coefficients of the radial basis functions at the l-th node of the level set grid belonging to the a-th lattice unit cell. This represents the design domain of lattice unit cell a and lattice unit cell b in the lattice structure. Let be the objective function of the distribution optimization subproblem for these two types of lattice unit cells; u is the macroscopic displacement field, and v represents the macroscopic virtual displacement field belonging to the kinematically admissible displacement space U. This represents the macroscopic strain corresponding to the macroscopic displacement field. This represents the macroscopic strain corresponding to the macroscopic virtual displacement field; It is the volume constraint of the a-th type of lattice unit cell. It is the volume fraction of the a-th type of lattice unit cell. p is the total volume of the lattice unit cell design domain; p is the lattice structure design domain. Volume forces on It acts on the boundary The traction force on the surface; These are design variables after regularization. and They are The upper and lower boundaries; The macroscopic finite element elastic tensor containing lattice unit cells a and b can be expressed as the macroscopic equivalent elastic tensor of lattice unit cell a. The macroscopic equivalent elastic tensor of lattice unit cell b The following was obtained through interpolation:

[0026]

[0027] Furthermore, in step 2.3, the optimization criterion method is used to optimize the design variables. Update to optimize the objective function Therefore, it is necessary to calculate the objective function. For design variables The sensitivity information is calculated using the following formula:

[0028] Sensitivity of the objective function to design variables:

[0029]

[0030] in , It is the Heaviside function The derivative of It is a tightly supported radial basis function. This represents the volume of the design domain for lattice unit cells a and b. Indicates in The strain field of the unit test under the direction, To represent an unknown strain field is to apply... The strain field of the unit test under the direction is generated in the lattice unit cell; Indicates in The strain field of the unit test under the direction, To represent an unknown strain field is to apply... The strain field of the unit test under the direction is generated in the lattice unit cell.

[0031] Sensitivity of volume constraints to design variables:

[0032]

[0033] Furthermore, step 3 specifically includes the following steps:

[0034] Using the geometric description parameters of the lattice unit cell as design variables, the given volume fraction of each lattice unit cell as constraints, and minimizing the overall compliance of the lattice structure as the objective function, an optimization mathematical model is constructed:

[0035]

[0036] in These are design variables, representing the diameter of the j-th member in the n-th lattice unit cell, N is the total number of lattice unit cell types, J is the total number of members in the lattice unit cell, and C is the overall flexibility of the lattice structure. The total load matrix, The total displacement matrix generated under load is given. It is the overall stiffness matrix of the lattice structure. This represents the volume fraction constraint of the nth lattice unit cell. This represents the volume of the nth lattice unit cell. This represents the given volume fraction of the nth lattice unit cell. This represents the design domain volume of the lattice unit cell; and These are the upper and lower limits of the rod diameter;

[0037] An improved ESPSO algorithm is used to determine the optimal diameter values ​​of each member in each type of lattice unit cell, ultimately obtaining the optimal diameter values ​​for N types of lattice unit cells. Compared with existing technologies, this invention, employing the above technical solution, has the following advantages:

[0038] 1. The technical solution provided by this invention, compared with existing lattice structure design methods, proposes a multi-scale design method for lattice structures that simultaneously considers multiple types of lattice configurations and their topological distributions. Specifically, at the microscale, the ESPSO algorithm is used to obtain the optimal configuration of multiple types of lattice unit cells; at the macroscale, a multi-material topology optimization algorithm is used to obtain the macroscopic topological distribution of multiple types of lattice unit cells.

[0039] 2. This invention proposes an intelligent optimization method for the microstructure of lattice unit cells by improving the ESPSO algorithm, enabling free design of lattice unit cell configurations. Specifically, this invention employs a restart strategy to improve the ESPSO algorithm, enhancing its global search capability and improving optimization efficiency; simultaneously, it designs a member deletion strategy, allowing the deletion of redundant members during the optimization process, thus increasing the flexibility of lattice unit cell configuration design.

[0040] 3. This invention employs a multi-material topology optimization algorithm to optimize the macroscopic topological distribution of multiple types of lattice unit cells, significantly expanding the design space of lattice structures. Specifically, this invention uses a difference-based multi-material level set (DS-MMLS) model to optimize the macroscopic topological distribution of multiple types of lattice unit cells, resulting in clear and non-overlapping boundaries of the multi-type lattice distribution regions. Furthermore, the alternating active phase algorithm decomposes the complex multiphase optimization problem into a series of two-phase sub-problems, reducing the design variables and constraints for the macroscopic distribution optimization of multiple types of lattice unit cells, improving optimization efficiency, and ensuring the stability of iterative convergence.

[0041] 4. This invention achieves synergistic optimization of the micro-configuration and macro-distribution of multiple types of lattice unit cells in lattice structures. Compared with existing design methods that use single or multiple types of lattice unit cells, this invention fully considers the coupling effect between the micro-configuration and macro-distribution of lattice unit cells, while giving full play to the configuration diversity of multiple types of lattice unit cells, greatly expanding the design space of lattice structures, fully utilizing the potential of materials, effectively improving the mechanical properties of lattice structures, and minimizing the weight of lattice structures.

[0042] The present invention will now be described in detail with reference to the accompanying drawings and embodiments. Attached Figure Description

[0043] Figure 1This is a flowchart illustrating the implementation of a multi-scale design method for lattice structures that considers various lattice configurations and their topological distributions.

[0044] Figure 2 Figure (a) is a schematic diagram of the design domain and boundary conditions of the structure to be optimized in the embodiment, and Figure (b) is the initial design of the lattice unit cell, which is discretized into 30×30×30 eight-node hexahedral elements.

[0045] Figure 3 It is the iterative process of optimizing the overall flexibility of the lattice structure and the volume fraction of the three lattice units when optimizing the macroscopic distribution of the three lattice units, as well as the intermediate results of the macroscopic distribution of the three lattice units.

[0046] Figure 4 It is an iterative process for optimizing the overall structural flexibility of the three lattice unit cells, as well as intermediate results of the three lattice unit cell configurations;

[0047] Figure 5 Figure (a) shows the final macroscopic distribution of the optimized multi-type lattice unit cells, while Figures (b) to (d) show the individual macroscopic distributions of the three types of lattice unit cells. It can be seen that the optimized macroscopic distributions of different lattice unit cells are concentrated and reasonable.

[0048] Figure 6 Figures (a), (c), and (e) show the final configurations of the three optimized lattice unit cells, with volume fractions of 30%, 20%, and 10%, respectively. Figure 5 Figures (b), (d), and (f) show the periodic structures obtained by arranging the three final configurations of the lattice unit cell in a 3×3×7 configuration; Detailed Implementation

[0049] The principles and features of the present invention are described below with reference to the accompanying drawings. The examples given are only for explaining the present invention and are not intended to limit the scope of the present invention.

[0050] like Figure 1 As shown, the method of the present invention includes the following steps:

[0051] (a) The lattice unit cell to be optimized consists of preset nodes and connecting rods. To ensure smooth and seamless connection of the rods at the nodes, each rod is designed as a combination of a central cylinder and two spheres at both ends, and its geometry is described using an explicit geometric topological function based on the level set method. Taking a three-dimensional lattice structure as an example, in specific implementation, the three-dimensional unit cell design domain is first meshed using finite element methods, and the spatial position is located using the coordinates of the mesh nodes. Then, level set values ​​are defined at each node to construct a four-dimensional level set function. The level set value represents the minimum distance from the node to the structural boundary, and the zero isosurface of the four-dimensional level set function is the structural boundary of the three-dimensional lattice. Unlike the traditional method of defining the level set function of a lattice structure using free functions or radial basis functions, this invention uses an explicit mathematical relation to define the level set function. This explicit geometric description method allows for precise control of the structural geometric features by simply adjusting the control parameters of the level set function. Finally, by connecting the preset nodes using the rods defined above, the initial design configuration of the three-dimensional lattice unit cell can be generated.

[0052] (b) Establishing a macroscopic topology optimization model for multiple types of lattice unit cells. First, the macroscopic equivalent elastic tensor of each type of three-dimensional lattice unit cell in step (a) is calculated using a numerical homogenization method, and the element stiffness matrix of each material phase in the macroscopic design domain is calculated accordingly. Different lattice unit cells are considered as different material phases at the macroscopic scale. Based on this, the macroscopic distribution parameters of different lattice materials (i.e., the level set function in the DS-MMLS model) are used as design variables, the overall compliance of the lattice structure under complex service conditions is minimized as the objective function, and the corresponding macroscopic volume fraction of each lattice material is used as the constraint condition to establish a macroscopic topology optimization model for multiple types of lattice materials. In order to efficiently solve this multi-material optimization problem, the Alternating Active-Phase Algorithm is introduced to decompose the complex multi-material topology optimization problem containing N+1 phases (N types of lattice materials and 1 type of void phase) into N(N+1) / 2 binary-phase topology optimization sub-problems. Compared to the original multi-material problem, each sub-problem involves fewer design variables and volume constraints, reducing the complexity of the optimization problem and improving the computational efficiency. Finally, the Optimality Criteria (OC) method is used to iteratively solve each sub-problem. By updating the single-level set function, the topological evolution of the active phases in a fixed domain is realized, thereby obtaining the macroscopic topological distribution of the heterogeneous lattice.

[0053] (c) Obtain the macroscopic topological distribution of the various types of lattice unit cells optimized in step (b). Based on this distribution, optimize the configuration of each type of lattice unit cell separately. Using the rod diameter of each lattice unit cell as the design variable and the given material volume ratio of each lattice unit cell as the constraint, and taking the minimization of the overall flexibility of the lattice structure under complex service conditions as the optimization objective, establish the microscopic configuration optimization model of each lattice unit cell, and use the improved ESPSO algorithm for efficient solution. First, the initial particle swarm size for the ESPSO algorithm is set, typically five times the number of design variables, generating a particle swarm that meets volume constraints. The fitness of each particle is evaluated, and a deletion threshold for design variables is set. Second, the velocity and position of the particles are updated using optimal solution information from global and local approximation models; particles below the deletion threshold are assigned a value of 0. Then, the volume fraction of the lattice structure is calculated based on the optimal particles found by the algorithm to determine if it meets the volume ratio constraint. If it does, the compliance of the lattice structure is calculated through optimization models; if not, a better particle is searched again. Finally, a restart strategy is used to periodically refresh the algorithm's optimization process, making the optimal particle from the previous optimization the initial particle for the next optimization, ensuring a more thorough exploration of the design space to obtain the global optimum.

[0054] (d) Extract the geometric parameters of each lattice unit cell after optimization and updating in step (c) and generate a new microscopic topological configuration. Recalculate the equivalent elastic tensor corresponding to each lattice unit cell using a numerical homogenization method and input it into step (b) for the next round of macroscopic topological distribution optimization. This establishes a macroscopic-microscopic alternating iterative optimization mechanism, so that steps (b) and (c) are executed alternately. During the alternating iteration process, convergence is judged. If the preset convergence criterion is met (e.g., after two adjacent iterations, the rate of change of the overall flexibility of the lattice structure is less than a set threshold and the preset maximum number of alternating cycles is reached), the optimization iteration is terminated, and the final multi-class lattice configuration and its macroscopic distribution form are output. If the criteria are not met, macroscopic-microscopic alternating optimization continues.

[0055] As a preferred embodiment, in step (a), taking a three-dimensional lattice unit cell as an example, the explicit topological description model of the lattice rods based on the level set is as follows:

[0056]

[0057] In the formula, D represents the three-dimensional spatial design domain. The solid area where the representative rod is located. For the boundary of the rod structure, Let be the coordinates of a point within the spatial design domain D. This represents a lattice member consisting of a cylinder and two spheres, whose geometry is determined by horizontal set functions. , and Explicit description is required. Specifically, the center coordinates of the two spherical units mentioned above are located at... and The centers of these two spheres coincide perfectly with the endpoints of the cylindrical element. To ensure a smooth and seamless connection at the nodes, the cylindrical element shares the same diameter parameter as the two spheres, both set to... The coordinates of the geometric center point and the axial length of the cylinder are respectively... and . It is a point The angle between the cylinder and the axis of the cylinder. It is a point to the midpoint distance, , , Representing points respectively to the midpoint The difference vector components, , , Representing points respectively to the midpoint Difference vector components

[0058] In a preferred embodiment, in steps (b) and (c), the equivalent elastic tensor of the lattice unit cell is calculated using a numerical homogenization method, and the calculation formula can be expressed as:

[0059]

[0060] in , , , =1,2,3,…,d represents the spatial dimensions of the design space; The elastic tensor representing the solid material; and These represent the design domain and volume of the e-th lattice unit cell, respectively. This is a Heaviside function used to identify different parts of a structural domain. This represents the initial strain field of the unit test. The unknown strain field can be obtained by solving the following linear elastic equilibrium equations:

[0061]

[0062] In the formula, It is a virtual displacement field. This represents the kinematically permissible displacement space under periodic boundary conditions. The equivalent elastic tensor of each lattice unit cell is obtained. To simplify the calculation, each lattice element is considered as a macroscopic element. By assembling the element stiffness matrices, the global stiffness matrix K of the lattice structure can be obtained:

[0063]

[0064] In the formula, B is the strain-displacement matrix, and NE is the total number of macroscopic finite elements.

[0065] After obtaining the overall stiffness matrix, the displacement field of the lattice structure can be obtained by solving the equilibrium equations of the lattice structure, and the overall compliance value of the lattice structure can be further calculated.

[0066]

[0067]

[0068] In a preferred embodiment, in step (b), different lattice unit cells are treated as different material phases. Using the calculated macroscopically equivalent elastic tensors of each lattice unit cell, a difference-based multi-material level set (DS-MMLS) topological description model is established. In this model, N level set functions are used to represent a multi-material structure containing N lattice material phases and 1 void phase, as shown in the following equation:

[0069]

[0070] in, Describes the function of the nth level set. express The physical area, Represents entity region The boundary, It is a fixed Euler reference space. In space The coordinates of the points inside, This is a time variable describing the motion of the zero level plane of the level set function at any given moment. According to the aforementioned DS-MMLS multi-material description model, the macroscopic topological distribution of each lattice can be described by different combinations of level set functions. Therefore, using the aforementioned multi-material description model, only N level set functions are needed to describe the topological distribution of N+1 different lattice materials (including porous phases).

[0071] As a preferred embodiment, in step (b), based on the DS-MMLS multi-material description model, the equivalent elastic tensor of the macroscopic finite element can be calculated using the following interpolation model:

[0072]

[0073] In the formula Let be the macroscopic equivalent elastic tensor of the nth lattice unit cell. For the elastic tensor of the void phase.

[0074] In a preferred embodiment, step (b) employs a parameterized level set topology optimization method based on radial basis functions to optimize the macroscopic topological distribution of the lattice unit cell. The optimization model is as follows:

[0075]

[0076] In the formula, is a design variable representing the expansion coefficient of the radial basis function at the l-th node of the level set mesh belonging to the n-th lattice unit cell; N represents the total number of lattice unit cell types; and L is the total number of nodes on the level set mesh within the lattice unit cell. J is the objective function, representing the overall compliance of the lattice structure. This represents the macroscopic design domain of the lattice structure. u is the macroscopic displacement field, and v represents the macroscopic virtual displacement field belonging to the kinematically permissible displacement space U. This represents the macroscopic strain corresponding to the macroscopic displacement field. This represents the macroscopic strain corresponding to the macroscopic virtual displacement field. and These represent the bilinear energy and linear load forms of the lattice structure, respectively. Vn is the volume fraction of the nth type of lattice unit cell, V0 is the total volume of the lattice unit cell design domain, and f is the lattice structure design domain. volume force, It acts on the boundary The traction force on the surface. These are design variables that have been regularized to facilitate subsequent numerical implementation. and These are design variables The upper and lower boundaries.

[0077] In a preferred embodiment, in step (b), the topology optimization problem of the original N+1 phase multi-type lattice unit cells is transformed into N(N+1) / 2 sub-problems of two-type lattice unit cell distribution optimization using the alternating active phase method. The optimization model of the two-type lattice unit cell distribution optimization sub-problems is as follows:

[0078]

[0079] Where a and b represent lattice cell a and lattice cell b in the distribution optimization subproblem of the two types of lattice cells, respectively. It is a design variable, representing the expansion coefficient of the radial basis function at the l-th node of the horizontal set grid belonging to the a-th lattice unit cell. Let be the objective function of the subproblem of optimizing the distribution of these two types of lattice unit cells. It is the volume constraint of the a-th type of lattice unit cell. It is the volume fraction of the a-th type of lattice unit cell. This represents the design domain of lattice unit cells a and b in the lattice structure. These are design variables after regularization. and They are The upper and lower boundaries. The total macroscopically equivalent elastic tensor of the lattice units within the lattice structure containing lattice unit a and lattice unit b can be expressed as the macroscopically equivalent elastic tensor of lattice unit a. The macroscopic equivalent elastic tensor of lattice unit cell b The following was obtained through interpolation:

[0080]

[0081] In a preferred embodiment, in step (b), the optimization criterion method is used to optimize the design variables. To perform the update, the objective function needs to be calculated. For design variables The sensitivity information is calculated using the following formula:

[0082] Sensitivity of the objective function to design variables:

[0083]

[0084] in , It is the differential of the Heaviside function. It is a tightly supported radial basis function.

[0085] Sensitivity of volume constraints to design variables:

[0086] In a preferred embodiment, in step (c), the geometric description parameters of the lattice unit cell are used as design variables, the given volume fraction of each lattice unit cell is used as a constraint, and minimizing the overall compliance of the lattice structure is used as the objective function to construct an optimization mathematical model:

[0087]

[0088] in These are design variables, representing the diameter of the j-th member in the n-th lattice unit cell, N is the total number of lattice unit cell types, J is the total number of members in the lattice unit cell, and C is the overall flexibility of the lattice structure. The total load matrix, The total displacement matrix generated under load is given. It is the overall stiffness matrix of the lattice structure. This represents the volume fraction constraint of the nth lattice unit cell. This represents the volume of the nth lattice unit cell. This represents the given volume fraction of the nth lattice unit cell. This represents the design domain volume of the lattice unit cell. and These are the upper and lower limits of the rod diameter.

[0089] As a further preferred option, in step (c), the ESPSO algorithm is used to determine the optimal diameter values ​​of each member of the lattice unit cell. To improve the optimization efficiency of the ESPSO algorithm, a new strategy is adopted to update the particle velocity, and the update method is as follows:

[0090]

[0091]

[0092] in

[0093]

[0094]

[0095]

[0096] d is the d-th dimension of the optimization problem. and These are the velocity and position of the i-th particle in the t-th iteration, respectively. It is the historical best position reached by the i-th particle of an individual. It is the global optimal position for all particles. It is the predicted response value of the global RBF model constructed from all particles in the design space; It is its optimal value point in the entire design space, that is, the global optimal position. It is composed of particles The predicted response value of a local RBF model composed of particles in the neighborhood; It is the optimal value point in its neighborhood, that is, the local optimum. (Particle) The position is updated by tracking these two optimal values. and These are two random numbers that are uniformly distributed in the range [0,1]. and This is the acceleration factor, which is usually greater than zero. .generally Greater than 4, therefore and The values ​​are 2.05 respectively. Within the range The constant is usually taken as 0.729.

[0097] To further expand the design space of lattice unit cells and fully utilize the material potential, this invention designs a low-efficiency rod diameter removal strategy to enhance the flexibility of lattice unit cell configuration design and improve the mechanical properties of lattice structures. Specifically, as the iteration progresses, the internal force transmission path causes the main load-bearing rods to thicken and the secondary rods to thin. Therefore, a minimum threshold is set during the algorithm optimization iteration process. When the nth member's diameter decreases due to low load-bearing efficiency... At that time, the algorithm will... Directly assigning zeros achieves the effect of removing the member. Simultaneously, addressing the risk of particle swarm optimization (ESPSO) getting trapped in local optima, this invention employs a fast restart strategy during the ESPSO algorithm optimization process, enabling the algorithm to explore the design space more comprehensively. Specifically, when the algorithm gets trapped in a local optimum, it forces the swarm particles to redistribute within the space, guiding them to perform a global domain search again based on the existing optimal solution, thereby obtaining a higher-quality global optimum solution with the same computational cost.

[0098] like Figure 2 As shown in Figure (a), the structural design domain of this embodiment has a length L=80 and a height H=40. The left edge is completely fixed, and a concentrated load F=1 is applied vertically at the upper right corner. The design domain is discretized into 80×40 four-node quadrilateral finite elements, as shown in Figure (a). Figure 2 As shown in Figure (b), the initial design of the lattice unit cell is discretized into 30×30×30 eight-node hexahedral elements; the above example is used to verify the feasibility and optimization effect of the method of the present invention;

[0099] like Figure 3 As shown, when optimizing the macroscopic distribution of the three lattice cells, the iterative process of the overall flexibility of the lattice structure and the volume fraction of the three lattice cells, as well as the intermediate results of the macroscopic distribution of the three lattice cells, are presented. It can be seen that by optimizing the macroscopic topological distribution of the three lattice cells (red lattice cell: volume fraction 0.3, blue lattice cell: volume fraction 0.2, green lattice cell: volume fraction 0.1), the overall flexibility of the lattice structure gradually decreases and eventually converges.

[0100] like Figure 4As shown, in the iterative optimization process of the overall structural flexibility of the three lattice unit cells, the diameter of the rods in the three lattice unit cells is continuously optimized, while low load-bearing efficiency rods are gradually removed, and the overall flexibility of the lattice structure gradually decreases. In addition, the second type of lattice unit cell is optimized after the optimization of the first type of lattice unit cell reaches convergence, and the third type of lattice unit cell is optimized after the optimization of the second type of unit cell reaches convergence. The optimal solution of each type of lattice unit cell will be used as the initial particle for the next optimization.

[0101] From such Figure 5 It can be seen that the macroscopic distribution of different lattice unit cells is concentrated and reasonable after optimization;

[0102] from Figure 6 As can be seen, there are significant differences in the thickness of the members in the lattice unit cell, and some members with low load-bearing efficiency have been removed. Compared with the initial lattice unit cell, it has better load-bearing performance and can better adapt to complex working conditions.

[0103] The above description provides examples of the preferred embodiments of the present invention. Parts not detailed herein are common knowledge to those skilled in the art. The scope of protection of the present invention is determined by the claims. Any equivalent modifications based on the technical teachings of the present invention are also within the scope of protection of the present invention.

Claims

1. A multi-scale design method for lattice structures considering multiple lattice configurations and their topological distributions, characterized in that, Includes the following steps: Step 1: Establish the initial design of the macroscopic topological distribution of multiple types of lattice unit cells, determine the number N of types of lattice unit cells in the macroscopic design domain, and each type of lattice unit cell is composed of preset nodes in three-dimensional space and rods connecting the preset nodes. The number and distribution of rods in different lattice unit cells are different. The lattice rod consists of a cylinder and two spheres at its two ends. The geometry of the cylinder and spheres is described by an explicit topological function based on level sets, thus realizing an explicit description of the geometry of the lattice rod. The rod is used to connect predefined nodes to form the initial design of the lattice unit cell. Step 2: Calculate the macroscopic equivalent elastic tensor of each type of lattice unit cell in Step 1 using a numerical homogenization method. Based on this, calculate the element stiffness matrix of each lattice unit cell in the macroscopic design domain. At the macroscopic scale, different types of lattice unit cells are considered as different material phases. On this basis, the macroscopic distribution parameters of different lattice material phases, i.e., the level set function in the DS-MMLS model, are used as design variables. The objective function is to minimize the overall compliance of the lattice structure under complex service conditions. The macroscopic volume fraction corresponding to each lattice material is used as a constraint condition to establish a macroscopic topology optimization model for multiple types of lattice materials. Then, using the alternating active phase algorithm, the multi-material distribution optimization problem containing N+1 phases (i.e., N types of lattice unit cells and 1 type of porous phase) is decomposed into N(N+1) / 2 two-phase material distribution optimization sub-problems. Finally, in each two-phase material distribution optimization sub-problem, the optimization criterion method is used to iteratively optimize the two-phase material distribution. By traversing all two-phase material distribution optimization sub-problems, the macroscopic topology distribution of each type of lattice unit cell in the macroscopic design domain is obtained. Step 3: Based on the macroscopic topological distribution of each type of lattice unit cell obtained in the previous step, optimize the configuration of each type of lattice unit cell. Using the rod diameter of each lattice unit cell as the design variable and the given material volume ratio of each lattice unit cell as the constraint, and taking the minimization of the overall flexibility of the lattice structure under complex service conditions as the optimization objective, a mathematical model for the microstructure optimization of various lattice unit cells is established. Finally, the improved ESPSO algorithm is used to efficiently solve the optimization model to obtain the rod diameter parameters of each lattice unit cell after optimization and update. Step 4: Extract the rod diameter parameters of each lattice unit cell after optimization and updating in Step 3, and generate a new microscopic topological configuration. Recalculate the equivalent elastic tensor corresponding to each lattice unit cell using the numerical homogenization method. Calculate the overall flexibility of the lattice structure based on this. Determine whether convergence has occurred. If it has, proceed to the next step; otherwise, return to Step 2. After updating the configuration of each type of lattice unit cell, perform the next round of macroscopic topological distribution optimization. This establishes an iterative optimization mechanism that alternates between macroscopic and microscopic levels, allowing Step 2 and Step 3 to be executed alternately. Step 5: Output the various lattice unit cell configurations obtained in the last iteration and their distribution in the macroscopic design domain, and fill each type of lattice unit cell configuration into its corresponding macroscopic distribution region to obtain the optimized lattice structure.

2. The multi-scale design method for lattice structures considering multiple lattice configurations and their topological distributions according to claim 1, characterized in that, Step 2 specifically includes the following steps: Step 2.1: Treat different lattice unit cells as different material phases. Using the calculated macroscopic equivalent elastic tensors of each lattice unit cell, establish a DS-MMLS multi-material level set topological description model based on difference sets. In this model, N level set functions are used to represent the multi-material structure containing N types of lattice material phases and 1 type of porous phase, as shown in the following equation: in, Describes the function of the nth level set. express The physical area, Represents entity region The boundary, It is a fixed Euler reference space. In space The coordinates of the points within the level plane, where t is the time variable describing the motion of the zero level plane of the level set function at any given moment. To represent the union, such as Describe the union of m level set functions. To represent the intersection, such as This represents the intersection of m-1 level set functions. To represent the difference set, such as Represents entity region Boundary of physical region The difference set; Step 2.2: Based on the DS-MMLS multi-material level set topological description model, the equivalent elastic tensor of the macroscopic finite element is calculated using the following interpolation model: ； In the formula, i, j, k, l = 1, 2, 3, ... d, where d is the spatial dimension of the design space. Let be the macroscopic equivalent elastic tensor of the nth lattice unit cell. The equivalent elastic tensor of the porous phase; It is the Heaviside function, used to identify level set functions. Characterizes different parts of a structural region; Step 2.3: Optimize the macroscopic topological distribution of multiple lattice unit cells using a topology optimization method based on parameterized level sets. The original N+1 phase multi-material distribution optimization problem is decomposed into N(N+1) / 2 sub-problems for two-phase material distribution optimization using the alternating active phase method. Multiple iterations are performed on each two-phase material distribution optimization sub-problem, obtaining the macroscopic topological distribution of N types of lattice unit cells in each iteration until convergence. The iteration stops, and the final macroscopic topological distribution of N types of lattice unit cells is output. Assuming N is 3, the macroscopic design domain contains 4 material phases: 3 types of lattice unit cells and 1 type of porous phase, namely lattice unit cells a, b, and c, and porous phase d. The 4 material phases are divided into 6 groups: (a, b), (a, c), (a, d), (b, c), (b, d), and (c, d). The optimization model of the two-phase material distribution optimization sub-problem is used to optimize the distribution of the 6 groups of two-phase phases sequentially. For the macroscopic topological distribution of lattice unit cell a: First, when optimizing the (a, b) group within the macroscopic distribution regions of lattice units a and b, the topological distributions of lattice units a and b are randomly initialized, and the topological distribution result of lattice unit cell a is extracted; then, based on the extracted topological distribution result of lattice unit cell a, the (a, c) group is optimized within the macroscopic distribution regions of lattice units a and c to update the topological distribution of lattice unit cell a; then, the (a, d) group is optimized within the macroscopic distribution regions of lattice units a and d, and the topological distribution of lattice unit cell a is updated again; after iterating through the optimization of the three groups of two-phase material distributions (a, b), (a, c), and (a, d) in sequence, the macroscopic topological distribution of lattice unit cell a is finally determined; For the macroscopic topological distribution of lattice unit cell b: Firstly, optimization is performed on group (b, c) within the macroscopic distribution regions of lattice units b and c to extract the topological distribution result of lattice unit cell b. Subsequently, based on the extracted topological distribution result of lattice unit cell b, optimization is performed on group (b, d) within the macroscopic distribution regions of lattice units b and d to update the topological distribution of lattice unit cell b. This process is repeated for both groups (b, c) and (b, d) to optimize the distribution of the two-phase materials, ultimately determining the macroscopic topological distribution of lattice unit cell b. For the macroscopic topological distribution of lattice unit cell c: Optimize the (c, d) group within the macroscopic distribution region of lattice unit cells c and d to obtain the topological distribution of lattice unit cells c and d; Thus, after iterating through the six groups of two-phase material distribution optimization problems (a, b), (a, c), (a, d), (b, c), (b, d), (c, d) in sequence, the macroscopic topological distribution of lattice unit cells a, b, c and porous phase d can be obtained; In the next iteration, the distribution of the six groups of biphase materials is optimized in the same order. When optimizing the (a, b) group, the topological distribution of lattice unit cells a and b is updated to the result obtained in the previous iteration. After optimizing the six groups of biphase materials in sequence, the topological distribution results of the three types of lattice unit cells and the one type of porous phase in this iteration are finally obtained.

3. The multi-scale design method for lattice structures considering multiple lattice configurations and their topological distributions according to claim 2, characterized in that, In step 2.3, the optimization model for the two-phase material distribution optimization subproblem is as follows: ； Where a and b represent lattice cell a and lattice cell b in the distribution optimization subproblem of the two types of lattice cells, respectively. These are design variables, representing the expansion coefficients of the radial basis functions at the l-th node of the level set grid belonging to the a-th lattice unit cell. This represents the design domain of lattice unit cell a and lattice unit cell b in the lattice structure. Let be the objective function of the distribution optimization subproblem for these two types of lattice unit cells; u is the macroscopic displacement field, and v represents the macroscopic virtual displacement field belonging to the kinematically admissible displacement space U. This represents the macroscopic strain corresponding to the macroscopic displacement field. This represents the macroscopic strain corresponding to the macroscopic virtual displacement field; It is the volume constraint of the a-th type of lattice unit cell. It is the volume fraction of the a-th type of lattice unit cell. p is the total volume of the lattice unit cell design domain; p is the lattice structure design domain. Volume forces on It acts on the boundary The traction force on the surface; These are design variables after regularization. and They are The upper and lower boundaries; The macroscopic finite element elastic tensor containing lattice unit cells a and b can be expressed as the macroscopic equivalent elastic tensor of lattice unit cell a. The macroscopic equivalent elastic tensor of lattice unit cell b The following was obtained through interpolation: 。 4. The multi-scale design method for lattice structures considering multiple lattice configurations and their topological distributions according to claim 2, characterized in that, In step 2.3, the optimization criterion method is used to optimize the design variables. Update to optimize the objective function Therefore, it is necessary to calculate the objective function. For design variables The sensitivity information is calculated using the following formula: Sensitivity of the objective function to design variables: ; ； in , It is the Heaviside function The derivative of It is a tightly supported radial basis function. This represents the volume of the design domain for lattice unit cells a and b. Indicates in The strain field of the unit test under the direction, To represent an unknown strain field is to apply... The strain field of the unit test under the direction is generated in the lattice unit cell; Indicates in The strain field of the unit test under the direction, To represent an unknown strain field is to apply... The strain field of the unit test under the direction is generated in the lattice unit cell; Sensitivity of volume constraints to design variables: 。 5. The multi-scale design method for lattice structures considering multiple lattice configurations and their topological distributions according to claim 1, characterized in that, Step 3 specifically includes the following steps: Using the geometric description parameters of the lattice unit cell as design variables, the given volume fraction of each lattice unit cell as constraints, and minimizing the overall compliance of the lattice structure as the objective function, an optimization mathematical model is constructed: ； in These are design variables, representing the diameter of the j-th member in the n-th lattice unit cell, N is the total number of lattice unit cell types, J is the total number of members in the lattice unit cell, and C is the overall flexibility of the lattice structure. The total load matrix, The total displacement matrix generated under load is given. It is the overall stiffness matrix of the lattice structure. This represents the volume fraction constraint of the nth lattice unit cell. This represents the volume of the nth lattice unit cell. This represents the given volume fraction of the nth lattice unit cell. This represents the design domain volume of the lattice unit cell; and These are the upper and lower limits of the rod diameter; An improved ESPSO algorithm is used to determine the optimal diameter value of each member of each type of lattice unit cell, and finally the optimal diameter value of N types of lattice unit cells is obtained.

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