Multi-scale hybrid lattice structure bivariate topological optimization method

Abstract

The invention relates to the technical field of lattice structure topological optimization, and discloses a multi-scale hybrid lattice structure double-variable topological optimization method, which comprises the steps of defining double variables, including a first design variable as a scaling scale and a second design variable as a relative density; determining a basic unit cell of the hybrid lattice structure and obtaining a corresponding unit cell size, wherein the second design variable is determined based on the unit cell size; obtaining a first filling unit cell and a second filling unit cell; determining a design domain, and filling the first filling unit cells and the second filling unit cells into the design domain by taking the flexibility minimization of the hybrid lattice structure as a target and the volume fraction as a constraint; and optimizing the filling process based on a moving asymptote optimization algorithm so as to carry out topological optimization of the hybrid lattice structure based on double variables, and outputting an optimized multi-scale hybrid lattice structure. According to the industrial bearing structure, higher structural specific stiffness, specific strength and energy absorption efficiency are achieved, and the requirements for light weight, self-adaption and high performance in an existing industrial bearing structure can be met.

Description

Technical Field

[0001] This application relates to the field of lattice structure topology optimization technology, specifically a bivariate topology optimization method for multi-scale hybrid lattice structures. Background Technology

[0002] Traditional lattice structure design methods typically use only single-scale lattice unit cells arranged periodically to form a uniform lattice structure. This singular configuration makes it highly susceptible to shear banding under compressive loads, as the support structure is prone to twisting and fracture, leading to shear slip and loss of stability, ultimately resulting in load-bearing failure. Furthermore, these methods lack design flexibility and have limited overall strength, making them unsuitable for demanding compressive and load-bearing requirements.

[0003] Most current topology optimization methods are limited to the optimal design of material distribution and have limited application in the field of lattice structure optimization design, or are limited to two-dimensional planar design, resulting in poor manufacturability and practicality. At the same time, most designs are limited to the optimization of a single configuration or different types of lattice configurations, without considering the impact of lattice filling at different scales and densities on the design from a macroscopic perspective. Summary of the Invention

[0004] The purpose of this application is to provide a bivariate topology optimization method for multi-scale hybrid lattice structures to solve the technical problems of insufficient flexibility in lattice structure design, limited overall strength, and difficulty in adapting to the needs of lightweight, high-pressure resistance, and load-bearing scenarios in the prior art.

[0005] To achieve the above objectives, this application provides a bivariate topology optimization method for multi-scale hybrid lattice structures, the method comprising: Define two variables, including a first design variable and a second design variable; wherein, the first design variable is the scaling scale, and the second design variable is the relative density; The basic unit cell of the hybrid lattice structure is determined and the corresponding unit cell size is obtained. The unit cell size is the length, width, and height of the basic unit cell and the diameter of the supporting rods. The second design variable is determined based on the unit cell size. The unit cell size is scaled according to different first design variables to obtain a variety of first filled unit cells with different scales and the same relative density; the length, width and height are kept constant, and the diameter of the support rod is adjusted to obtain a variety of second filled unit cells with different relative densities and the same scale. A design domain is determined, and a filling process is performed. The filling process aims to minimize the compliance of the hybrid lattice structure and is constrained by the volume fraction. The first filling unit cell and the second filling unit cell are filled into the design domain. The filling process is optimized based on the moving asymptote optimization algorithm to perform topology optimization of the bivariate hybrid lattice structure and output the optimized multi-scale hybrid lattice structure.

[0006] Preferably, the topology optimization based on the bivariate hybrid lattice structure includes: Import the design domain and construct the topological relationships, then initialize the bivariate; An iterative loop based on the moving asymptote optimization algorithm is performed, sequentially carrying out finite element analysis, sensitivity calculation and filtering, and bivariate update until the results converge. The optimized bivariate model is discretized and visualized for verification, and a standardized file is exported. The standardized file includes the center coordinates, scaling scale, relative density, and node association information of the basic unit cell.

[0007] Preferably, the filling process is provided with a corresponding mathematical model, which is specifically as follows: in: Represents the second design variable; Represents the first design variable; This represents the number of units in the overall hybrid lattice structure after it has been discretized. Describe the compliance of the objective function, when C At its minimum, the overall stiffness of the hybrid lattice structure is maximized, satisfying the static equilibrium equations. , Represents the nodal displacement matrix. Represents the external load array; Representing the The volume of each unit; Volume fraction representing the overall structure; To optimize the volume of materials used in the process; Represents the total volume of the design domain; This represents the upper limit of the design volume fraction.

[0008] Preferably, the geometric parameters are converted into optimized data before the filling process is performed, specifically as follows: Based on the design domain, a geometric matrix is ​​generated, which is used to provide geometric relationships for stiffness matrix calculation; Based on the pre-acquired density-scale-elastic constant sample data, the effective elastic constants and partial derivatives of each order under any bivariate combination are obtained by two-dimensional interpolation and stored as global variables. The global variables are used for stiffness matrix derivative calculation. Receive the first design variable and the second design variable, read the geometric matrix and elastic parameters, construct the elastic matrix and its derivative, calculate the stiffness matrix and corresponding derivative of the unit through Gaussian integral, and output it for global assembly and sensitivity calculation; Receive grid data and filter radius, and construct a sparse filter matrix by calculating the center point coordinates of the cells and the Euclidean distance between cells to smooth the sensitivity distribution.

[0009] Preferably, the optimization of the filling process based on the moving asymptote optimization algorithm includes: Based on the moving asymptote method, the non-convex optimization problem is transformed into a series of convex subproblems; the upper and lower bounds of the asymptote are dynamically adjusted to generate the approximation coefficient matrix of the subproblems, and the convergence accuracy is controlled by residual checking; The primal-dual Newton method is used to solve the convex subproblem, and the optimal update values ​​for the two variables are output.

[0010] Preferably, the basic unit cell is at least a face-centered cubic lattice, wherein the length, width, and height of the face-centered cubic lattice are all equal to 1 / 2. The diameter of the support rod is ; For the face-centered cubic lattice, the unit cell size is scaled according to different first design variables. Specifically, the unit cell size is scaled according to a ratio of 1:2 and 1:3 to obtain the first filling unit cell, which includes a large lattice corresponding to the original scale, a medium lattice corresponding to the 1:2 scale, and a small lattice corresponding to the 1:3 scale. For the face-centered cubic lattice, while keeping the length, width, and height constant, the diameter of the support rod is adjusted, specifically: the diameter of the support rod... Scaling, relative density The calculation formula is The second filled unit cell is obtained.

[0011] Preferably, the first design variable Relaxation is a continuous variable, taking values ​​in... Between, and Corresponding to large lattice Corresponding lattice, Corresponding to small crystal lattice.

[0012] Preferably, the filter radius is twice the unit size.

[0013] As a preferred approach, when solving the convex problem, the dual gap calculation and step size adaptive adjustment are integrated to optimize the output of the optimal update values ​​of the two design variables.

[0014] Preferably, the method is computer-aided. After completing the topology optimization, the support modeling information of the lattice unit in the design domain is generated based on the first and second design variables of each lattice unit cell in the design domain. By iteratively traversing the lattice unit, a frustum is constructed according to the start and end diameters of the supports of the first and second filled unit cells, and finally, a multi-scale hybrid lattice is formed.

[0015] Beneficial effects: The bivariate topology optimization method for multi-scale hybrid lattice structures in this application breaks through the performance limitations of traditional single-scale lattice structures by combining topology optimization with the design of multi-scale hybrid lattice structures, so as to achieve higher structural specific stiffness, specific strength and energy absorption efficiency, thereby expanding the applicability of lattice structures in lightweight, high-requirement load-bearing and impact-resistant fields; it can solve the requirements of lightweight, adaptive and high-performance in current industrial load-bearing structures. Attached Figure Description

[0016] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0017] Figure 1 A flowchart illustrating the bivariate topology optimization method for multi-scale hybrid lattice structures provided in this application embodiment; Figure 2 A schematic diagram of a single FCC lattice unit cell provided in an embodiment of this application; Figure 3 This is a schematic diagram of FCC lattice unit cells scaled to different scales at the same density, provided in the embodiments of this application; in the figure: (a) represents values ​​of and A schematic diagram of the time; (b) shows the value of and A schematic diagram of the time; (c) represents the value. and A diagram showing the time; Figure 4 The figures are schematic diagrams of FCC lattice unit cells with different relative densities at the same scale, provided in the embodiments of this application; in the figures: (a) is a schematic diagram of a unit cell with a relative density of 0.5; (b) is a schematic diagram of a unit cell with a relative density of 0.3; (c) is a schematic diagram of a unit cell with a relative density of 0.1; Figure 5 A binary interpolation model for the effective elastic constant of a lattice unit cell on a density scale, provided in the embodiments of this application; Figure 6This is an example of a topology optimization problem provided in an embodiment of this application, where H=64mm and L=16mm; Figure 7 A flowchart of density-scale bivariate topology optimization provided for embodiments of this application; Figure 8 The objective function and volume fraction changes during the bivariate topology optimization process provided in this application embodiment; Figure 9 The density and scale results are for topology optimization of bivariate lattice structures; Figure 10 The topology-optimized lattice structure provided in the embodiments of this application; Figure 11 The following are comparative examples of all-large, all-medium, and all-small lattice structures composed of a single scale and the same density, provided for the purposes of this application. In the figures: (a) is an all-large lattice; (b) is an all-medium lattice; and (c) is an all-small lattice. Figure 12 Quasi-static compression experimental images of all-large, all-medium, all-small, and optimized lattices provided in the embodiments of this application; in the figures: (a) is the all-large lattice; (b) is the all-medium lattice; (c) is the all-small lattice; (d) is the optimized lattice; Figure 13 The specific stress-strain curves of all-large, all-medium, and all-small lattices and the optimized lattice provided for embodiments of this application; Figure 14 A comparison diagram of the mechanical properties of the topology-optimized multi-scale lattice structure provided in the embodiments of this application and other uniform lattice structures.

[0018] The implementation, functional features, and advantages of this invention will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation

[0019] The technical solutions in the embodiments of this application will be clearly and completely described below. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments in this application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of this application.

[0020] In this document, the term "comprising" is intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0021] Lattice structures are lightweight, high-performance materials built using porous unit cells as basic units. Their internal porous structure endows them with low relative density and excellent specific strength and impact resistance, better meeting the modern industrial demand for synergistic improvement in lightweighting and high strength compared to solid structures of the same material. In recent years, with the increasingly stringent requirements for material performance in aerospace, transportation, and biomedical fields, lattice structures such as body-centered cubic (BCC) and face-centered cubic (FCC) have become research hotspots, and the precise fabrication of complex configurations has been achieved through additive manufacturing technology.

[0022] However, traditional lattice designs often employ a periodic, uniform arrangement of unit cells on a single scale. Under compressive loads, this configuration is prone to shear band formation due to local buckling of the supports, leading to shear slip failure of the entire structure and a significant reduction in stability and load-bearing capacity. For example, uniform BCC structures are prone to stress concentration at nodes, weakening their compressive strength. Furthermore, insufficient rigidity and limited design freedom also restrict their application potential in high-end applications.

[0023] Topology optimization, as a key technology for breaking through traditional design constraints, occupies an important position in the research of lattice unit cells. Its deep integration with additive manufacturing provides an excellent strategy for achieving algorithm-driven lightweight, high-performance designs. In lattice structures, topology optimization can design solid-lattice hybrid structures, fully leveraging the geometric freedom of additive manufacturing through collaborative design to achieve optimal material distribution and performance breakthroughs.

[0024] This embodiment aims to overcome the performance limitations of traditional single-scale lattice structures by combining topology optimization with multi-scale hybrid configuration lattice design, thereby achieving higher structural specific stiffness, specific strength, and energy absorption efficiency. This expands the applicability of lattice structures in lightweight, high-load-bearing, and impact-resistant applications. It belongs to the fields of computer-aided design and structural design technology, and specifically relates to a scale-density dual-objective topology optimization design method for multi-scale lattice structures, which can address the lightweight, adaptive, and high-performance requirements of current industrial load-bearing structures.

[0025] The technical solution and effects of this embodiment are briefly described below. Inspired by various strengthening mechanisms in metallurgy, such as precipitation strengthening and heterogeneous strengthening, this embodiment provides a topology optimization design method for lattice structures that introduces multiple scales and relative densities, enabling bivariate topology optimization including density and scale design factors. Specifically, based on the original cubic unit cell, multiple scaling levels are formed to create lattice unit cells with different scales. Simultaneously, the diameter of the support rods is changed based on the original cubic unit cell to create lattice unit cells with different relative densities. These lattice unit cells, determined by different density and scale variables, are macroscopically arranged using the topology optimization algorithm results. Minimizing compliance is used as the objective function, and maintaining volume is used as the constraint function. The obtained topology optimization results are then reconstructed to achieve bivariate design for multi-scale lattice structures and improve their mechanical properties. Furthermore, the design domain of this embodiment is not limited to simple design domains such as cubes; it can also achieve adaptive design optimization for complex design domains including curved surface factors. This optimization scheme can achieve optimal structural customization and design based on specific stress scenarios. It can be used in sandwich panels and shell-type devices, bringing better performance improvement and more flexible design space to structures subjected to multiple loads such as compression and impact. Furthermore, this embodiment is mainly implemented using MATLAB and the model is built using Spaceclaim. The methods include FCC lattice bivariate design (including mesh import, geometric matrix generation, two-dimensional interpolation and derivative calculation, element stiffness matrix calculation, finite element analysis, and sensitivity filtering), MMA optimization (including iterative control parameter definition, optimization iteration, and sub-problem solving), and visualization (including hexahedral mesh visualization, density field visualization, and result export).

[0026] Reference Figure 1 , Figure 1 This is a flowchart illustrating the bivariate topology optimization method for multi-scale hybrid lattice structures provided in this application embodiment.

[0027] like Figure 1 As shown in the figure, this embodiment discloses a bivariate topology optimization method for multi-scale hybrid lattice structures, the method including: S10: Define two variables, including a first design variable and a second design variable; wherein, the first design variable is the scaling scale and the second design variable is the relative density.

[0028] S20: Determine the basic unit cell of the hybrid lattice structure and obtain the corresponding unit cell size, wherein the unit cell size is the length, width, height of the basic unit cell and the diameter of the supporting rods; and the second design variable is determined based on the unit cell size.

[0029] S30: Scaling the unit cell size according to different first design variables to obtain a variety of first filled unit cells with different scales and the same relative density; keeping the length, width and height constant, adjusting the diameter of the support rod to obtain a variety of second filled unit cells with different relative densities and the same scale.

[0030] S40: Determine the design domain and execute the filling process, wherein the filling process aims to minimize the compliance of the hybrid lattice structure and is constrained by the volume fraction, and fills the first filling unit cell and the second filling unit cell into the design domain.

[0031] S50: The filling process is optimized based on the moving asymptote optimization algorithm to perform topology optimization of the hybrid lattice structure based on bivariate, and the optimized multi-scale hybrid lattice structure is output.

[0032] Specifically, the basic unit cell is at least a face-centered cubic lattice, and the length, width, and height of the face-centered cubic lattice are all... The diameter of the support rod is ; For the face-centered cubic lattice, the unit cell size is scaled according to different first design variables. Specifically, the unit cell size is scaled according to a ratio of 1:2 and 1:3 to obtain the first filling unit cell, which includes a large lattice corresponding to the original scale, a medium lattice corresponding to the 1:2 scale, and a small lattice corresponding to the 1:3 scale. For the face-centered cubic lattice, while keeping the length, width, and height constant, the diameter of the support rod is adjusted, specifically: the diameter of the support rod... Scaling, relative density The calculation formula is The second filled unit cell is obtained.

[0033] Reference Figure 2 , Figure 2 This is a schematic diagram of a single FCC lattice unit cell provided in an embodiment of this application.

[0034] In this specific application, the first step is the construction of the lattice unit cell. The lattice example used in this embodiment employs the FCC face-centered cubic lattice as the basic unit, such as... Figure 2 As shown.

[0035] Reference Figure 3 , Figure 3 This is a schematic diagram of FCC lattice unit cells scaled to different scales at the same density, provided in the embodiments of this application; in the figure: (a) represents values ​​of and A schematic diagram of the time; (b) shows the value of and A schematic diagram of the time; (c) represents the value. and A diagram showing the time.

[0036] With length, width and height as The diameter of the support rod is Taking the FCC lattice unit cell as an example, when the relative density of the FCC lattice unit cell remains constant (i.e., and (With parameters unchanged), it is scaled at ratios of 1:2 and 1:3 respectively, resulting in smaller lattices with half the original size and even smaller lattices with one-third the original size, and then stacked together, retaining the same size as the original basic lattice unit cell, such as... Figure 3 As shown, multi-scale design variables are introduced in this way.

[0037] Reference Figure 4 , Figure 4 The figures are schematic diagrams of FCC lattice unit cells with different relative densities at the same scale according to the embodiments of this application; in the figures: (a) is a schematic diagram of a lattice with a relative density of 0.5; (b) is a schematic diagram of a lattice with a relative density of 0.3; and (c) is a schematic diagram of a lattice with a relative density of 0.1.

[0038] When the FCC lattice unit cell maintains its scale invariant, its support rod diameter By scaling up and down, we can obtain lattice unit cells with different relative densities at the same scale, such as... Figure 4 As shown, this introduces a multi-density design variable. The relative density of the lattice unit cell... ,volume and geometric parameters (length of lattice unit cell is The diameter of the support rod is The relationship between them is as follows: In the specific application of this embodiment, scale and density are used as dual design variables in topology optimization, and the optimization part is left to fill the discrete units in the optimization results of different scales and densities.

[0039] Reference Figure 5 , Figure 5 The binary interpolation model of the effective elastic constant of the lattice unit cell to the density scale is provided for the embodiments of this application.

[0040] In the specific application of this embodiment, the effective elastic properties of FCC lattice unit cells at different scales and densities are evaluated as follows: A numerical homogenization method is used to obtain interpolation models of the material equivalent properties of FCC lattice unit cells at different scales and densities, such as... Figure 5 As shown, where, Represents the relative density of a single crystal unit cell. Representative scale.

[0041] Reference Figure 6 , Figure 6 An example of a topology optimization problem provided in the embodiments of this application.

[0042] In the specific application of this embodiment, the construction of the design domain takes into account printing and experimental costs, and the example used is... Figure 6 As shown, FCC lattice unit cells of different densities and scales were filled within a cube-shaped design domain with dimensions of 64 mm. Each lattice unit cell was designed to have dimensions of 16 mm.

[0043] Specifically, before performing the filling process, the geometric parameters are converted into optimized data, specifically: Based on the design domain, a geometric matrix is ​​generated, which is used to provide geometric relationships for stiffness matrix calculation; Based on the pre-acquired density-scale-elastic constant sample data, the effective elastic constants and partial derivatives of each order under any bivariate combination are obtained by two-dimensional interpolation and stored as global variables. The global variables are used for stiffness matrix derivative calculation. Receive the first design variable and the second design variable, read the geometric matrix and elastic parameters, construct the elastic matrix and its derivative, calculate the stiffness matrix and corresponding derivative of the unit through Gaussian integral, and output it for global assembly and sensitivity calculation; Receive grid data and filter radius, and construct a sparse filter matrix by calculating the center point coordinates of the cells and the Euclidean distance between cells to smooth the sensitivity distribution.

[0044] In the specific application of this embodiment, the density-scale bivariate topology optimization algorithm specifically includes: Geometric matrix generation: Based on the shape functions of hexahedral elements, a strain-displacement relationship matrix is ​​derived for element stiffness calculation in finite element analysis. Geometric matrix generation constructs an element-level strain-displacement matrix by mapping the coordinates of Gaussian integral points to the derivatives of the shape functions, supporting stress-strain relationship transformation in multi-scale optimization.

[0045] Two-dimensional interpolation and derivative calculation: Based on a pre-set density-scale-elastic constant sample database, equivalent elastic parameters are obtained through bilinear interpolation, and their first and second derivatives with respect to density and scale are calculated to provide data support for sensitivity analysis.

[0046] Element stiffness matrix calculation: Gaussian numerical integration method is used to integrate strain-displacement matrix and material constitutive relation to generate element stiffness matrix and its derivative with respect to design variables (density, scale), which is used for global stiffness matrix assembly.

[0047] 3D sensitivity filtering: Construct a distance-weighted filtering matrix and perform convolutional smoothing on density and scale sensitivity. Specifically, the filtering radius is defined as twice the cell size, which can eliminate the checkerboard phenomenon and improve the numerical stability of the optimization results.

[0048] Specifically, optimizing the filling process based on the moving asymptote optimization algorithm includes: Based on the moving asymptote method, the non-convex optimization problem is transformed into a series of convex subproblems; the upper and lower bounds of the asymptote are dynamically adjusted to generate the approximation coefficient matrix of the subproblems, and the convergence accuracy is controlled by residual checking; The primal-dual Newton method is used to solve the convex subproblem, and the optimal update values ​​for the two variables are output.

[0049] Specifically, when solving the convex problem, the dual gap calculation and step size adaptive adjustment are integrated to optimize the output of the optimal update values ​​of the two design variables.

[0050] In this specific application, MMA iterative control is based on the Moving Asymptotes (MMA) method, which transforms the non-convex optimization problem into a series of convex subproblems. The upper and lower bounds of the asymptotes are dynamically adjusted to generate the approximate coefficient matrix of the subproblems, and the convergence accuracy is controlled through residual checks. When solving the subproblems, the primal-dual Newton method is used to solve the convex subproblems, outputting the optimal updated values ​​of the design variables. The dual gap calculation and adaptive step size adjustment are integrated to ensure strict satisfaction of volume constraints during the iteration process.

[0051] Specifically, the topology optimization based on the bivariate hybrid lattice structure includes: Import the design domain and construct the topological relationships, then initialize the bivariate; An iterative loop based on the moving asymptote optimization algorithm is performed, sequentially carrying out finite element analysis, sensitivity calculation and filtering, and bivariate update until the results converge. The optimized bivariate model is discretized and visualized for verification, and a standardized file is exported. The standardized file includes the center coordinates, scaling scale, relative density, and node association information of the basic unit cell.

[0052] Reference Figures 7 to 9 ,in: Figure 7 A flowchart of density-scale bivariate topology optimization provided for embodiments of this application; Figure 8 The objective function and volume fraction changes during the bivariate topology optimization process provided in this application embodiment; Figure 9 The density and scale results are for topology optimization of bivariate lattice structures.

[0053] In the specific application of this embodiment, after the development and verification of each core sub-function are completed, mesh generation, finite element analysis, MMA optimization algorithms, and visualization functions are integrated to achieve density-scale dual-design-variable topology optimization of the FCC lattice structure with compliance minimization as the objective and volume fraction as the constraint. The specific description is as follows: First, the hexahedral mesh data is imported and topological relationships are constructed, initializing design variables and optimization parameters. Then, an iterative loop based on the MMA algorithm is entered, sequentially performing finite element analysis, sensitivity calculation and filtering, and design variable updates until the results converge. Finally, the optimized density and scale fields are discretized and visualized for verification, and a standardized CSV file containing element center coordinates, density, scale, and node association information is exported. The program flowchart is shown below. Figure 7 As shown. During the optimization process, the changes in the objective function (compliance) and volume fraction are as follows. Figure 8 As shown. The optimization results are as follows. Figure 9 As shown.

[0054] Specifically, the bivariate topology optimization method for multi-scale hybrid lattice structures in this embodiment is computer-aided. After the topology optimization is completed, the support modeling information of the lattice units in the design domain is generated based on the first and second design variables of each lattice unit cell in the design domain. By iteratively traversing the lattice, a frustum is constructed according to the start and end diameters of the supports of the first and second filled unit cells, and finally the overall multi-scale hybrid lattice is formed.

[0055] In the specific application of this embodiment, after completing topology optimization and obtaining the relative density and scale parameters of each lattice unit cell within the design domain, the previously generated CSV data, including cell center coordinates, cell-node associations, and node coordinates, is loaded into the Python module. Based on the scale and density parameters, the support modeling information of the lattice units within the design domain is then generated. The specific process is as follows: Based on the node coordinates and node numbers of each lattice unit cell, a center coordinate matrix for each unit cell is constructed. Then, this matrix is ​​traversed, and the strut diameter of each unit cell is calculated based on its density and scale information. Finally, a dataset mapping the strut coordinates and strut diameters of this lattice unit cell is constructed and output as a JSON file.

[0056] Using the Spaceclaim software, the system accepts the output strut coordinates and strut diameter mapping dataset and uses scripts to convert the topology optimization results into a solid lattice structure model. Specifically, it constructs frustums based on the start and end diameters of the struts that make up the FCC lattice unit cell through a loop, ultimately forming the overall lattice structure.

[0057] Reference Figure 10 , Figure 10The lattice structure provided in the embodiments of this application is the result of topology optimization and variable cross-section optimization.

[0058] Through the above process, computer-aided multi-scale and density-variable design of lattice structures was achieved, significantly improving the design efficiency of lattice structures and effectively enhancing their mechanical properties compared to traditional homogeneous lattice structures. The generated structures are as follows: Figure 10 As shown.

[0059] The program logic in this embodiment is described in detail below. This embodiment implements density-scale bivariate topology optimization, specifically: In bivariate optimization, after acquiring hexahedral mesh data and initializing optimization parameters, multi-scale optimization collaboratively prepares core data for finite element analysis through four types of functional units (geometric matrix generation, two-dimensional interpolation and derivative calculation, element stiffness matrix and derivative calculation, and 3D sensitivity filtering), providing key inputs for the MMA optimization algorithm, supporting the iterative update of the relative density and scale of lattice unit cells, and forming a closed loop of transformation from geometric parameters to optimization data.

[0060] For geometric matrix generation, the strain-displacement matrix of an 8-node hexahedral element is derived through symbolic computation. After steps such as natural coordinate construction, shape function definition, and Jacobian matrix calculation, a 6×24-dimensional matrix is ​​obtained and passed as a global variable to provide accurate geometric relationships for stiffness matrix calculation.

[0061] For two-dimensional interpolation and derivative calculation, based on density-scale-elastic constant sample data, the effective elastic constants and partial derivatives of each order under any combination of design variables are obtained through two-dimensional interpolation, stored as global variables, and directly support the calculation of stiffness matrix derivatives.

[0062] As the core of finite element analysis, this function calculates the element stiffness matrix and its derivatives. It receives relative density and scale variables, reads geometric matrices and elastic parameters, constructs the elastic matrix and its derivatives, calculates the element stiffness matrix and its corresponding derivatives through Gaussian integration, and outputs the results for global assembly and sensitivity calculation.

[0063] For 3D sensitivity filtering, the system receives grid data and filtering radius, and constructs a sparse filtering matrix by calculating the coordinates of the cell center point and the Euclidean distance between cells. This smooths the sensitivity distribution, solves the problem of chessboard and grid dependency in topology optimization, and improves iterative stability.

[0064] After the above processing, the core data such as geometric matrix, stiffness matrix and derivative, elastic constant and derivative, and filtering matrix are output, which helps to achieve bivariate optimization closed loop with compliance minimization and volume fraction constraint.

[0065] After completing finite element analysis, objective function and sensitivity calculation, and 3D sensitivity filtering, the MMA optimization algorithm transforms the topology optimization problem into a convex approximation subproblem, outputting the optimal solution for the design variables and supporting iterative updates of density and scale. This part can be understood as forming a closed loop of construction, solution, and feedback based on the MMA iterative control unit and the subproblem solving unit.

[0066] For the MMA iterative control unit, based on the current optimization state, the asymptote is dynamically calculated (the first iteration covers the range of variable changes, and subsequent iterations are adjusted as needed), balancing the approximation accuracy and search space, constructing convex approximation coefficients and constant terms, calling the subproblem solving unit to obtain the optimal solution and the updated asymptote, and completing one iteration.

[0067] For the subproblem solving unit, the original dual Newton method is used to solve the problem. The variables are initialized to ensure that they are in the feasible region. The outer loop reduces the control precision of the obstacle parameters and calculates the residual to judge the degree of satisfaction of the KKT optimal conditions. If the residual does not meet the standard, the inner Newton iteration is started to solve and update the step size. The variable compliance and residual reduction are ensured by using a safe step size and line search. Finally, the optimal solution is output.

[0068] After the above processing, the optimal solution of the design variables and the updated asymptote are used as inputs for the next stage. The process is repeated until the change in the variables reaches the target. After convergence, a CSV file is exported to provide core parameters for modeling in Python.

[0069] In the dual-design-variable topology optimization of FCC lattice, the aforementioned functions are integrated and run in the Matlab environment to achieve full automation from mesh import to result export, completing the closed loop of multi-scale optimization of FCC lattice and connecting the core links to ensure that the design variable iteration meets engineering constraints. Specifically: First, the mesh model is imported to obtain the element-node association and coordinate matrix, and core parameters such as volume fraction constraints and filtering radius are defined to generate the strain-displacement matrix; loads and fixed nodes are selected, and finite element initialization is completed (calculating degrees of freedom, generating load matrices, constructing stiffness matrix indexes, and generating sensitivity filtering matrices); elastic constants and derivatives are obtained through two-dimensional interpolation to support stiffness matrix calculation; design variables and MMA parameters are initialized, and the iteration loop is started with the condition "variable change > convergence threshold and iteration number < maximum value" to generate stiffness matrices and derivatives in batches, assemble solutions, calculate objective functions and sensitivity, and update filtering variables; after convergence, the density field and scale field are visualized, the scale is discretized and the density is re-optimized, symmetric results are obtained through mirroring operations, and finally the data is integrated and exported to a CSV file to provide parameter support for solid modeling.

[0070] In constructing the optimized lattice structure support dataset, after exporting three types of core CSV files, parameterized modeling information for the lattice structure is generated through data loading and transformation, density-rod diameter interpolation, FCC unit cell modeling, block integration, and full lattice assembly. The output includes JSON and optional CSV files that can be parsed downstream. The CSV data is loaded and converted to NumPy arrays. The start and end diameters of the frustum support are calculated through interpolation (adapting to different lattice scales, including extrapolation). Coordinate data for a single FCC unit cell support is generated, and multi-unit cell modeling information is integrated according to lattice scale. All elements are traversed, generating modeling information for each element and encapsulating it into a dictionary. The output is then serialized into a JSON file to ensure data format standardization, providing standardized coordinate support for SpaceClaim frustum modeling.

[0071] In the reconstruction of the optimization results, after generating a JSON file containing support modeling information, this embodiment runs in the SpaceClaimV21 environment. Through environment initialization, entity construction, JSON parsing, batch generation, and model saving, the standardized support coordinates are transformed into a solid frustum model, completing the closed loop of automated modeling for non-transitional structures. The process involves clearing historical selections and geometric objects, importing the core API and Python standard library, converting coordinate units, creating spatial points, and generating frustum entities to ensure that the support dimensions and positions match the upstream optimization results. The JSON file is parsed, and frustums are generated in batches according to data dimensions. Post-processing solidifies the sketched objects and saves the model to a preset directory. This solid model can be combined and assembled with transitional structures, or directly imported into finite element software and exported as an STL format for 3D printing, achieving a seamless process from parametric design to solid application.

[0072] Based on the above, this embodiment achieves at least the following technical innovations and corresponding technical effects: By introducing multi-scale factors, the lattice unit cell is scaled to three levels and combined, which can effectively change the slip deformation mode of the original uniform lattice structure and improve the stability of stress bearing. A bivariate topology optimization algorithm for lattice structures considering relative density and scale is designed. This algorithm can achieve dual-objective optimization of structural density and scale for different customized load-bearing scenarios, effectively improving the load-bearing capacity of the structure. It has achieved a fully automated system construction process that integrates optimization, simulation, and modeling, enabling rapid response generation from customized scenarios to customized structures.

[0073] With a flexible and variable design domain, it can adapt to complex structures, creating conditions for the optimization and design of lattice structures in complex application scenarios.

[0074] Reference Figure 11 , Figure 11The following are comparative examples of all-large, all-medium, and all-small lattice structures composed of a single scale and the same density, provided for the purposes of this application. In the figures: (a) is an all-large lattice; (b) is an all-medium lattice; and (c) is an all-small lattice.

[0075] To verify the effectiveness of the proposed bivariate topology optimization method for multi-scale hybrid lattice structures in this embodiment, it was experimentally compared with a single-scale, uniform-density lattice structure. The three comparison lattice structures are as follows: Figure 11 As shown, they are composed of FCC lattice unit cells of all large, all medium and all small scales, respectively, with a uniform relative density of 0.3, which is consistent with the volume fraction (relative density) constraint of the topology-optimized lattice.

[0076] All lattice structure samples were prepared using fused deposition modeling (FDM) technology, with Onyx as the printing material. The main mechanical properties of Onyx are detailed in Table 1. During printing, an additional 1.28 mm thick pressure plate was printed on both the top and bottom surfaces of each sample to facilitate subsequent stress calculations.

[0077] Table 1. Main mechanical properties of Onyx printing material Reference Figure 12 , Figure 12 The images show quasi-static compression experiments of all-large, all-medium, all-small, and optimized lattices provided in the embodiments of this application; in the figures: (a) is the all-large lattice; (b) is the all-medium lattice; (c) is the all-small lattice; and (d) is the optimized lattice.

[0078] After the structures were fabricated, quasi-static compression tests were performed on all specimens using a general-purpose electromechanical servo testing device (model: SUST-CMT5205). Load-displacement curve data were acquired in real time, and the entire deformation process of the specimens was recorded in real time using a camera. The indenter was equipped with a force sensor with a range of 100 kN to monitor the load in real time, and the compression speed was set to 1.5 mm / min. Compression test images are shown below. Figure 12 As shown.

[0079] Reference Figure 13 , Figure 13 The specific stress-strain curves of all-large, all-medium, all-small lattices and the optimized lattice provided for embodiments of this application.

[0080] The obtained experimental curves were processed into specific stress-strain curves using the following formula, as follows: Figure 13 As shown.

[0081] in, , , , , and These represent specific stress, strain, compressive load, pressure plate area, compression distance, and lattice structure, respectively. , and These represent the relative density, mass, and cubic area of ​​the crystal lattice structure, respectively. The curves for all crystal lattice structures are shown below. Figure 13 As shown.

[0082] To accurately obtain the performance advantages of the optimized lattice structure compared to the uniform lattice structure, the following performance indicators were used to evaluate the experimental curves and data: specific stress reduction. The parameters include specific elastic modulus, specific average crushing stress (SMCS), specific energy absorption (SEA), crushing force efficiency (CSE), and specific average plateau stress (SPS). Among these, the specific stress drop is defined as the peak value of the specific stress curve. The difference between the trough and the peak. Specific modulus of elasticity is defined as the slope of the straight segment of the specific stress curve. Other performance indices are defined as follows.

[0083] in, This represents dense strain, defined as the strain at 0.55. Representing 0.2% offset strain, it is the inflection point between the elastic and plastic stages of each curve.

[0084] Reference Figure 14 , Figure 14 A comparison diagram of the mechanical properties of the topology-optimized multi-scale lattice structure provided in the embodiments of this application and other uniform lattice structures.

[0085] The comparison results of the optimized multiscale variable density lattice structure and the uniform single-scale lattice under these performance index evaluations are shown as follows: Figure 14 As shown in Table 2, the specific performance data is as follows.

[0086] Table 2 Performance data for all crystal structures Experimental results and analysis verified that the optimized lattice has balanced stiffness, strength and energy absorption capacity, and has significant performance advantages over uniform single-scale lattices.

[0087] In the embodiments provided in this application, it should be understood that the embodiments described herein can be implemented in hardware, software, firmware, middleware, code, or any suitable combination thereof. For hardware implementation, the processor may be implemented in one or more of the following: application-specific integrated circuits (ASICs), digital signal processors (DSPs), digital signal processing devices (DSPDs), programmable logic devices (PLDs), field-programmable gate arrays (FPGAs), processors, controllers, microcontrollers, microprocessors, other electronic units designed to implement the functions described herein, or combinations thereof. For software implementation, some or all of the processes of the embodiments may be performed by a computer program instructing the associated hardware. During implementation, the program may be stored in a computer-readable storage medium or transmitted as one or more instructions or code on a computer-readable storage medium. Computer-readable storage media include computer storage media and communication media, wherein communication media include any medium that facilitates the transmission of a computer program from one place to another. Storage media may be any available medium accessible to a computer. Computer-readable storage media may include, but are not limited to, RAM, ROM, EEPROM, CD-ROM or other optical disk storage, magnetic disk storage media or other magnetic storage devices, or any other medium capable of carrying or storing desired program code having the form of instructions or data structures and accessible to a computer.

[0088] Finally, it should be noted that the above description is only a preferred embodiment of this application and is not intended to limit this application. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the protection scope of this application.

Claims

1. A bivariate topology optimization method for multi-scale hybrid lattice structures, characterized in that, The method includes: Define two variables, including a first design variable and a second design variable; wherein, the first design variable is the scaling scale, and the second design variable is the relative density; The basic unit cell of the hybrid lattice structure is determined and the corresponding unit cell size is obtained. The unit cell size is the length, width, and height of the basic unit cell and the diameter of the supporting rods. The second design variable is determined based on the unit cell size. The unit cell size is scaled according to different first design variables to obtain a variety of first filled unit cells with different scales and the same relative density; the length, width and height are kept constant, and the diameter of the support rod is adjusted to obtain a variety of second filled unit cells with different relative densities and the same scale. A design domain is determined, and a filling process is performed. The filling process aims to minimize the compliance of the hybrid lattice structure and is constrained by the volume fraction. The first filling unit cell and the second filling unit cell are filled into the design domain. The filling process is optimized based on the moving asymptote optimization algorithm to perform topology optimization of the bivariate hybrid lattice structure and output the optimized multi-scale hybrid lattice structure.

2. The bivariate topology optimization method for multi-scale hybrid lattice structures according to claim 1, characterized in that, The topology optimization based on bivariate hybrid lattice structures includes: Import the design domain and construct the topological relationships, then initialize the bivariate; An iterative loop based on the moving asymptote optimization algorithm is performed, sequentially carrying out finite element analysis, sensitivity calculation and filtering, and bivariate update until the results converge. The optimized bivariate model is discretized and visualized for verification, and a standardized file is exported. The standardized file includes the center coordinates, scaling scale, relative density, and node association information of the basic unit cell.

3. The bivariate topology optimization method for multi-scale hybrid lattice structures according to claim 1, characterized in that, The filling process is equipped with a corresponding mathematical model, which is specifically as follows: in: Represents the second design variable; Represents the first design variable; This represents the number of units in the overall hybrid lattice structure after it has been discretized. Describe the compliance of the objective function, when C At its minimum, the overall stiffness of the hybrid lattice structure is maximized, satisfying the static equilibrium equations. , Represents the nodal displacement matrix. Represents the external load array; Representing the The volume of each unit; Volume fraction representing the overall structure; To optimize the volume of materials used in the process; Represents the total volume of the design domain; This represents the upper limit of the design volume fraction.

4. The bivariate topology optimization method for multi-scale hybrid lattice structures according to claim 1, characterized in that, Before performing the filling process, the geometric parameters are converted into optimized data, specifically as follows: Based on the design domain, a geometric matrix is ​​generated, which is used to provide geometric relationships for stiffness matrix calculation; Based on the pre-acquired density-scale-elastic constant sample data, the effective elastic constants and partial derivatives of each order under any bivariate combination are obtained by two-dimensional interpolation and stored as global variables. The global variables are used for stiffness matrix derivative calculation. Receive the first design variable and the second design variable, read the geometric matrix and elastic parameters, construct the elastic matrix and its derivative, calculate the stiffness matrix and corresponding derivative of the unit through Gaussian integral, and output for global assembly and sensitivity calculation; Receive grid data and filter radius, and construct a sparse filter matrix by calculating the center point coordinates of the cells and the Euclidean distance between the cells to smooth the sensitivity distribution.

5. The bivariate topology optimization method for multi-scale hybrid lattice structures according to claim 2, characterized in that, The optimization of the filling process based on the moving asymptote optimization algorithm includes: Based on the moving asymptote method, the non-convex optimization problem is transformed into a series of convex subproblems; the upper and lower bounds of the asymptote are dynamically adjusted to generate the approximation coefficient matrix of the subproblems, and the convergence accuracy is controlled by residual checking; The primal-dual Newton method is used to solve the convex subproblem, and the optimal update values ​​for the two variables are output.

6. The bivariate topology optimization method for multi-scale hybrid lattice structures according to claim 3, characterized in that, The basic unit cell is at least a face-centered cubic lattice, and the length, width, and height of the face-centered cubic lattice are all equal to 1 / 2. The diameter of the support rod is ; For the face-centered cubic lattice, the unit cell size is scaled according to different first design variables. Specifically, the unit cell size is scaled according to a ratio of 1:2 and 1:3 to obtain the first filling unit cell, which includes a large lattice corresponding to the original scale, a medium lattice corresponding to the 1:2 scale, and a small lattice corresponding to the 1:3 scale. For the face-centered cubic lattice, while keeping the length, width, and height constant, the diameter of the support rod is adjusted, specifically: the diameter of the support rod... Scaling, relative density The calculation formula is: The second filled unit cell is obtained.

7. The bivariate topology optimization method for multi-scale hybrid lattice structures according to claim 6, characterized in that, The first design variable Relaxation is a continuous variable, taking values ​​in... Between, and Corresponding to large lattice Corresponding lattice, Corresponding to small crystal lattice.

8. The bivariate topology optimization method for multi-scale hybrid lattice structures according to claim 4, characterized in that, The filter radius is twice the unit size.

9. The bivariate topology optimization method for multi-scale hybrid lattice structures according to claim 5, characterized in that, When solving the convex problem, the dual gap calculation and step size adaptive adjustment are integrated to optimize the output of the optimal update values ​​of the two design variables.

10. The bivariate topology optimization method for multi-scale hybrid lattice structures according to any one of claims 1 to 9, characterized in that, The method is computer-aided. After topology optimization is completed, the support modeling information of the lattice unit in the design domain is generated based on the first and second design variables of each lattice unit cell in the design domain. By iteratively traversing, a frustum is constructed according to the start and end diameters of the supports of the first and second filled unit cells, and finally a multi-scale hybrid lattice is formed.

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