A topology optimization method and system for connectable multiconfiguration lattice structures based on transition unit cells

Abstract

This invention discloses a method, system, device, and storage medium for topology optimization of connectable multi-configuration lattice structures based on transitional unit cells. The method includes: interpolating the rod diameters of M basic unit cells to obtain transitional unit cells; calculating the equivalent elastic matrices of the M basic unit cells and transitional unit cells using a homogenization method; calculating the relative density and elastic matrix of the elements using multi-material interpolation formulas based on the relative densities and equivalent elastic matrices of the basic and transitional unit cells; constructing a topology optimization model of the connectable multi-configuration lattice structure based on transitional unit cells; optimizing the sensitivity of the objective function and volume constraints within the design domain to design variables based on the topology optimization model until the topology optimization model converges; updating the design variables using the moving asymptote method during the optimization process; and obtaining the optimized structure based on the design variables corresponding to the converged topology optimization model. This invention utilizes transitional unit cells to solve the connectivity problem between microstructures, without restricting the geometric configuration of the basic unit cells, thus improving the mechanical potential of the structure.

Description

Technical Field

[0001] This invention relates to the field of structural optimization technology, and in particular to a method, system, terminal device, and computer-readable storage medium for topology optimization of connectable multi-configuration lattice structures based on transition unit cells. Background Technology

[0002] Lattice structures, with their lightweight, multifunctionality, and superior designability, are increasingly being used in high-tech fields such as aerospace, automotive, and biomedicine. Simultaneously considering lattice unit cells with different geometries can fully unleash the design potential of the structure and improve its mechanical properties. However, since most current homogenization-based topology optimization methods ignore the boundary behavior of unit cells, connectivity issues exist between unit cells with different configurations, making it impossible to fabricate the optimized structure and limiting the application of lattice structures in practical engineering.

[0003] Currently, solving the connectivity problem of multi-configuration lattice structures can be broadly categorized into two methods: The first is to impose geometric constraints on the basic unit cells, enabling them to generate self-connected lattice structures. However, this approach actually reduces the design space of the lattice unit cells, thus sacrificing structural performance and failing to tap the design potential of the lattice structure. The second method involves forced connections based on interpolation methods such as rod diameter and shape after traditional topology optimization, which may cause the optimized structure to lose its optimal form. To minimize the sacrifice of structural design space and ensure connectivity between microstructures, recent researchers have applied geometric constraints only to the structures at the interfaces. However, although this method of applying simple constraints can ensure that adjacent unit cells can connect to each other, it still has drawbacks, especially for complex microstructures, which may cause the microstructure to lose its continuity and smoothness. Summary of the Invention

[0004] To address at least one of the technical problems in the prior art, the present invention provides a method, system, terminal device, and computer-readable storage medium for topology optimization of connectable multi-configuration lattice structures based on transitional unit cells.

[0005] The first objective of this invention is to provide a topology optimization method for connectable multi-configuration lattice structures based on transitional unit cells.

[0006] The second objective of this invention is to provide a topology optimization system for connectable multi-configuration lattice structures based on a transitional unit cell.

[0007] The third objective of this invention is to provide a terminal device.

[0008] A fourth objective of this invention is to provide a computer-readable storage medium.

[0009] The first object of the present invention can be achieved by adopting the following technical solutions:

[0010] A topology optimization method for a connectable multi-configuration lattice structure based on transitional unit cells, the method comprising:

[0011] Interpolating the rod diameters of M basic unit cells to obtain transitional unit cells; M is a positive integer greater than 1;

[0012] Adopting the homogenization method to calculate the equivalent elastic matrices of M basic unit cells and transitional unit cells respectively;

[0013] According to the relative densities and equivalent elastic matrices of the basic unit cells and transitional unit cells, respectively calculate the relative density and elastic matrix of the unit by using the multi-material interpolation formula;

[0014] Construct a topology optimization model for a connectable multi-configuration lattice structure based on transitional unit cells, and optimize the sensitivities of the objective function and volume constraint in the design domain to the design variables based on the topology optimization model until the topology optimization model converges; during the optimization process, adopt the moving asymptote method to update the design variables;

[0015] According to the design variables corresponding to the topology optimization model after convergence, obtain the optimized structure.

[0016] Further, the formula for calculating the relative density and elastic matrix of the unit by using the multi-material interpolation formula is:

[0017]

[0018] Where ρ e and D e are respectively the relative density and elastic matrix interpolated for the e-th unit in the design domain, ρ( i ) and D( i ) respectively represent the relative density and homogenized elastic matrix of the i-th basic unit cell. When i = M + 1, it is set as a weak material; ρ (ij) and D (ij) respectively represent the relative density and homogenized elastic matrix of the transitional unit cell on the interface Γ ij between the i-th basic unit cell and the j-th basic unit cell, i < j. When j = M + 1, it is set as a weak material; χ e,i and ψ e,i respectively represent the interpolation coefficients of the relative density and elastic matrix of the i-th basic unit cell in the e-th unit, χ e,ij and ψ e,ij respectively represent the interpolation coefficients of the relative density and elastic matrix of the transitional unit cell on the interface Γ ij in the e-th unit; χ e,i , ψ e,i , χ e,ij and ψe,ij Represent each of these expressions using the following formulas:

[0019]

[0020]

[0021] In the formula, μ e,m , and γ e,m All are the m-th intermediate variables of unit e, m = 1,...,M; μ e,m , and γ e,m Represented as vectors: μ m , and γ m μ m , and γ m From the initial variable x m The results were obtained after three steps of filtering.

[0022] Furthermore, μ m It is obtained through the following process:

[0023] First, for the initial variable x m PDE filtering is performed to obtain

[0024]

[0025] Among them, ζ and These represent the fields before and after filtration, respectively. r is a parameter controlling the filtration radius, and its relationship with the standard filtration radius R is as follows:

[0026] Then, to Perform a Heaviside projection operation:

[0027]

[0028] in, Let be the projected field, and β and η be the parameters that control the steepness and threshold of the projection function, respectively, with η taking the value of 0.5;

[0029] right The field after projection is represented by μ m To indicate;

[0030] It is obtained through the following process:

[0031] To identify the boundaries of the structure, μ m PDE filtering is performed to obtain right Perform a Heaviside projection, where the parameter η2 for controlling the projection threshold is taken as 0.95, aiming to obtain μ m The erosion field that shrinks inward by a certain distance Then, for the field μ m and Subtract them to obtain the interface of the structure; where the interface thickness is expressed as t≈0.67R2, and R2 is the PDE filtering radius for the second time;

[0032] γ m Is obtained through the following process:

[0033] To construct the gradient interface, for the field Perform a Heaviside projection, and the parameter η3 of its projection threshold is taken as 0.842 to obtain the projected field κ m ;

[0034] For κ m Perform linear density filtering, and γ m Is the filtered field; γ m Is linearly distributed on the interface and is used to map the constructed transition elements.

[0035] Furthermore, the mathematical expression of the topological optimization model is:

[0036] Find: x1,...,x M

[0037] Minimize: C = F T U(x1,...,x M )

[0038] Subject to:

[0039] 0 ≤ x e,m ≤ 1

[0040] With: KU = F, When i < M + 1,

[0041] where, x e,m Is the m-th design variable of element e, N is the number of elements used to discretize the structure, C is the compliance of the structure, F and U are the load vector and displacement vector respectively; V M+1 Is the total material usage of the structure; when i < M + 1, V i Is the material usage of each phase corresponding to each basic unit cell; Is the specified volume fraction constraint.

[0042] Furthermore, the sensitivity of the objective function to the design variable is:

[0043]

[0044]

[0045] in:

[0046] D n To calculate the elasticity matrix of the nth element using multi-material interpolation formulas, u n Let k be the displacement vector of element n. n Let Ω be the stiffness matrix of element n. n Let B be the element domain and B be the strain-displacement matrix. The data was obtained from the microstructure database through numerical derivative calculations.

[0047] According to the multi-material interpolation formula, in order to obtain and Calculation required and When i ≠ m When i = m:

[0048]

[0049] In the formula:

[0050] Obtained from the PDE filtering formula;

[0051]

[0052] Similarly, Obtained from the PDE filtering formula;

[0053]

[0054] In the formula, N n Let n be the set of cells within a defined square neighborhood; similarly,

[0055]

[0056] Furthermore, the sensitivity of volume constraints to design variables is:

[0057]

[0058] in:

[0059] ρ n To calculate the relative density of the nth element using a multi-material interpolation formula, The data was obtained from the microstructure database through numerical derivative calculations.

[0060] According to the multi-material interpolation formula, in order to obtain and Calculation required and When i ≠ m When i = m:

[0061]

[0062] In the formula:

[0063] Obtained from the PDE filtering formula;

[0064]

[0065] Similarly, Obtained from the PDE filtering formula;

[0066]

[0067] In the formula, N n Let n be the set of elements within a defined square neighborhood.

[0068] Similarly,

[0069]

[0070] Furthermore, the convergence condition of the topology optimization model is: the cumulative relative error within a specified series of iterations exceeds a set threshold.

[0071] Furthermore, during the optimization process, the parameter controlling the steepness of the projection function gradually increases from k0 to k1, and doubles every k2 steps or when the convergence condition is met; where k0, k1 and k2 are all specified values, and k0 is much smaller than k1.

[0072] The second objective of this invention can be achieved by adopting the following technical solution:

[0073] A topology optimization system for connectable multi-configuration lattice structures based on a transition unit cell, the system comprising:

[0074] The interpolation module is used to interpolate the rod diameters of M basic unit cells to obtain transition unit cells; M is a positive integer greater than 1.

[0075] The first calculation module is used to calculate the equivalent elasticity matrix of M basic unit cells and transition unit cells respectively using a homogenization method;

[0076] The second calculation module is used to calculate the relative density and elastic matrix of the element based on the relative density and equivalent elastic matrix of the basic unit cell and the transition unit cell, using multi-material interpolation formulas respectively.

[0077] The optimization module is used to construct a topology optimization model for a connectable multi-configuration lattice structure based on a transition unit cell, and to optimize the sensitivity of the objective function and volume constraints within the design domain to the design variables based on the topology optimization model until the topology optimization model converges. During the optimization process, the moving asymptote method is used to update the design variables. Based on the design variables corresponding to the converged topology optimization model, the optimized structure is obtained.

[0078] The third objective of this invention can be achieved by adopting the following technical solution:

[0079] A terminal device includes a processor and a memory for storing a processor-executable program. When the processor executes the program stored in the memory, it implements the above-described topology optimization method for connectable multi-configuration lattice structures based on transitional unit cells.

[0080] The fourth objective of this invention can be achieved by adopting the following technical solution:

[0081] A computer-readable storage medium storing a program that, when executed by a processor, implements the above-described topology optimization method for connectable multi-configuration lattice structures based on transitional unit cells.

[0082] The present invention has the following advantages over the prior art:

[0083] 1. This invention utilizes transitional unit cells to solve the connectivity problem between microstructures without restricting the geometric configuration of basic unit cells, thereby enhancing the mechanical potential of the structure;

[0084] 2. This invention considers the influence of transition unit cells on structural performance in multi-material interpolation formulas and sensitivity analysis, making the optimized structure closer to the optimal form;

[0085] 3. When calculating the relative density and elasticity matrix of the unit cells, this invention constructs a gradient interface through a filtering method to obtain the mapping relationship with the transition unit cell, thereby accurately defining the transition unit at the interface according to the specified change pattern, so that the optimized microstructure does not lose its original continuity and smoothness.

[0086] 4. This invention can specify multiple transition modes to deal with situations involving more than two lattice phases, making it more adaptable to complex connectivity problems. Attached Figure Description

[0087] To more clearly illustrate the technical solutions in the embodiments of the present invention 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 the present invention. For those skilled in the art, other drawings can be obtained based on the structures shown in these drawings without creative effort.

[0088] Figure 1 This is a flowchart of the topology optimization method for connectable multiconfiguration lattice structures based on transitional unit cells according to Embodiment 1 of the present invention;

[0089] Figure 2 This is a schematic diagram of the topology optimization method for connectable multi-configuration lattice structures based on transitional unit cells according to Embodiment 1 of the present invention.

[0090] Figure 3 This is a schematic diagram of the cross and x-shape microstructures and their corresponding transitional unit cells in Embodiment 1 of the present invention;

[0091] Figure 4 This is an example of an embodiment of the present invention using an MBB beam;

[0092] Figure 5 As in Embodiment 1 of the present invention Figure 3 For basic unit cells, Figure 4 This is a schematic diagram of the optimized structure of the design domain;

[0093] Figure 6 These are the three basic unit cells, cubic, x-shape, and cubic-x, and their corresponding transitional unit cells, as described in Embodiment 1 of the present invention.

[0094] Figure 7 This is a calculation example using a simply supported beam in Embodiment 1 of the present invention;

[0095] Figure 8 As in Embodiment 1 of the present invention Figure 6 For basic unit cells, Figure 7 This is a schematic diagram of the optimized structure of the design domain;

[0096] Figure 9 This is a structural block diagram of the topology optimization system for a connectable multi-configuration lattice structure based on a transitional unit cell, according to Embodiment 2 of the present invention.

[0097] Figure 10 This is a structural block diagram of the terminal device according to Embodiment 3 of the present invention. Detailed Implementation

[0098] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. It should be understood that the specific embodiments described are merely used to explain this application and are not intended to limit this application.

[0099] Example 1:

[0100] like Figure 1 , 2 As shown, this embodiment provides a topology optimization method for connectable multi-configuration lattice structures based on transitional unit cells, including the following steps:

[0101] S101. Interpolate the rod diameter of the basic unit cell to obtain the transition unit cell.

[0102] This embodiment considers two basic unit cells: cross and x-shape. The design domain contains three basic phases (M=2): cross, x-shape, and empty phase (represented by phase M+1). First, the rod diameters of the cross and x-shape basic unit cells are linearly interpolated to obtain two sets of microstructure configurations. Then, the two interpolated microstructure configurations are combined using a Boolean union operation to obtain a hybrid transition unit cell.

[0103] The relative densities of the basic unit cell and the transition unit cell can be obtained by the following formula:

[0104]

[0105] Where ρ is the relative density of the basic unit cell / transitional unit cell, ρ * V represents the density of the micro-units (basic material) inside the basic unit cell / transitional unit cell, and V represents the design domain of the basic unit cell / transitional unit cell.

[0106] S102. Using the homogenization method, calculate the equivalent elasticity matrix of the basic unit cell and the transition unit cell respectively.

[0107] The calculation formula for the homogenization method is as follows:

[0108]

[0109] in, Let |V| be the equivalent elastic tensor of the basic unit cell / transitional unit cell, and D be the volume of the basic unit cell / transitional unit cell. pqrs The elastic tensor of the basic material For a given macroscopic test strain field, V is the design domain of the basic unit cell / transition unit cell; ε pq (u ij ) is the locally varying microscopic strain field, and u ij is the displacement field;

[0110] u ij can be obtained by the following formula:

[0111]

[0112] where v is the virtual displacement field.

[0113] Store the relative density and equivalent elastic matrix of each basic unit cell and transition unit cell in the database for subsequent optimization processes and sensitivity analysis.

[0114] S103. Calculate the relative density and elastic matrix of the element using the multi-material interpolation formula based on the relative density and equivalent elastic matrix of the basic unit cell and transition unit cell.

[0115] Calculate the relative density and elastic matrix of the element using the multi-material interpolation formula considering the M+1 phases of the basic unit cell and transition unit cell:

[0116]

[0117] where ρ e and D e are the relative density and elastic matrix interpolated for the e-th element in the design domain, ρ (i) and D( i ) represent the relative density and homogenized elastic matrix of the i-th basic unit cell (set as the weak material when i = M+1); ρ (ij) and D (ij) represent the relative density and homogenized elastic matrix of the transition unit cell on the interface Γ ij between the i-th basic unit cell and the j-th basic unit cell (i < j, set as the weak material when j = M+1); χ e,i and ψ e,i represent the interpolation coefficients of the relative density and elastic matrix of the i-th basic unit cell in the e-th element, χ e,ij and ψ e,ij represent the interpolation coefficients of the relative density and elastic matrix of the transition unit cell on the interface Γ ij in the e-th element, and are expressed by the following formula:

[0118] [[ID=六一]]

[0119]

[0120] μe,m , and γ e,m Each of these is the m-th intermediate variable of unit e, where m = 1, ..., M; they can be represented as vectors: μ m , and γ m μ m , and γ m It can be determined by the initial variable x m The result is obtained through the following three filtering steps:

[0121] (1) Obtain μ m The process:

[0122] First, for the initial variable x m PDE filtering is performed to obtain

[0123]

[0124] Among them, ζ and These represent the fields before and after filtration, respectively. r is a parameter controlling the filtration radius, and its relationship with the standard filtration radius R is as follows:

[0125] Then, to Perform a Heaviside projection operation:

[0126]

[0127] in, Let be the projected field, and β and η be the parameters that control the steepness and threshold of the projection function, respectively. The value of η is usually 0.5.

[0128] right The field after projection is represented by μ m To express.

[0129] (2) Obtain The process:

[0130] To identify the boundaries of the structure, μ m PDE filtering is performed to obtain right Heaviside projection is performed, where the parameter η2 controlling the projection threshold is set to 0.95, with the aim of obtaining μ. m Erosion field that shrinks inward by a certain distance Then, the field μ m and The interface of the structure can be obtained by subtraction. The thickness of the interface can be expressed as t≈0.67R2, where R2 is the second PDE filtering radius.

[0131] (3) Obtain γ m The process:

[0132] To construct the gradient interface, the field Heaviside projection is performed, with the projection threshold parameter η3 set to 0.842, to obtain the projected field κ. m .

[0133] For κ m Perform linear density filtering:

[0134]

[0135] Where, N e Let γ be the set of elements within a square neighborhood of size (t+1)×(t+1) for element e. e,m The filtered quantity is linearly distributed at the interface and is used to map the transition unit constructed.

[0136] S104. Construct a topology optimization model based on a connectable multi-configuration lattice structure using a transitional unit cell; optimize the sensitivity of the objective function and volume constraints within the design domain to the design variables based on the topology optimization model until the topology optimization model converges.

[0137] (1) Based on the relative density of the units, a topology optimization model for a connectable multi-configuration lattice structure based on the transition unit cell is constructed.

[0138] The mathematical expression for the topology optimization model of a connectable multi-configuration lattice structure based on a transitional unit cell is as follows:

[0139] Find: x1,...,x M

[0140] Minimize: C = F T U(x1,...,x M )

[0141] Subject to:

[0142] 0≤x e,m ≤1

[0143] With: KU = F, For i <M+1,

[0144] Where m = 1,...,M, x m x is the initial variable; e,mis the m-th design variable of unit e, N is the number of units used for the discrete structure, C is the compliance of the structure, F and U are the load vector and displacement vector respectively; V M+1 is the total material usage of the structure, V i (i < M + 1) is the material usage of each basic unit cell; is the specified volume fraction constraint.

[0145] (2) Optimize the sensitivities of the objective function and volume constraint in the design domain with respect to the design variables based on the topology optimization model until the topology optimization model converges.

[0146] The sensitivity of the objective function with respect to the design variable is:

[0147]

[0148] Meanwhile, the sensitivity of the volume constraint with respect to the design variable is:

[0149]

[0150] Where:

[0151] D n and ρ n are the elastic matrix and relative density obtained by interpolation for the n-th unit in the design domain respectively, and can be calculated by the formulas in step S103; u n is the displacement vector of unit n, k n is the stiffness matrix of unit n, Ω n is the unit domain, and B is the strain-displacement matrix;

[0152] and are obtained by using numerical derivatives from the microstructure database; can be obtained by the following formula:

[0153]

[0154] In the formula, N n is the set of units of unit n within a square neighborhood of size (t + 1)×(t + 1);

[0155] According to the multi-material interpolation formula, to obtain in equations (2) and (3) and it is necessary to calculate and And when i ≠ m, When i = m: <0​​​

[0157]

[0158] It can be obtained from equation (1).

[0159] The calculation formula is:

[0160]

[0161] Similarly, It can be obtained from equation (1).

[0162] in:

[0163]

[0164] Similarly, in order to calculate equation (4), It can be given by the following formula:

[0165]

[0166] in:

[0167]

[0168] and The derivation has been given above.

[0169] The design variables are updated using the MMA (Moving Asymptote Method) optimization algorithm, with the convergence condition being that the cumulative relative error exceeds 0.1% after 10 steps. β gradually increases from 1 to 128 during the optimization process: β doubles every 50 steps (or when the convergence condition is met).

[0170] S105. Based on the design variables corresponding to the converged topology optimization model, the optimized structure is obtained.

[0171] Based on the obtained design variables, intermediate variables are calculated using the three-step filtering method in step S103, and the interpolation coefficients χ of the basic unit cell and the transition unit cell are further obtained using the multi-material interpolation formula. e,i , χ e,ij The optimized distribution of each basic unit cell and transition unit cell is obtained based on the interpolation coefficients. The configuration of the transition unit cell is determined by the intermediate variable γ. e,m The mapping is obtained.

[0172] like Figure 3 As shown, this embodiment selects two microstructures: cross and x-shape, with transition elements interpolated to the rod diameter. The relative densities of the transition elements and the basic unit cell, as well as the equivalent elastic tensor, are given. Figure 4As shown, an MBB beam with a size L = 50 is selected as the example. The design domain is discretized using 100 × 50 four-node elements. The external force magnitude F = 1. The basic material properties are elastic modulus E = 1, the elastic modulus of the weaker material is set to 1e-9, and the Poisson's ratio is 0.3. A total material constraint v3 = 0.2 and volume constraints v1 = v2 = 0.1 for each of the two microstructures are set. The first filter radius is set to 10, and the interface width is set to 2. Correspondingly, the second filter radius is set to 3.

[0173] Figure 5 In the optimized structure, the cross microstructures are mainly distributed in the nearly horizontal members on the top and bottom sides, while the x-shape microstructures are distributed in the inclined members. Meanwhile, due to... Figure 5 As shown in the magnified view of the local area, the presence of transition units allows for good connection between adjacent positions of the two microstructures, enabling the optimized structure to be fabricated using the manufacturing process. Furthermore, the optimized transition unit configuration follows a specified variation pattern, validating the effectiveness of the proposed method.

[0174] In another embodiment, three basic microstructures are selected: cubic, x-shape, and cubic-x microstructures, such as... Figure 6 As shown. Simultaneously, to achieve a connectable structure, three variation modes are specified to connect each pair of microstructures. Each transition unit is obtained by rod diameter interpolation. The relative density of the transition unit cell and the basic unit cell, and the equivalent elastic tensor, are as follows: Figure 6 As shown. Figure 7 As shown, a simply supported beam is selected as the example, with a size L = 50. The design domain is discretized using 100 × 50 four-node elements. The external force magnitude F = 1. The material properties are consistent with the previous embodiment. A total material constraint v4 = 0.24 and volume constraints v1 = v2 = v3 = 0.08 are set for each of the two microstructures. The first filter radius is set to 10, and the interface width is set to 2. Correspondingly, the second filter radius is set to 3.

[0175] Figure 8 The optimized structure is shown. It can be observed that the proposed method can identify the interfaces between basic unit cells and accurately distinguish each interface segment. Furthermore, the transition units on each interface segment can follow a specified variation pattern. Therefore, the proposed method is also applicable to cases with more than two lattice domains.

[0176] Those skilled in the art will understand that all or part of the steps in the methods of the above embodiments can be implemented by a program instructing related hardware, and the corresponding program can be stored in a computer-readable storage medium.

[0177] It should be noted that although the method operations of the above embodiments are described in a specific order in the accompanying drawings, this does not require or imply that these operations must be performed in that specific order, or that all the operations shown must be performed to achieve the desired result. On the contrary, the order of execution of the described steps may be changed. Additionally or alternatively, certain steps may be omitted, multiple steps may be combined into one step, and / or one step may be broken down into multiple steps.

[0178] Example 2:

[0179] like Figure 9 As shown, this embodiment provides a topology optimization system for connectable multi-configuration lattice structures based on a transitional unit cell. The system includes an interpolation module 901, a first calculation module 902, a second calculation module 903, and an optimization module 904, wherein:

[0180] Interpolation module 901 is used to interpolate the rod diameters of M basic unit cells to obtain transition unit cells; M is a positive integer greater than 1.

[0181] The first calculation module 902 is used to calculate the equivalent elasticity matrix of M basic unit cells and transition unit cells respectively using a homogenization method;

[0182] The second calculation module 903 is used to calculate the relative density and elastic matrix of the element based on the relative density and equivalent elastic matrix of the basic unit cell and the transition unit cell, using multi-material interpolation formulas respectively.

[0183] The optimization module 904 is used to construct a topology optimization model for a connectable multi-configuration lattice structure based on a transition unit cell, and to optimize the sensitivity of the objective function and volume constraints within the design domain to the design variables based on the topology optimization model until the topology optimization model converges. During the optimization process, the moving asymptote method is used to update the design variables. Based on the design variables corresponding to the converged topology optimization model, the optimized structure is obtained.

[0184] The specific implementation of each module in this embodiment can be found in Embodiment 1 above, and will not be repeated here. It should be noted that the system provided in this embodiment is only illustrated by the division of the above functional modules. In actual applications, the above functions can be assigned to different functional modules as needed, that is, the internal structure can be divided into different functional modules to complete all or part of the functions described above.

[0185] Example 3:

[0186] This embodiment provides a terminal device, which can be a computer, such as... Figure 10As shown, the processor 1002, memory, input device 1003, display 1004, and network interface 1005 are connected via system bus 1001. The processor provides computing and control capabilities. The memory includes a non-volatile storage medium 1006 and internal memory 1007. The non-volatile storage medium 1006 stores the operating system, computer programs, and database. The internal memory 1007 provides an environment for the operation of the operating system and computer programs in the non-volatile storage medium. When the processor 1002 executes the computer programs stored in the memory, it implements the topology optimization method for connectable multi-configuration lattice structures based on transitional unit cells in Embodiment 1, as follows:

[0187] Interpolate the rod diameters of M basic unit cells to obtain the transition unit cell; M is a positive integer greater than 1;

[0188] Using a homogenization method, the equivalent elasticity matrices of the M basic unit cells and transition unit cells are calculated respectively;

[0189] Based on the relative density and equivalent elastic matrix of the basic unit cell and the transition unit cell, the relative density and elastic matrix of the element are calculated using the multi-material interpolation formula.

[0190] A topology optimization model based on a connectable multi-configuration lattice structure using a transitional unit cell is constructed. The sensitivity of the objective function and volume constraints within the design domain to the design variables is optimized based on the topology optimization model until the topology optimization model converges. During the optimization process, the moving asymptote method is used to update the design variables.

[0191] Based on the design variables corresponding to the converged topology optimization model, the optimized structure is obtained.

[0192] Example 4:

[0193] This embodiment provides a computer-readable storage medium storing a computer program. When executed by a processor, the computer program implements the topology optimization method for connectable multi-configuration lattice structures based on transitional unit cells as described in Embodiment 1 above, as follows:

[0194] Interpolate the rod diameters of M basic unit cells to obtain the transition unit cell; M is a positive integer greater than 1;

[0195] Using a homogenization method, the equivalent elasticity matrices of the M basic unit cells and transition unit cells are calculated respectively;

[0196] Based on the relative density and equivalent elastic matrix of the basic unit cell and the transition unit cell, the relative density and elastic matrix of the element are calculated using the multi-material interpolation formula.

[0197] A topology optimization model based on a connectable multi-configuration lattice structure using a transitional unit cell is constructed. The sensitivity of the objective function and volume constraints within the design domain to the design variables is optimized based on the topology optimization model until the topology optimization model converges. During the optimization process, the moving asymptote method is used to update the design variables.

[0198] Based on the design variables corresponding to the converged topology optimization model, the optimized structure is obtained.

[0199] It should be noted that the computer-readable storage medium in this embodiment can be a computer-readable signal medium or a computer-readable storage medium, or any combination thereof. The computer-readable storage medium can be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples of a computer-readable storage medium may include, but are not limited to: an electrical connection having one or more wires, a portable computer disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage device, magnetic storage device, or any suitable combination thereof.

[0200] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope disclosed in the present invention, based on the technical solution and inventive concept of the present invention, shall fall within the scope of protection of the present invention.

Claims

1. A topology optimization method for connectable multi-configuration lattice structures based on transitional unit cells, characterized in that, The method includes: Interpolate the rod diameters of M basic unit cells to obtain the transition unit cell; M is a positive integer greater than 1; Using a homogenization method, the equivalent elasticity matrices of the M basic unit cells and transition unit cells are calculated respectively; Based on the relative density and equivalent elastic matrix of the basic unit cell and the transition unit cell, the relative density and elastic matrix of the element are calculated using the multi-material interpolation formula. A topology optimization model based on a connectable multi-configuration lattice structure using a transitional unit cell is constructed. The sensitivity of the objective function and volume constraints within the design domain to the design variables is optimized based on the topology optimization model until the topology optimization model converges. During the optimization process, the moving asymptote method is used to update the design variables. Based on the design variables corresponding to the converged topology optimization model, the optimized structure is obtained; The formulas for calculating the relative density and elasticity matrix of the element using multi-material interpolation are as follows: Among them, ρ e and D e are the relative density and elastic matrix interpolated from the e-th unit in the design domain, ρ (i) and D( i ) represent the relative density and homogenized elastic matrix of the i-th basic unit cell respectively. When i = M + 1, it is set as the weak material; ρ (ij) and D (ij) represent the relative density and homogenized elastic matrix of the transition unit cell on the interface Γ ij between the i-th basic unit cell and the j-th basic unit cell respectively. i < j. When j = M + 1, it is set as the weak material; χ e,i and ψ e,i represent the interpolation coefficients of the relative density and elastic matrix of the i-th basic unit cell in the e-th unit respectively. χ e,ij and ψ e,ij represent the interpolation coefficients of the relative density and elastic matrix of the transition unit cell on the interface Γ ij in the e-th unit respectively; χ e,i , ψ e,i , χ e,ij and ψ e,ij are expressed by the following formulas respectively: In the formula, μ e,m , and γ e,m All are the m-th intermediate variables of unit e, m = 1,...,M; μ e,m , and γ e,m Represented as vectors: μ m , and γ m μ m , and γ m From the initial variable x m The results were obtained after three filtering steps.

2. The topology optimization method for connectable multi-configuration lattice structures according to claim 1, characterized in that, μ m It is obtained through the following process: First, for the initial variable x m PDE filtering is performed to obtain Among them, ζ and These represent the fields before and after filtration, respectively. r is a parameter controlling the filtration radius, and its relationship with the standard filtration radius R is as follows: Then, to Perform a Heaviside projection operation: in, Let be the projected field, and β and η be the parameters that control the steepness and threshold of the projection function, respectively, with η taking the value of 0.5; right The field after projection is represented by μ m To indicate; It is obtained through the following process: To identify the boundaries of the structure, μ m PDE filtering is performed to obtain right Heaviside projection is performed, where the parameter η2 controlling the projection threshold is set to 0.95, with the aim of obtaining μ. m Erosion field that shrinks inward by a certain distance Then, the field μ m and The interface of the structure can be obtained by subtraction; where the interface thickness is expressed as t≈0.67R2, and R2 is the second PDE filtering radius; γ m It is obtained through the following process: To construct the gradient interface, the field... Heaviside projection is performed, with the projection threshold parameter η3 set to 0.842, to obtain the projected field κ. m ; For κ m Perform linear density filtering, γ m The filtered field; γ m They are linearly distributed at the interface and are used to construct transition units through mapping.

3. The topology optimization method for connectable multi-configuration lattice structures according to claim 1 or 2, characterized in that, The mathematical expression for the topology optimization model is: Find:x1,...,x M Minimize:C=F T U(x1,...,x M ) Subject to: 0≤x e,m ≤1 With: KU = F, when i < M + 1, where x e,m is the m-th design variable of element e, N is the number of elements used to discretize the structure, C is the compliance of the structure, F and U are the load vector and displacement vector, respectively; V M+1 is the total material usage of the structure; when i < M + 1, V i is the material usage of each phase corresponding to each basic unit cell; is the specified volume fraction constraint.

4. The topology optimization method for connectable multi-configuration lattice structures according to claim 3, characterized in that, The sensitivity of the objective function to the design variables is: in: D n To calculate the elasticity matrix of the nth element using multi-material interpolation formulas, u n Let k be the displacement vector of element n. n Let Ω be the stiffness matrix of element n. n Let B be the element domain and B be the strain-displacement matrix. The data was obtained from the microstructure database through numerical derivative calculations. According to the multi-material interpolation formula, in order to obtain and Calculation required and When i ≠ m When i = m: In the formula: Obtained from the PDE filtering formula; Similarly, Obtained from the PDE filtering formula; In the formula, N n Let n be the set of elements within a defined square neighborhood. Similarly, 5. The topology optimization method for connectable multi-configuration lattice structures according to claim 3, characterized in that, The sensitivity of volume constraints to design variables is: in: ρ n To calculate the relative density of the nth element using a multi-material interpolation formula, The data was obtained from the microstructure database through numerical derivative calculations. According to the multi-material interpolation formula, in order to obtain and Calculation required and When i ≠ m When i = m: In the formula: Obtained from the PDE filtering formula; Similarly, Obtained from the PDE filtering formula; In the formula, N n Let n be the set of elements within a defined square neighborhood. Similarly, 6. The topology optimization method for connectable multi-configuration lattice structures according to any one of claims 1 to 2, characterized in that, The convergence condition of the topology optimization model is: the cumulative relative error within a specified number of consecutive iterations exceeds a set threshold.

7. The topology optimization method for connectable multi-configuration lattice structures according to claim 6, characterized in that, During the optimization process, the parameter controlling the steepness of the projection function gradually increases from k0 to k1, and doubles every k2 steps or when the convergence condition is met; where k0, k1 and k2 are all specified values, and k0 is much smaller than k1.

8. A topology optimization system for connectable multi-configuration lattice structures based on a transitional unit cell, characterized in that, The system includes: The interpolation module is used to interpolate the rod diameters of M basic unit cells to obtain transition unit cells; M is a positive integer greater than 1. The first calculation module is used to calculate the equivalent elasticity matrix of M basic unit cells and transition unit cells respectively using a homogenization method; The second calculation module is used to calculate the relative density and elastic matrix of the element based on the relative density and equivalent elastic matrix of the basic unit cell and the transition unit cell, using multi-material interpolation formulas respectively. The optimization module is used to construct a topology optimization model for a connectable multi-configuration lattice structure based on a transitional unit cell, and to optimize the sensitivity of the objective function and volume constraints within the design domain to design variables based on the topology optimization model until the topology optimization model converges. During the optimization process, the moving asymptote method is used to update the design variables. Based on the design variables corresponding to the converged topology optimization model, the optimized structure is obtained. The formulas for calculating the relative density and elasticity matrix of the element using multi-material interpolation are as follows: Among them, ρ e and D e are respectively the relative density and elastic matrix interpolated from the e-th unit in the design domain. ρ (i) and D( i) respectively represent the relative density and homogenized elastic matrix of the i-th basic unit cell, and are set as the weak material when i = M + 1; ρ (ij) and D (ij) respectively represent the relative density and homogenized elastic matrix of the transitional unit cell on the interface Γ ij between the i-th basic unit cell and the j-th basic unit cell, i < j, and are set as the weak material when j = M + 1; χ e,i and ψ e,i respectively represent the interpolation coefficients of the relative density and elastic matrix of the i-th basic unit cell in the e-th unit. χ e,ij and ψ e,ij respectively represent the interpolation coefficients of the relative density and elastic matrix of the transitional unit cell on the interface Γ ij in the e-th unit; χ e,i , ψ e,i , χ e,ij and ψ e,ij are respectively expressed by the following formulas: In the formula, μ e,m , and γ e,m All are the m-th intermediate variables of unit e, m = 1,...,M; μ e,m , and γ e,m Represented as vectors: μ m , and γ m μ m , and γ m From the initial variable x m The results were obtained after three filtering steps.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the topology optimization method for connectable multi-configuration lattice structures as described in any one of claims 1 to 7.

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