Transition unit cell-based connectable multi-configuration lattice structure topological optimization method and system

Abstract

The invention discloses a connectable multi-configuration lattice structure topological optimization method, system and device based on transition unit cells and a storage medium. The method comprises the steps that interpolation is conducted on rod diameters of M kinds of basic unit cells to obtain the transition unit cells; respectively calculating equivalent elastic matrixes of the M basic unit cells and the transition unit cells by adopting a homogenization method; according to the relative densities and the equivalent elastic matrixes of the basic unit cells and the transition unit cells, respectively calculating the relative densities and the elastic matrixes of the units by utilizing a multi-material interpolation formula; constructing a topological optimization model of the connectable multi-configuration lattice structure based on the transition unit cell, and optimizing the sensitivity of the target function and the volume constraint to the design variables in the design domain based on the topological optimization model until the topological optimization model converges; in the optimization process, a moving asymptote method is adopted to update design variables; and obtaining an optimized structure according to a design variable corresponding to the converged topological optimization model. According to the invention, the problem of connectivity between microstructures is solved by using the transition unit cells, the geometric configuration of the basic unit cells does not need to be limited, and the mechanical potential of the structure is improved.

Description

Technical Field

[0001] The present invention relates to the technical field related to structural optimization, and in particular to a topology optimization method, system, terminal device and computer-readable storage medium for a connectable multi-configuration lattice structure based on a transition unit cell. Background Art

[0002] Lattice structures are increasingly used in high-tech fields such as aerospace, automobiles, and biomedicine due to their light weight, multifunctionality, and superior designability. Considering lattice unit cells with different geometric configurations at the same time can fully tap the design potential of the structure and improve the mechanical properties of the lattice structure. However, since most of the current homogenization-based topology optimization methods ignore the boundary behavior of unit cells, there are connectivity problems between unit cells with different configurations, which makes it impossible to prepare the optimized structure, limiting the application of lattice structures in practical engineering.

[0003] At present, there are roughly two methods to solve the connectivity problem of multi-configuration lattice structures: the first is to impose geometric constraints on the basic unit cells so that they can generate self-connected lattice structures. However, this method actually reduces the design space of the lattice unit cells, thereby sacrificing the performance of the structure and failing to tap the design potential of the lattice structure; the second is to perform mandatory connections based on interpolation methods such as rod diameter and shape after the traditional topology optimization method, which may cause the optimized structure to lose its optimal form. In order to sacrifice the design space of the structure as little as possible and ensure the connectivity between microstructures, relevant researchers have recently imposed geometric constraints only on the structure at the interface. However, although it can ensure that adjacent unit cells can be connected to each other, this method of imposing simple constraints still has defects, especially for microstructures with complex configurations, which may cause the microstructure to lose its continuity and smoothness. Summary of the invention

[0004] In order to solve at least one technical problem in the above-mentioned prior art, the present invention provides a topology optimization method, system, terminal device and computer-readable storage medium for a connectable multi-configuration lattice structure based on a transition unit cell.

[0005] The first object of the present invention is to provide a topology optimization method for a connectable multi-configuration lattice structure based on a transition unit cell.

[0006] The second object of the present invention is to provide a connectable multi-configuration lattice structure topology optimization system based on transition unit cells.

[0007] The third object of the present invention is to provide a terminal device.

[0008] A fourth object of the present 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] Using 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, use the multi-material interpolation formula to calculate the unit relative density and elastic matrix respectively;

[0014] Construct a topology optimization model for a connectable multi-configuration lattice structure based on transitional unit cells, and optimize the sensitivity 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, use 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 formulas for calculating the unit relative density and elastic matrix using the multi-material interpolation formula are:

[0017]

[0018] where ρ e and D e are the relative density and elastic matrix interpolated for the e-th unit in the design domain respectively, ρ( i ) and D( i ) represent the relative density and homogenized elastic matrix of the i-th basic unit cell respectively, and are set as weak materials when i = M + 1; ρ (ij) and D (ij) 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 respectively, i < j, and are set as weak materials 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 unit respectively, χ e,ij and ψ e,ij 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 respectively; χ e,i , ψ e,i , χ e,ij and ψe,ij They are respectively expressed by the following formula:

[0019]

[0020]

[0021] In the formula, μ e,m , and γ e,m are the mth intermediate variables of unit e, m=1,...,M; μ e,m , and γ e,m Respectively expressed in the form of vectors: μ m , and γ m ;μ m , and γ m From the initial variable x m After three steps of filtration, they were obtained.

[0022] Furthermore, μ m 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 are the fields before and after filtering, respectively, r is the parameter controlling the filtering radius, and its relationship with the standard filtering radius R is:

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

[0027]

[0028] in, is the projected field, β and η are the parameters that control the steepness and threshold of the projection function, and the value of η is 0.5;

[0029] right The field after projection is μ m To express;

[0030] Obtained through the following process:

[0031] In order to identify the boundaries of the structure, μ m PDE filtering is performed to obtain right Perform the Heaviside projection, where the parameter η2 for controlling the projection threshold is taken as 0.95, with the aim of obtaining μ m The erosion field that shrinks inward by a certain distance Then, for the field μ m and Subtraction gives 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 the Heaviside projection, with the parameter η3 of its projection threshold 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 is the elastic matrix of the nth element calculated using the multi-material interpolation formula, u n is the displacement vector of unit n, k n is the stiffness matrix of element n, Ω n is the unit domain, B is the strain-displacement matrix, It is calculated by numerical derivative from the data in the microstructure database;

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

[0048]

[0049] Where:

[0050] Obtained by PDE filtering formula;

[0051]

[0052] Likewise, Obtained by PDE filtering formula;

[0053]

[0054] Where N n is the set of cells within the set square neighborhood of cell n; similarly,

[0055]

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

[0057]

[0058] in:

[0059] ρ n is the relative density of the nth element calculated using the multi-material interpolation formula, It is calculated by numerical derivative from the data in the microstructure database;

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

[0061]

[0062] Where:

[0063] Obtained by PDE filtering formula;

[0064]

[0065] Likewise, Obtained by PDE filtering formula;

[0066]

[0067] Where N n is the set of cells within the set square neighborhood of cell n;

[0068] Similarly,

[0069]

[0070] Furthermore, the convergence condition of the topology optimization model is that the cumulative relative error within the specified continuous iteration steps exceeds the 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; wherein k0, k1 and k2 are all specified values, and k0 is much smaller than k1.

[0072] The second object of the present invention can be achieved by adopting the following technical solutions:

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

[0074] An 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 elastic matrices of M basic unit cells and transition unit cells respectively by using a homogenization method;

[0076] The second calculation module is used to calculate the unit relative density and elastic matrix respectively according to the relative density and equivalent elastic matrix of the basic unit cell and the transition unit cell by using the multi-material interpolation formula;

[0077] The optimization module is used to construct a topology optimization model of a connectable multi-configuration lattice structure based on a transition unit cell, and optimize the sensitivity of the objective function and volume constraints in 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; and the optimized structure is obtained based on the design variables corresponding to the converged topology optimization model.

[0078] The third object of the present invention can be achieved by adopting the following technical solutions:

[0079] A terminal device comprises a processor and a memory for storing a program executable by the processor. When the processor executes the program stored in the memory, the above-mentioned method for topology optimization of a connectable multi-configuration lattice structure based on a transition unit cell is implemented.

[0080] The fourth object of the present invention can be achieved by adopting the following technical solutions:

[0081] A computer-readable storage medium stores a program, which, when executed by a processor, implements the above-mentioned topology optimization method for a connectable multi-configuration lattice structure based on a transition unit cell.

[0082] The present invention has the following beneficial effects compared with the prior art:

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

[0084] 2. The present invention considers the influence of transitional unit cells on structural performance in the multi-material interpolation formula and sensitivity analysis, so that the optimized structure is closer to the optimal form;

[0085] 3. When calculating the relative density and elastic matrix of the unit, the present invention constructs a gradient interface through a filtering method to obtain a mapping relationship with the transition unit cell, thereby accurately defining the transition unit at the interface according to the specified change mode, so that the microstructure obtained after optimization does not lose its original continuity and smoothness;

[0086] 4. The present invention can specify multiple transition modes to deal with situations with more than two lattice phases, making it more adaptable to complex connectivity issues. BRIEF DESCRIPTION OF THE DRAWINGS

[0087] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the structures shown in these drawings without paying creative work.

[0088] Figure 1 It is a flow chart of a topology optimization method for a connectable multi-configuration lattice structure based on a transition unit cell according to Example 1 of the present invention;

[0089] Figure 2 Schematic diagram of a topology optimization method for a connectable multi-configuration lattice structure based on a transition unit cell according to Example 1 of the present invention;

[0090] Figure 3 Schematic diagram of two microstructures, cross and x-shape, and corresponding transitional unit cells according to Example 1 of the present invention;

[0091] Figure 4 The MBB beam is used as an example in Example 1 of the present invention;

[0092] Figure 5 For example 1 of the present invention, Figure 3 For the basic unit cell, Figure 4 This is the schematic diagram of the structure after the design domain is optimized;

[0093] Figure 6 The three basic unit cells of cubic, x-shape, and cubic-x and the corresponding transition unit cells of Example 1 of the present invention;

[0094] Figure 7 The simply supported beam is used as an example in Example 1 of the present invention;

[0095] Figure 8 For example 1 of the present invention, Figure 6 For the basic unit cell, Figure 7 This is the schematic diagram of the structure after the design domain is optimized;

[0096] Fig. 9 It is a structural block diagram of a topology optimization system for a connectable multi-configuration lattice structure based on a transition unit cell according to Example 2 of the present invention;

[0097] Fig.10 This is a structural block diagram of the terminal device of embodiment 3 of the present invention. DETAILED DESCRIPTION

[0098] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention. It should be understood that the specific embodiments described are only used to explain the present application and are not used to limit the present application.

[0099] Embodiment 1:

[0100] like Figure 1 , 2 As shown, this embodiment provides a topology optimization method for a connectable multi-configuration lattice structure based on a transition unit cell, comprising the following steps:

[0101] S101. Interpolate the rod diameter of the basic unit cell to obtain a 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 M+1 phase). First, linear interpolation is performed on the rod diameters of the cross basic unit cell and the x-shape basic unit cell to obtain two sets of microstructure configurations; then, the two interpolated microstructure configurations are subjected to a union Boolean operation to obtain a transition unit cell in a mixed form.

[0103] Among them, the relative density 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 / transition unit cell, ρ * is the density of the microscopic unit (basic material) inside the basic unit cell / transition unit cell, and V is the design domain of the basic unit cell / transition unit cell.

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

[0107] The calculation formula of the homogenization method is:

[0108]

[0109] in, is the equivalent elastic tensor of the basic unit cell / transition unit cell, |V| is the volume of the basic unit cell / transition unit cell, D pqrs is the elastic tensor of the base 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, u ij being 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 element relative density and elastic matrix 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] Use the multi-material interpolation formula considering the M + 1 phases of the basic unit cell and transition unit cell to calculate the element relative density and elastic matrix:

[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, respectively, 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), respectively; 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, 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 element, respectively, expressed by the following formula:

[0118]

[0119]

[0120] μe,m , and γ e,m are the mth intermediate variables of unit e, m=1,...,M; they can be expressed in the form of vectors: μ m , and γ m .μ m , and γ m The initial variable x m Filtered through the following three steps:

[0121] (1) Get μ m The process:

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

[0123]

[0124] Among them, ζ and are the fields before and after filtering, respectively, r is the parameter controlling the filtering radius, and its relationship with the standard filtering radius R is:

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

[0126]

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

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

[0129] (2) Get The process:

[0130] In order to identify the boundaries of the structure, μ m PDE filtering is performed to obtain right Perform Heaviside projection, where the parameter η2 that controls the projection threshold is taken as 0.95, in order to obtain μ m Erosion field shrinking inwards Then, the field μ m and Subtracting them will give the interface of the structure. The thickness of the interface can be expressed as t≈0.67R2, where R2 is the second PDE filtering radius.

[0131] (3) Get γ m The process:

[0132] In order to construct the gradient interface, the field Perform Heaviside projection, and take the projection threshold parameter η3 as 0.842 to obtain the projected field κ m .

[0133] κ m To perform linear density filtering:

[0134]

[0135] Among them, N e is the set of units within the square neighborhood of unit e of size (t+1)×(t+1), γ e,m It is a filtered quantity that is linearly distributed on the interface and is used to map the constructed transition unit.

[0136] S104. Construct a topology optimization model of a connectable multi-configuration lattice structure based on a transition unit cell; optimize the sensitivity of the objective function and volume constraints in 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 units, a topology optimization model of a connectable multi-configuration lattice structure based on transitional unit cells is constructed.

[0138] The mathematical expression of the topology optimization model of the connectable multi-configuration lattice structure based on the transition unit cell is:

[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 is the initial variable; x e,mis the m-th design variable of element e, N is the number of elements 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 respectively the elastic matrix and relative density obtained by interpolation for the n-th element in the design domain, which can be calculated by the formula in step S103; u n is the displacement vector of element n, k n is the stiffness matrix of element n, Ω n is the element domain, and B is the strain-displacement matrix;

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

[0153]

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

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

[0156] can be obtained by the following formula:

[0157]

[0158] It can be obtained by formula (1).

[0159] The calculation formula is:

[0160]

[0161] Likewise, It can be obtained by formula (1).

[0162] in:

[0163]

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

[0165]

[0166] in:

[0167]

[0168] and The derivation of has been given above.

[0169] The MMA (Moving Asymptote) optimization algorithm is used to update the design variables, and the convergence condition is that the cumulative relative error of 10 steps exceeds 0.1%. 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. Obtain an optimized structure according to the design variables corresponding to the converged topology optimization model.

[0171] According to the obtained design variables, the intermediate variables are calculated according to 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 through the multi-material interpolation formula. e,i , χ e,ij , the distribution of each basic unit cell and transition unit cell after optimization is obtained according to the interpolation coefficient. The configuration of the transition unit cell is determined by the intermediate variable γ e,m Mapping obtained.

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

[0173] Figure 5 For the optimized structure, the cross microstructure is mainly distributed in the nearly horizontal bars on the upper and lower sides, while the x-shape microstructure is distributed in the inclined bars. Figure 5 The local enlarged image shows that due to the presence of the transition unit, the adjacent positions of the two microstructures can be well connected, which enables the optimized structure to be prepared through the manufacturing process. At the same time, the configuration of the optimized transition unit can follow the specified change pattern, verifying 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. At the same time, in order to realize a connectable structure, three change modes are specified to connect each two microstructures. Each transition unit is obtained by interpolation of the rod diameter. Among them, 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 an example with a size of L = 50. The design domain is discretized with 100×50 four-node elements. The external force size F = 1. The material properties are consistent with the above embodiment. The total material constraint v4 = 0.24 and the volume constraints of the two microstructures v1 = v2 = v3 = 0.08 are set. The first filtering radius is set to 10 and the interface width is set to 2. Correspondingly, the second filtering radius is set to 3.

[0175] Figure 8 is the optimized structure. It can be found that the proposed method can identify the interface between the basic unit cells and can accurately distinguish the interface segments. At the same time, the transition units on each interface segment can also follow the specified change pattern. Therefore, the proposed method can also be applied to the case of more than two lattice domains.

[0176] Those skilled in the art will appreciate that all or part of the steps in the method for implementing the above embodiments may be completed by instructing related hardware through a program, and the corresponding program may 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 this specific order, or that all the operations shown must be performed to achieve the desired results. On the contrary, the steps depicted can be performed in a different order. Additionally or alternatively, some steps can be omitted, multiple steps can be combined into one step, and / or one step can be decomposed into multiple steps.

[0178] Embodiment 2:

[0179] like Fig. 9 As shown, this embodiment provides a topology optimization system for a connectable multi-configuration lattice structure based on a transition unit cell, the system comprising an interpolation module 901, a first calculation module 902, a second calculation module 903 and an optimization module 904, wherein:

[0180] An 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 elastic matrices of M basic unit cells and transition unit cells respectively by using a homogenization method;

[0182] The second calculation module 903 is used to calculate the unit relative density and elastic matrix respectively according to the relative density and equivalent elastic matrix of the basic unit cell and the transition unit cell using the multi-material interpolation formula;

[0183] The optimization module 904 is used to construct a topology optimization model of a connectable multi-configuration lattice structure based on a transition unit cell, and optimize the sensitivity of the objective function and volume constraints in 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; and the optimized structure is obtained according to the design variables corresponding to the converged topology optimization model.

[0184] The specific implementation of each module in this embodiment can refer to the above-mentioned embodiment 1, which will not be described one by one here; it should be noted that the system provided in this embodiment is only illustrated by the division of the above-mentioned functional modules. In actual applications, the above-mentioned 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] Embodiment 3:

[0186] This embodiment provides a terminal device, which can be a computer. Fig.10As shown, it comprises a processor 1002, a memory, an input device 1003, a display 1004 and a network interface 1005 connected via a system bus 1001. The processor is used to provide computing and control capabilities. The memory comprises a non-volatile storage medium 1006 and an internal memory 1007. The non-volatile storage medium 1006 stores an operating system, a computer program and a database. The internal memory 1007 provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. When the processor 1002 executes the computer program stored in the memory, the topology optimization method of the connectable multi-configuration lattice structure based on the transition unit cell of the above-mentioned embodiment 1 is implemented as follows:

[0187] The rod diameters of M basic unit cells are interpolated to obtain transition unit cells; M is a positive integer greater than 1;

[0188] The equivalent elastic matrices of M basic unit cells and transition unit cells are calculated respectively by homogenization method.

[0189] According to 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 unit cell are calculated respectively by using the multi-material interpolation formula;

[0190] A topology optimization model of a connectable multi-configuration lattice structure based on a transition unit cell is constructed, and the sensitivity of the objective function and volume constraint in 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] According to the design variables corresponding to the topology optimization model after convergence, the optimized structure is obtained.

[0192] Embodiment 4:

[0193] This embodiment provides a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, the method for topology optimization of a connectable multi-configuration lattice structure based on a transition unit cell of the above embodiment 1 is implemented as follows:

[0194] The rod diameters of M basic unit cells are interpolated to obtain transition unit cells; M is a positive integer greater than 1;

[0195] The equivalent elastic matrices of M basic unit cells and transition unit cells are calculated respectively by homogenization method.

[0196] According to 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 unit cell are calculated respectively by using the multi-material interpolation formula;

[0197] A topology optimization model of a connectable multi-configuration lattice structure based on a transition unit cell is constructed, and the sensitivity of the objective function and volume constraint in 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] According to the design variables corresponding to the topology optimization model after convergence, the optimized structure is obtained.

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

[0200] The above is only a preferred embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can make equivalent replacements or changes according to the technical solution and inventive concept of the present invention within the scope disclosed by the present invention, which shall fall within the protection scope of the present invention.

Claims

1. A topology optimization method for a connectable multi-configuration lattice structure based on a transition unit cell, characterized in that: The method comprises: The rod diameters of M basic unit cells are interpolated to obtain transition unit cells; M is a positive integer greater than 1; The equivalent elastic matrices of M basic unit cells and transition unit cells are calculated respectively by homogenization method. According to the relative density and equivalent elastic matrix of the basic unit cell and the transition unit cell, the unit relative density and elastic matrix are calculated respectively by using the multi-material interpolation formula; A topology optimization model of a connectable multi-configuration lattice structure based on a transition unit cell is constructed, and the sensitivity of the objective function and volume constraint in 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; According to the design variables corresponding to the topology optimization model after convergence, the optimized structure is obtained.

2. The method for topology optimization of a connectable multi-configuration lattice structure according to claim 1, characterized in that: The formula for calculating the relative density and elastic matrix of the unit using the multi-material interpolation formula is: where ρ e and D e are the relative density and elastic matrix interpolated from the e-th element in the design domain, respectively. 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 transitional 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 element, respectively. χ e,ij and ψ e,ij 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 element, respectively; χ e,i 、ψ e,i 、χ e,ij and ψ e,ij are expressed by the following equations, respectively: In the formula, μ e,m , and γ e,m are the mth intermediate variables of unit e, m=1,...,M; μ e,m , and γ e,m Respectively expressed in the form of vectors: μ m , and γ m ;μ m , and γ m From the initial variable x m After three steps of filtration, they were obtained.

3. The method for topology optimization of a connectable multi-configuration lattice structure according to claim 2, characterized in that: μ m Obtained through the following process: First, for the initial variable x m PDE filtering is performed to obtain Among them, ζ and are the fields before and after filtering, respectively, r is the parameter controlling the filtering radius, and its relationship with the standard filtering radius R is: Then, yes Perform a Heaviside projection operation: in, is the projected field, β and η are the parameters that control the steepness and threshold of the projection function, and the value of η is 0.5; right The field after projection is μ m To express; Obtained through the following process: In order to identify the boundaries of the structure, μ m PDE filtering is performed to obtain right Perform Heaviside projection, where the parameter η2 that controls the projection threshold is taken as 0.95, in order to obtain μ m Erosion field shrinking inwards Then, the field μ m and Subtracting them will give the interface of the structure; the thickness of the interface is expressed as t≈0.67R2, where R2 is the second PDE filtering radius; γ m Obtained through the following process: In order to construct the gradient interface, the field Perform Heaviside projection, and take the projection threshold parameter η3 as 0.842 to obtain the projected field κ m ; κ m Perform linear density filtering, γ m is the filtered field; γ m They are distributed linearly on the interface and are used to map the transition units of the structure.

4. The method for topology optimization of a connectable multi-configuration lattice structure according to claim 2 or 3, characterized in that: The mathematical expression of 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 amount of material used for the structure; when i < M + 1, V i is the amount of material for each phase corresponding to each basic unit cell; is the specified volume fraction constraint.

5. The method for topology optimization of a connectable multi-configuration lattice structure according to claim 4, characterized in that: The sensitivity of the objective function to the design variables is: in: D n is the elastic matrix of the nth element calculated using the multi-material interpolation formula, u n is the displacement vector of unit n, k n is the stiffness matrix of element n, Ω n is the unit domain, B is the strain-displacement matrix, It is calculated by numerical derivative from the data in the microstructure database; According to the multi-material interpolation formula, in order to obtain and Need to calculate and When i≠m, When i=m: Where: Obtained by PDE filtering formula; Likewise, Obtained by PDE filtering formula; Where N n is the set of cells within the set square neighborhood of cell n; Similarly, 6. The method for topology optimization of a connectable multi-configuration lattice structure according to claim 4, characterized in that: The sensitivity of the volume constraint to the design variables is: in: ρ n is the relative density of the nth element calculated using the multi-material interpolation formula, It is calculated by numerical derivative from the data in the microstructure database; According to the multi-material interpolation formula, in order to obtain and Need to calculate and When i≠m, When i=m: Where: Obtained by PDE filtering formula; Likewise, Obtained by PDE filtering formula; Where N n is the set of cells within the set square neighborhood of cell n; Similarly, 7. The method for topology optimization of a connectable multi-configuration lattice structure according to any one of claims 1 to 3, characterized in that: The convergence condition of the topology optimization model is that the cumulative relative error in the specified continuous iteration steps exceeds the set threshold.

8. The method for topology optimization of a connectable multi-configuration lattice structure according to claim 7, 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; k0, k1 and k2 are all specified values, and k0 is much smaller than k1.

9. A topology optimization system for connectable multi-configuration lattice structures based on transitional unit cells, characterized in that: The system comprises: An 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 elastic matrices of M basic unit cells and transition unit cells respectively by using a homogenization method; The second calculation module is used to calculate the unit relative density and elastic matrix respectively according to the relative density and equivalent elastic matrix of the basic unit cell and the transition unit cell by using the multi-material interpolation formula; The optimization module is used to construct a topology optimization model of a connectable multi-configuration lattice structure based on a transition unit cell, and optimize the sensitivity of the objective function and volume constraints in 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; and the optimized structure is obtained based on the design variables corresponding to the converged topology optimization model.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the method for topology optimization of a connectable multi-configuration lattice structure as claimed in any one of claims 1 to 8 is implemented.

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