A method and device for topology optimization of discrete body structures based on PnP-ADMM algorithm

Abstract

Embodiments of the present invention provide a method and apparatus for topology optimization of discrete body structures based on the PnP-ADMM algorithm. The method comprises: determining a design domain for the discrete body structure, discretizing the design domain into a finite element mesh using the finite element method, establishing a topology optimization model using volume and discrete density as constraints and minimizing flexibility as the objective function, and solving the topology optimization model using the PnP-ADMM algorithm to obtain an optimal topology. The topology optimization results obtained by this method are numerically stable, and when initial parameters are appropriately adjusted, they avoid defects such as checkerboard patterns, structural ambiguity, or strong mesh dependence, resulting in highly manufacturable optimized structures.

Description

Technical Field

[0001] The present invention relates to the field of structural optimization technology, and in particular to a discrete body structure topology optimization method based on a PnP-ADMM algorithm, a discrete body structure topology optimization device based on a PnP-ADMM algorithm, an electronic device, and a computer-readable medium. Background Art

[0002] As a material distribution problem, topology optimization aims to find the optimal structural form or material distribution to meet given performance requirements and constraints. The topology optimization objects of structures include discrete structures and continuum structures. Although some problems of topology optimization of discrete structures have been solved in some studies, topology optimization of discrete structures still faces several challenges. First, changes in unit density can easily lead to singular optimal solutions, which means that when certain units are deleted, unreasonable or unstable structures may be obtained. Second, due to the complexity of the design space, finding the global optimal solution is often very difficult.

[0003] In response to the challenges of topology optimization of discrete structures, various methods have been developed over the past two decades to overcome the combinatorial complexity inherent in topology optimization with discrete variables. For example, one approach utilizes branch-and-bound methods to obtain global optimal solutions for topology optimization with discrete variables. Another approach proposes a relaxation method for topology optimization with discrete variables that inherits traditional sequential approximate programming methods and transforms the topology optimization problem into a series of separable integer programming subproblems. Still another approach approximates the topology optimization problem of minimum compliance under material volume constraints with a sequence of discrete variable subprogramming with discrete variable sensitivity.

[0004] Although the above methods have certain effects on the topology optimization of discrete body structures, if the volume is constrained and flexibility minimization is the optimization goal, they all have numerical instability problems such as checkerboard format and the disadvantage of poor manufacturability of the optimization results. Summary of the Invention

[0005] In view of the above problems, embodiments of the present invention are proposed to provide a discrete body structure topology optimization method based on the PnP-ADMM algorithm and a corresponding discrete body structure topology optimization device based on the PnP-ADMM algorithm, an electronic device and a computer-readable medium to overcome the above problems or at least partially solve the above problems.

[0006] The embodiment of the present invention discloses a discrete body structure topology optimization method based on the PnP-ADMM algorithm, comprising:

[0007] Determine the design domain of discrete body structures;

[0008] The design domain is discretized into a finite element grid using a finite element method;

[0009] A topology optimization model was established with volume and discrete density as constraints and flexibility minimization as the objective function;

[0010] The PnP-ADMM algorithm is used to solve the topology optimization model and obtain the optimal topology structure.

[0011] Optionally, the step of solving the topology optimization model using the PnP-ADMM algorithm to obtain the optimal topology structure includes:

[0012] Converting the topology optimization model into a Lagrangian function;

[0013] The PnP-ADMM algorithm is used to solve the Lagrangian function;

[0014] Iterative calculation is performed and when the volume and the discrete density meet a convergence condition, the optimal topological structure is output.

[0015] Optionally, the step of converting the topology optimization model into a Lagrangian function includes:

[0016] Weights, penalty factors, and dual variables are added to the objective function, the volume, and the discrete density, respectively, to transform the topology optimization model into the Lagrangian function; the Lagrangian function includes sub-variables corresponding to the objective function, the volume, and the discrete density, respectively.

[0017] Optionally, the step of solving the Lagrangian function using the PnP-ADMM algorithm includes:

[0018] Based on the PnP-ADMM solution framework, the cyclic iterative relationship between the sub-variables of the objective function, the sub-variables of the volume, the sub-variables of the discrete density and the discrete density is derived respectively.

[0019] Optionally, the step of performing iterative calculation and outputting the optimal topological structure when the volume and the discrete density meet convergence conditions includes:

[0020] Performing cyclic iteration using the cyclic iteration relationship until a convergence condition of the discrete density is satisfied;

[0021] A movement restriction strategy is executed on the volume until a convergence condition of the volume is satisfied, and the optimal topology structure is output.

[0022] Optionally, the step of performing cyclic iteration using the cyclic iteration relation until a convergence condition of the discrete density is satisfied includes:

[0023] Performing cyclic iteration using the cyclic iteration relationship to determine whether the change in the discrete density is lower than a preset threshold;

[0024] If the variation of the discrete density is lower than a preset first threshold, it is determined that a convergence condition of the discrete density is satisfied.

[0025] Optionally, the step of executing a movement restriction strategy on the volume until a convergence condition of the volume is satisfied and outputting the optimal topological structure comprises:

[0026] cyclically reducing the volume according to a preset reduction factor and determining whether the volume fraction is lower than a preset second threshold;

[0027] If the volume fraction is lower than a preset second threshold, it is determined that the convergence condition of the volume is met, and the optimal topological structure is output.

[0028] The embodiment of the present invention further discloses a discrete body structure topology optimization device based on the PnP-ADMM algorithm, comprising:

[0029] A determination module is used to determine the design domain of the discrete body structure;

[0030] A discretization module, configured to discretize the design domain into a finite element grid using a finite element method;

[0031] Model building module, used to build topology optimization models using volume and discrete density as constraints and flexibility minimization as the objective function;

[0032] The solution module is used to solve the topology optimization model using the PnP-ADMM algorithm to obtain the optimal topology structure.

[0033] Optionally, the solution module includes:

[0034] A conversion submodule, used to convert the topology optimization model into a Lagrangian function;

[0035] A solution submodule, for solving the Lagrangian function using a PnP-ADMM algorithm;

[0036] The output submodule is used to perform iterative calculation and output the optimal topological structure when the volume and the discrete density meet the convergence condition.

[0037] Optionally, the conversion submodule includes:

[0038] A conversion unit is used to add weights, penalty factors, and dual variables to the objective function, the volume, and the discrete density, respectively, to convert the topology optimization model into the Lagrangian function; the Lagrangian function contains sub-variables corresponding to the objective function, the volume, and the discrete density, respectively.

[0039] Optionally, the solution submodule includes:

[0040] A solving unit is used to derive, based on a PnP-ADMM solving framework, cyclic iterative relationships between the sub-variables of the objective function, the sub-variables of the volume, the sub-variables of the discrete density and the discrete density.

[0041] Optionally, the output submodule includes:

[0042] an iterative unit, configured to perform cyclic iteration using the cyclic iterative relation until a convergence condition of the discrete density is satisfied;

[0043] The movement restriction unit is used to execute a movement restriction strategy on the volume until a convergence condition of the volume is satisfied, and output the optimal topological structure.

[0044] Optionally, the iteration unit includes:

[0045] A judging unit, configured to perform cyclic iteration using the cyclic iteration relationship to judge whether a change in the discrete density is lower than a preset threshold;

[0046] A determining unit is configured to determine whether a convergence condition of the discrete density is satisfied if the variation of the discrete density is lower than a preset first threshold.

[0047] Optionally, the movement limiting unit includes:

[0048] a reduction unit, configured to cyclically reduce the volume according to a preset reduction factor and determine whether the volume fraction is lower than a preset second threshold;

[0049] An output unit is configured to determine that a convergence condition of the volume is satisfied if the volume fraction is lower than a preset second threshold value, and output the optimal topological structure.

[0050] An embodiment of the present invention further discloses an electronic device, comprising a processor, a communication interface, a memory, and a communication bus, wherein the processor, the communication interface, and the memory communicate with each other via the communication bus;

[0051] The memory is used to store computer programs;

[0052] The processor is used to implement the discrete body structure topology optimization method based on the PnP-ADMM algorithm as described in the embodiment of the present invention when executing the program stored in the memory.

[0053] An embodiment of the present invention further discloses one or more computer-readable media having instructions stored thereon, which, when executed by one or more processors, enable the processors to execute the discrete body structure topology optimization method based on the PnP-ADMM algorithm as described in the embodiment of the present invention.

[0054] The embodiments of the present invention include the following advantages:

[0055] The discrete body structure topology optimization method based on the PnP-ADMM algorithm in an embodiment of the present invention determines the design domain of the discrete body structure, discretizes the design domain into a finite element mesh using the finite element method, establishes a topology optimization model using volume and discrete density as constraints and flexibility minimization as the objective function, and solves the topology optimization model using the PnP-ADMM algorithm to obtain the optimal topology structure. The topology optimization results processed by this method are numerically stable and, when the initial parameters are properly adjusted, avoid defects such as checkerboard patterns, structural ambiguity, or strong mesh dependence. The optimized results are highly manufacturable. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 1 is a flowchart of a discrete body structure topology optimization method based on the PnP-ADMM algorithm provided in an embodiment of the present invention;

[0057] Figure 2 is a schematic diagram of an MBB beam structure provided in an embodiment of the present invention;

[0058] Figure 3 is a schematic diagram of a cantilever beam structure provided in an embodiment of the present invention;

[0059] Figure 4 1 is a structural block diagram of a discrete body structure topology optimization device based on the PnP-ADMM algorithm provided in an embodiment of the present invention;

[0060] Figure 5 is a block diagram of an electronic device provided in an embodiment of the present invention;

[0061] Figure 6 is a schematic diagram of a computer-readable medium provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0062] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0063] Reference Figure 1 , shows a flowchart of a discrete body structure topology optimization method based on the PnP-ADMM algorithm provided in an embodiment of the present invention, which may specifically include the following steps:

[0064] Step 101, determining the design domain of the discrete body structure;

[0065] In an embodiment of the present invention, in order to perform topological optimization on a discrete body structure, the design domain of the discrete body structure can be first determined. The design domain of the discrete body structure can be generated by inputting design conditions and parameters, for example, the size and boundary range of the output design domain can be output.

[0066] Step 102: discretize the design domain into a finite element grid using the finite element method;

[0067] After determining the design domain, the finite element method can be used to discretize the design domain of the discrete body structure into a finite element mesh. Using the finite element method, the mathematical expression can be expressed as:

[0068]

[0069] Where ρ represents the density design variable matrix, which can only be 0 or 1. c(ρ) is the structural flexibility, and U, F, and K are the matrices of overall displacement, external load, and structural stiffness, respectively. i is the volume of the i-th finite element, V is the total material usage, and N is the number of finite elements.

[0070] Step 103, establishing a topology optimization model with volume and discrete density as constraints and flexibility minimization as the objective function;

[0071] Based on the finite element method mathematical expression (1) above, a discrete sensitivity method is used to introduce discrete sensitivities compatible with discrete variables to solve the objective function. Specifically, with flexibility minimization as the objective function and volume and discrete density as constraints, this method is applied to the mathematical model (1) to obtain the topology optimization model to be solved in the present invention.

[0072] The topology optimization model is as follows:

[0073]

[0074] Among them, b i is the discrete sensitivity. The discrete sensitivity is calculated as follows:

[0075]

[0076] Among them, p is the penalty parameter, U e is the unit displacement matrix, K e is the element stiffness matrix.

[0077] Step 104: Use the PnP-ADMM algorithm to solve the topology optimization model to obtain the optimal topology structure.

[0078] After obtaining the topology optimization model to be solved, the PnP-ADMM algorithm can be used to solve the topology optimization model. Specifically, a penalty term and a dual variable can be added to the objective function and each constraint, and the optimization problem with complex constraints can be converted into a series of sub-problems. The iterative formula of each constraint is derived, and the target variable is iteratively solved through each constraint iterative formula, so as to obtain the structural distribution in the discrete body structure problem.

[0079] In one embodiment of the present invention, the step of solving the topology optimization model using the PnP-ADMM algorithm to obtain the optimal topology structure includes:

[0080] S11, converting the topology optimization model into a Lagrangian function;

[0081] S12, solving the Lagrangian function using a PnP-ADMM algorithm;

[0082] S13, performing iterative calculation and outputting the optimal topological structure when the volume and the discrete density meet convergence conditions.

[0083] In one embodiment of the present invention, the step of converting the topology optimization model into a Lagrangian function includes:

[0084] S21, adding weights, penalty factors, and dual variables to the objective function, the volume, and the discrete density, respectively, to convert the topology optimization model into the Lagrangian function; the Lagrangian function contains sub-variables corresponding to the objective function, the volume, and the discrete density, respectively.

[0085] In one embodiment of the present invention, the step of solving the Lagrangian function using the PnP-ADMM algorithm includes:

[0086] S31, based on the PnP-ADMM solution framework, derive the cyclic iterative relationship between the sub-variables of the objective function, the sub-variables of the volume, the sub-variables of the discrete density and the discrete density.

[0087] In one embodiment of the present invention, the step of performing iterative calculation and outputting the optimal topological structure when the volume and the discrete density meet convergence conditions includes:

[0088] S41, performing cyclic iteration using the cyclic iteration relationship until a convergence condition of the discrete density is satisfied;

[0089] S42: Execute a movement restriction strategy on the volume until a convergence condition of the volume is met, and output the optimal topology structure.

[0090] In one embodiment of the present invention, the step of performing cyclic iteration using the cyclic iteration relation until a convergence condition of the discrete density is satisfied includes:

[0091] S51, performing loop iteration using the loop iteration relationship to determine whether the variation of the discrete density is lower than a preset threshold;

[0092] S52: If the variation of the discrete density is lower than a preset first threshold, determine that a convergence condition of the discrete density is satisfied.

[0093] In one embodiment of the present invention, the step of executing a movement restriction strategy on the volume until a convergence condition of the volume is satisfied and outputting the optimal topological structure comprises:

[0094] S61, cyclically reducing the volume according to a preset reduction factor and determining whether the volume fraction is lower than a preset second threshold;

[0095] S62: If the volume fraction is lower than a preset second threshold, determine that the convergence condition of the volume is met, and output the optimal topological structure.

[0096] To solve the topology optimization model based on the PnP-ADMM algorithm, we can first add weights, penalty factors, and dual variables to the objective function, volume, and discrete density, convert the topology optimization model into a Lagrangian function, and then solve the Lagrangian function. After solving the Lagrangian function, we can determine whether the volume constraints and discrete density constraints meet the convergence conditions. If the convergence conditions are met, the optimal topology structure can be obtained.

[0097] Specifically, weight terms are added to the objective function and each constraint, and the topology optimization model (2) is transformed into a Lagrangian function (4). The Lagrangian function formula is as follows:

[0098]

[0099] The discrete density variable ρ is:

[0100]

[0101] In Equations (4) and (5), v represents the corresponding discrete subvariable of the objective function, u represents the variable of the volume constraint, and ω represents the variable of the discrete constraint. For the convenience of subsequent calculations, the m×n matrix ρ in model (2) is modified. ρ, ν, u, and ω in Equation (4) are all changed from ρ in (2) to mn×1 column matrices. θ1, θ2, and θ3 are scalars representing the weights of the objective function, volume constraint, and discrete variable constraint, respectively. B is the mn×1 discrete sensitivity column matrix, and T is the mn×1 unit volume matrix of each discrete unit. is the maximum volume for the volume constraint, a scalar. E is represented by an mn×1 matrix with all elements set to 1. μ1 and γ1 are the penalty factor and dual variable for the flexibility objective function, μ2 and γ2 are the penalty factor and dual variable for the volume constraint, and μ3 and γ3 are the penalty factor and dual variable for the discrete constraint. μ1, μ2, and μ3 are scalars, and γ1, γ2, and γ3 are mn×1 matrices.

[0102] The values of variables υ, u, ω are expressed as:

[0103]

[0104]

[0105]

[0106] According to the PnP-ADMM solution framework, the value of the density variable ρ is:

[0107]

[0108] Therefore, solving the optimal structure density release problem is decomposed into the sub-problems of solving the three intermediate variables υ, u, and ω. The cyclic iterative relationship of updating υ, u, and ω through ρ and then iteratively calculating ρ through the three variables is derived.

[0109] In order to solve the optimal value of υ, u, ω in each iteration, the three equations (6), (7), and (8) are differentiated and solved respectively, and the derivative of equation (6) is used to find the local optimal value:

[0110]

[0111] Derived the iterative formula of variable v:

[0112]

[0113] Similarly, take the derivative of (7):

[0114]

[0115] The iterative formula of u is derived:

[0116]

[0117] Where E is an mn×1 matrix.

[0118] Similarly, take the derivative of (8):

[0119]

[0120] The iterative formula of ω is derived:

[0121]

[0122] According to formulas (11), (13), and (15), the new values of υ, u, and ω can be solved by iteratively solving the old density variable ρ.

[0123] The three new variable values υ, u, and ω are obtained and used to update the density variable ρ. Similarly, the ρ expression (9) is derived to find the local optimum of ρ:

[0124]

[0125] Obtain the ρ iteration formula:

[0126]

[0127] According to the PnP-ADMM solution framework, each time the design variable ρ is updated, the penalty factors μ1, μ2, and μ3 need to be judged and updated. First, the original residuals ε1, ε2, and ε3 of each design sub-variable are calculated:

[0128] ε1=||ρ k+1 -v k+1 ||2 (18)

[0129] ε2=||ρ k+1 -u k+1 ||2 (19)

[0130] ε3=||ρ k+1 -ω k+1 ||2 (20)

[0131] Calculate the dual residual q of the design variables:

[0132]

[0133] According to the original residual and the dual residual, μ1, μ2, μ3 are updated as follows.

[0134]

[0135] Where τ is the balancing factor and σ is the residual tolerance. σ>1,τ>1 is satisfied.

[0136] When the iteration reaches the density variable change Within a point error, and the penalty factor μ of each constraint i It no longer changes, which can be regarded as the density variable converging to the optimal distribution under its constraints. The conditions for determining the termination of iteration are:

[0137]

[0138] Among them, η represents the density change, φ represents the tolerance, and takes 0<φ<10 -3 .

[0139] According to the PnP-ADMM solution framework, if the convergence judgment condition of formula (23) is not met, the dual variables corresponding to each constraint need to be updated:

[0140]

[0141] Then continue the iteration until the convergence condition of formula (23) is met.

[0142] To ensure the existence of a solution to the topology optimization problem and avoid checkerboarding, a sensitivity filtering method is also required. Specifically, a filter radius is set and a linear convolution factor is introduced to modify the sensitivity of the objective function. This method calculates the weighted average distance between the central cell and other cells, constructs the mean sensitivity of all elements within the range, and updates the sensitivity for subsequent iterations to resolve the checkerboarding problem.

[0143] The formula for sensitivity filtering is:

[0144]

[0145] Where, ρ e As the central unit. is the sensitivity, obtained by filtering the sensitivity of the central unit, and γ is the minimum value 0.001 to prevent the denominator from being 0; r min Indicates the filter radius; N e Is all r min Units within the range; ρ i is r min The relative density of cells around the central cell e in the range.

[0146] After ρ meets the convergence judgment condition, the movement restriction strategy described below can be executed until the volume constraint is met and convergence is obtained to the optimal solution.

[0147] Specifically, for the minimum compliance problem, this study selected volume fraction control as a motion-limiting strategy. Specifically, the module's calculations gradually reduce material usage by a predefined volume reduction factor, χ, which is less than but close to 1, to constrain the range of variation of the design variables. After convergence within the current volume fraction constraint, the calculations continue according to the reduced volume fraction constraint. This volume fraction reduction factor, χ, was chosen to be 0.999, removing only 0.1% of the material volume with each iteration. This approach controls the range of variation in the structural distribution and ensures the accuracy of the approximation of the integer programming subproblem based on discrete sensitivity.

[0148] The condition for determining whether the volume constraint iteration has terminated is to sum all the density variable values and divide them by the total volume (x * y) to obtain the volume fraction. Then, determine whether the volume fraction is less than a preset second threshold. If the volume fraction is greater than or equal to the preset second threshold, the iterative calculation continues. If it is less than the preset second threshold, the volume constraint is determined to be satisfied, the iteration terminates, and the optimal solution can be output, obtaining the optimal topology corresponding to the optimal solution. The preset second threshold can be set according to actual conditions, for example, 0.5.

[0149] To verify the effectiveness of the improved algorithm using the PnP-ADMM method, we provide the following two verification examples, using two classic structures: an MBB beam and a cantilever beam. For ease of introduction, the improved algorithm in this paper is named the PNPDETOP algorithm.

[0150] Specifically, the DVTOPCRA method (Liang Y, Cheng G. Further elaborations ontopology optimization via sequential integer programming and Canonical relaxation algorithm and 128-line MATLAB code [J]. Structural and Multidisciplinary Optimization, 2019, 61 (1).) and the improved PNP-ADMM algorithm PNPDETOP in this paper were used to conduct experiments under the same conditions, and the result data of the two methods were compared to verify the effectiveness of this study.

[0151] The basic parameter settings in the experiment are: the balance factor τ and the residual tolerance σ are τ = 1.1, σ = 1.5; the penalty factor and the dual variable are

[0152] The effectiveness of the improved algorithm is discussed using the MBB beam as an example. The MBB beam is a symmetrical structure, so the 1 / 2 model is taken for optimization. Figure 2 As shown in the figure. The right bottom corner of the beam constrains vertical displacement, and a point load F of magnitude 1 is applied vertically downward at the upper left corner of the beam. The design domain is discretized into 120*40 elements and 150*50 elements. In the improved algorithm in this paper and the algorithm in the literature, the following parameters are kept the same for both examples: Young's modulus E = 1, Poisson's ratio λ = 0.3, filter radius r min =3, penalty factor p=3, target volume fraction of the material f=0.5, volume reduction factor χ=0.999. The constraint weights of the proposed algorithm are θ1=0.3, θ2=2.0, θ3=0.5, and the parameter β of the method in the literature is β=2000.

[0153] According to the above set parameters, the experimental results of MBB beam structure are obtained:

[0154] Table 1 MBB beam example comparison and verification experiment

[0155]

[0156] Analysis of experimental results shows that the improved variable-density optimization algorithm PNPDETOP, based on the PnP-ADMM framework, can also iteratively produce target optimization results that meet the constraints. Compared with the flexibility values obtained after DVTOPCRA iterations, the flexibility of the optimized examples with aspect ratios of 150*50 and 120*40 is significantly reduced. The flexibility of the 150*50 MBB beam example is reduced by 2.48%, and the flexibility of the 120*40 MBB beam example is reduced by 2.09%. Therefore, the experimental tests on MBB beams demonstrate the effectiveness and good results of the improved optimization algorithm proposed in this paper.

[0157] The effectiveness of the improved algorithm is discussed using a cantilever beam as an example. The design domain, loads and boundary conditions of the structure are as follows: Figure 3 As shown, the load magnitude is 1. Experimental examples are performed using the same discretization of the design domain into 150*50 and 120*40 elements. The penalty factor parameter for the PNPDETOP and DVTOPCRA algorithms is set to p = 2. The other algorithm parameter settings are consistent with the MBB beam experiments.

[0158] The following are the experimental results of the cantilever beam structure:

[0159] Table 2 Cantilever beam example comparison and verification experiment

[0160]

[0161] Analysis of experimental results shows that the improved PNPDETOP algorithm is also effective for cantilever beam optimization. Compared to the DVTOPCRA algorithm, the post-optimization flexibility of the 150*50 and 120*40 aspect ratio examples decreased by 2.70% and 2.09%, respectively. Therefore, the improved algorithm based on the PnP-ADMM algorithm framework is effective for both MBB and cantilever beam optimization examples.

[0162] By determining the design domain of a discrete structure, the finite element method is used to discretize the design domain into a finite element mesh. A topology optimization model is established using volume and discrete density as constraints and flexibility minimization as the objective function. The PnP-ADMM algorithm is used to solve the topology optimization model and obtain the optimal topology structure. The topology optimization results obtained by this method are stable and, when the initial parameters are adjusted appropriately, avoid defects such as checkerboard patterns, structural ambiguity, or strong mesh dependence. The optimized results are highly manufacturable.

[0163] It should be noted that for the sake of simplicity, the method embodiments are described as a series of actions. However, those skilled in the art should be aware that the embodiments of the present invention are not limited by the order of the actions described, because according to the embodiments of the present invention, certain steps can be performed in other orders or simultaneously. Secondly, those skilled in the art should also be aware that the embodiments described in this specification are all preferred embodiments, and the actions involved are not necessarily required by the embodiments of the present invention.

[0164] Reference Figure 4 , shows a structural block diagram of a discrete body structure topology optimization device based on the PnP-ADMM algorithm provided in an embodiment of the present invention, which may specifically include the following modules:

[0165] Determination module 401, used to determine the design domain of the discrete body structure;

[0166] A discretization module 402 is configured to discretize the design domain into finite element grids using a finite element method;

[0167] A model building module 403 is used to build a topology optimization model using volume and discrete density as constraints and flexibility minimization as an objective function;

[0168] The solving module 404 is used to solve the topology optimization model using the PnP-ADMM algorithm to obtain the optimal topology structure.

[0169] Optionally, the solution module includes:

[0170] A conversion submodule, used to convert the topology optimization model into a Lagrangian function;

[0171] A solution submodule, for solving the Lagrangian function using a PnP-ADMM algorithm;

[0172] The output submodule is used to perform iterative calculation and output the optimal topological structure when the volume and the discrete density meet the convergence condition.

[0173] Optionally, the conversion submodule includes:

[0174] A conversion unit is used to add weights, penalty factors, and dual variables to the objective function, the volume, and the discrete density, respectively, to convert the topology optimization model into the Lagrangian function; the Lagrangian function contains sub-variables corresponding to the objective function, the volume, and the discrete density, respectively.

[0175] Optionally, the solution submodule includes:

[0176] A solving unit is used to derive, based on a PnP-ADMM solving framework, cyclic iterative relationships between the sub-variables of the objective function, the sub-variables of the volume, the sub-variables of the discrete density and the discrete density.

[0177] Optionally, the output submodule includes:

[0178] an iterative unit, configured to perform cyclic iteration using the cyclic iterative relation until a convergence condition of the discrete density is satisfied;

[0179] The movement restriction unit is used to execute a movement restriction strategy on the volume until a convergence condition of the volume is satisfied, and output the optimal topological structure.

[0180] Optionally, the iteration unit includes:

[0181] A judging unit, configured to perform cyclic iteration using the cyclic iteration relationship to judge whether a change in the discrete density is lower than a preset threshold;

[0182] A determining unit is configured to determine whether a convergence condition of the discrete density is satisfied if the variation of the discrete density is lower than a preset first threshold.

[0183] Optionally, the movement limiting unit includes:

[0184] a reduction unit, configured to cyclically reduce the volume according to a preset reduction factor and determine whether the volume fraction is lower than a preset second threshold;

[0185] An output unit is configured to determine that a convergence condition of the volume is satisfied if the volume fraction is lower than a preset second threshold value, and output the optimal topological structure.

[0186] As for the device embodiment, since it is basically similar to the method embodiment, the description is relatively simple, and the relevant parts can be referred to the partial description of the method embodiment.

[0187] In addition, an embodiment of the present invention further provides an electronic device, such as Figure 5 As shown, it includes a processor 501, a communication interface 502, a memory 503 and a communication bus 504, wherein the processor 501, the communication interface 502, and the memory 503 communicate with each other through the communication bus 504.

[0188] Memory 503, used for storing computer programs;

[0189] The processor 501 is configured to implement the discrete body structure topology optimization method based on the PnP-ADMM algorithm as described in the embodiment when executing the program stored in the memory 503 .

[0190] The communication bus mentioned in the terminal can be a Peripheral Component Interconnect (PCI) bus or an Extended Industry Standard Architecture (EISA) bus. This communication bus can be divided into an address bus, a data bus, a control bus, etc. For ease of illustration, only one thick line is used in the figure, but this does not mean that there is only one bus or only one type of bus.

[0191] The communication interface is used for communication between the above terminal and other devices.

[0192] The memory may include random access memory (RAM) or non-volatile memory, such as at least one disk storage. Alternatively, the memory may be at least one storage device located away from the processor.

[0193] The above-mentioned processor can be a general-purpose processor, including a central processing unit (CPU), a network processor (NP), etc.; it can also be a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, and discrete hardware components.

[0194] like Figure 6 As shown, in another embodiment provided by the present invention, a computer-readable storage medium 601 is also provided, in which instructions are stored. When the computer-readable storage medium is run on a computer, the computer executes the discrete body structure topology optimization method based on the PnP-ADMM algorithm described in the above embodiment.

[0195] In another embodiment provided by the present invention, a computer program product containing instructions is also provided, which, when executed on a computer, enables the computer to execute the discrete body structure topology optimization method based on the PnP-ADMM algorithm described in the above embodiment.

[0196] In the above embodiments, all or part of the embodiments can be implemented by software, hardware, firmware, or any combination thereof. When implemented using software, all or part of the embodiments can be implemented in the form of a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of the present invention are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another computer-readable storage medium. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via a wired (e.g., coaxial cable, optical fiber, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) method. The computer-readable storage medium can be any available medium that can be accessed by a computer or a data storage device such as a server or data center that includes one or more available media. The available medium can be a magnetic medium (e.g., a floppy disk, a hard disk, a tape), an optical medium (e.g., a DVD), or a semiconductor medium (e.g., a solid-state drive (SSD)).

[0197] It should be noted that, in this document, relational terms such as first and second, etc., are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply the existence of any such actual relationship or order between these entities or operations. Moreover, the terms "comprises," "comprising," or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article, or device comprising a series of elements includes not only those elements, but also other elements not explicitly listed, or elements inherent to such process, method, article, or device. In the absence of further limitations, an element defined by the phrase "comprising a ..." does not exclude the presence of other identical elements in the process, method, article, or device comprising the element.

[0198] Each embodiment in this specification is described in a related manner. Similar parts between the various embodiments can be referred to in conjunction with each other. Each embodiment focuses on the differences between the other embodiments. In particular, the system embodiment is generally similar to the method embodiment, so the description is relatively simple. For related parts, refer to the description of the method embodiment.

[0199] The above description is only a preferred embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention are included in the scope of protection of the present invention.

Claims

1. A discrete body structure topology optimization method based on the PnP-ADMM algorithm, characterized in that: include: Determine the design domain of discrete body structures; The design domain is discretized into a finite element grid using a finite element method; A topology optimization model was established with volume and discrete density as constraints and flexibility minimization as the objective function; The topology optimization model is solved using the PnP-ADMM algorithm to obtain the optimal topology structure; The step of using the PnP-ADMM algorithm to solve the topology optimization model to obtain the optimal topology structure includes: Converting the topology optimization model into a Lagrangian function; The PnP-ADMM algorithm is used to solve the Lagrangian function; Performing iterative calculations and outputting the optimal topological structure when the volume and the discrete density meet convergence conditions; The step of converting the topology optimization model into a Lagrangian function comprises: adding weights, penalty factors, and dual variables to the objective function, the volume, and the discrete density, respectively, and converting the topology optimization model into the Lagrangian function; the Lagrangian function includes sub-variables corresponding to the objective function, the volume, and the discrete density, respectively; The step of solving the Lagrangian function using the PnP-ADMM algorithm includes: Based on the PnP-ADMM solution framework, the cyclic iterative relationship between the sub-variables of the objective function, the sub-variables of the volume, the sub-variables of the discrete density and the discrete density is derived respectively; The step of performing iterative calculation and outputting the optimal topological structure when the volume and the discrete density meet convergence conditions includes: Performing cyclic iteration using the cyclic iteration relationship until a convergence condition of the discrete density is satisfied; A movement restriction strategy is executed on the volume until a convergence condition of the volume is satisfied, and the optimal topology structure is output.

2. The method according to claim 1, characterized in that The step of performing cyclic iteration using the cyclic iteration relation until the convergence condition of the discrete density is satisfied comprises: Performing cyclic iteration using the cyclic iteration relationship to determine whether the variation of the discrete density is lower than a preset first threshold; If the variation of the discrete density is lower than a preset first threshold, it is determined that a convergence condition of the discrete density is satisfied.

3. The method according to claim 1, characterized in that The step of executing a movement restriction strategy on the volume until a convergence condition of the volume is satisfied and outputting the optimal topological structure comprises: cyclically reducing the volume according to a preset reduction factor and determining whether the volume fraction is lower than a preset second threshold; If the volume fraction is lower than a preset second threshold, it is determined that the convergence condition of the volume is met, and the optimal topological structure is output.

4. A discrete body structure topology optimization device based on the PnP-ADMM algorithm, characterized in that: include: A determination module is used to determine the design domain of the discrete body structure; A discretization module, configured to discretize the design domain into a finite element grid using a finite element method; Model building module, used to build topology optimization models using volume and discrete density as constraints and flexibility minimization as the objective function; A solution module, configured to solve the topology optimization model using a PnP-ADMM algorithm to obtain an optimal topology structure; The solution module includes: A conversion submodule, used to convert the topology optimization model into a Lagrangian function; A solution submodule, for solving the Lagrangian function using a PnP-ADMM algorithm; an output submodule, configured to perform iterative calculation and output the optimal topological structure when the volume and the discrete density meet convergence conditions; The transformation submodule comprises: a conversion unit, configured to add weights, penalty factors, and dual variables to the objective function, the volume, and the discrete density, respectively, to convert the topology optimization model into the Lagrangian function; the Lagrangian function includes subvariables corresponding to the objective function, the volume, and the discrete density, respectively; The solution submodule includes: A solving unit, configured to derive, based on a PnP-ADMM solving framework, cyclic iterative relationships between the subvariables of the objective function, the subvariables of the volume, the subvariables of the discrete density, and the discrete density; The output submodule includes: an iterative unit, configured to perform cyclic iteration using the cyclic iterative relation until a convergence condition of the discrete density is satisfied; The movement restriction unit is used to execute a movement restriction strategy on the volume until a convergence condition of the volume is satisfied, and output the optimal topological structure.

5. An electronic device, characterized in that: comprising a processor, a communication interface, a memory and a communication bus, wherein the processor, the communication interface and the memory communicate with each other via the communication bus; The memory is used to store computer programs; The processor is used to implement the discrete body structure topology optimization method based on the PnP-ADMM algorithm as described in any one of claims 1 to 3 when executing the program stored in the memory.

6. A computer-readable medium having instructions stored thereon, which, when executed by one or more processors, causes the processors to execute the discrete body structure topology optimization method based on the PnP-ADMM algorithm as described in any one of claims 1 to 3.

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