Frame structure optimization method and system based on SIMP-PLSM fusion method

Abstract

The invention relates to the technical field of vehicle frame structure optimization, and discloses a vehicle frame structure optimization method and system based on an SIMP-PLSM fusion method, and the method comprises the steps: building a vehicle frame geometric model, and defining a design domain of the vehicle frame geometric model and a plurality of preset first boundary conditions under different working conditions; topological optimization software is adopted to carry out topological optimization calculation on the geometric model of the vehicle frame under each working condition by utilizing an SIMP-PLSM fusion method, and a first topological optimization model under each working condition is obtained; carrying out rigidity analysis on the first topological optimization model under each working condition by adopting finite element analysis software, and obtaining a weight value of each working condition according to a rigidity analysis result; and performing weighted average processing on the topological optimization target of each working condition by adopting topological optimization software according to the weight value of each working condition, and performing topological optimization on the geometric model of the frame again by utilizing an SIMP-PLSM fusion method to obtain a topological optimized frame model under multiple working conditions. The optimization efficiency is high, the optimization result is good, and the manufacturability and practicability of the optimized structure are high.

Description

Technical Field

[0001] The present invention relates to the technical field of frame structure optimization, and particularly to a frame structure optimization method and system based on the SIMP-PLSM fusion method. Background Art

[0002] With the rapid development of social economy, the automotive industry is gradually moving towards lightweight and energy-saving directions. Making the vehicle lighter while ensuring structural stiffness can effectively reduce energy consumption. Relevant research shows that if the vehicle's total mass is reduced by 10%, the fuel efficiency can be increased by 6% - 8%. Among them, in order to reduce costs, the total mass limit of road transport semi-trailers also urgently needs to be reduced, so it is necessary to optimize the structure of this type of vehicle. As the main load-bearing component of the semi-trailer, the frame accounts for a large proportion of the vehicle's total mass. Lightweight design of the frame can effectively reduce energy consumption and costs. Among various vehicle lightweight technologies, topology optimization is undoubtedly one of the key technologies. However, there are some defects in various current topology optimization methods. The variable density method SIMP (Solid Isotropic Material with Penalization) discretizes the continuum through finite elements, and the final obtained topological configuration consists of elements with different densities. There are discontinuities between the boundaries of the elements, making the structure boundary appear serrated and the manufacturability poor. At the same time, to avoid the checkerboard phenomenon in the optimization result, density filtering technology needs to be adopted, introducing a large number of gray-scale elements, and it is impossible to obtain a clear topological structure with only 0 or 1. The final obtained result still requires a large amount of post-processing; moreover, the boundary of the optimization result is not clear and the manufacturability is poor. The parameterized level set method PLSM (Parameterized Level Set Method) can obtain a clear boundary, but the convergence speed is slow. Secondly, in practical engineering applications, there is only one type of frame, and the topological optimization result under a single working condition is difficult to meet the requirements of both the bending stiffness and torsional stiffness of the frame at the same time.

[0003] Therefore, there is an urgent need for a frame structure optimization method and system based on the SIMP-PLSM fusion method to solve the above problems. Summary of the Invention

[0004] Based on the above, the purpose of the present invention is to provide a frame structure optimization method and system based on the SIMP-PLSM fusion method, with high optimization efficiency, good optimization results, and strong manufacturability and practicability of the optimized structure.

[0005] To achieve the above object, the present invention adopts the following technical solutions:

[0006] A frame structure optimization method based on the SIMP-PLSM fusion method, comprising:

[0007] Establish a frame geometric model, and define the design domain of the frame geometric model and the first boundary conditions under multiple preset different working conditions;

[0008] Use topology optimization software to perform topology optimization calculations on the frame geometric model under each working condition by using the SIMP-PLSM fusion method to obtain the first topology optimization model under each working condition;

[0009] Use finite element analysis software to perform stiffness analysis on the first topology optimization model under each working condition, and obtain the weight value of each working condition according to the stiffness analysis results;

[0010] Use the topology optimization software to perform weighted average processing on the topology optimization objectives of each working condition according to the weight value of each working condition, and use the SIMP-PLSM fusion method to perform secondary topology optimization on the frame geometric model to obtain a frame model with topology optimization under multiple working conditions;

[0011] Regularize the frame model according to the production process requirements to obtain the final optimized frame model.

[0012] As a preferred solution of a frame structure optimization method based on the SIMP-PLSM fusion method, performing topology optimization calculations on the frame geometric model under each working condition by using the SIMP-PLSM fusion method includes:

[0013] Perform primary topology optimization on the frame geometric model by using the SIMP topology optimization method, set the sensitivity filtering radius, penalty factor, and retained volume fraction of the design domain as the second boundary conditions in the topology optimization software, and perform iterative calculations with the minimum structural compliance as the objective function to obtain an optimized force transmission path model. There are n units in the force transmission path model, each unit contains density information, and the unit density is ρ n ;

[0014] Convert the unit density ρ n into the node density ρ i available for the PLSM topology optimization method to obtain the initial input level set function of the PLSM topology optimization method;

[0015] Use the PLSM topology optimization method to perform secondary topology optimization on the frame geometric model after primary topology optimization, and set the minimum density sensitivity n min , the maximum expansion coefficient |α i | max in the topology optimization software, and the steepness coefficient μ. With the minimum structural compliance as the objective function and the volume constraint as the constraint condition, iterate to calculate the force transmission path model of the PLSM topology optimization method to obtain the first topology optimization model.

[0016] As an optimal solution of a frame structure optimization method based on the SIMP-PLSM fusion method, according to the following formula (1), the element density ρ n is transformed into the node density ρ available for the PLSM topology optimization method i :

[0017]

[0018] where M represents the number of elements directly connected to node i;

[0019] The obtained node density value is used as the initial input of the parametric level set function in the PLSM topology optimization method to obtain the level set function describing the structure boundary:

[0020]

[0021] where N is the number of nodes, is the basis function used in the PLSM topology optimization method, and α i (t) represents the expansion coefficient corresponding to the basis function at x at time t i ;

[0022] The level set function is shifted down by ξ until there is a situation where the level set function value is less than 0 to obtain the initial input level set function of the PLSM topology optimization method:

[0023] Φ(t 0 ) = Aα(t) = {ρ 1 - ξ... ρ N - ξ} T (3)

[0024] where,

[0025]

[0026] α(t) = {α 1 (t)... α N (t)} T (5)

[0027] where A is the basis function matrix composed of basis function values;

[0028] Under the fixed grid, all elements in A are constant values, the matrix A is invertible, and the initial value of the expansion coefficient can be calculated according to the following formula:

[0029] α(t 0 ) = A -1 {ρ 1 - ξ... ρ N - ξ} T (6)

[0030] As an optimal solution of a frame structure optimization method based on the SIMP-PLSM fusion method, the element density ρ n is converted into the node density ρ available for the PLSM topology optimization method i After that, it further includes using the bilateral smoothing method to perform density smoothing on the node density ρ i :

[0031] The smoothed density value

[0032]

[0033] where W p is the normalization factor:

[0034]

[0035] In the formula, ρ i is the density value of the i-th neighboring node; d pi is the spatial distance between node p and node i; σ s is the standard deviation controlling the influence of the spatial distance, and σ r determines the intensity of spatial smoothing;

[0036] Substitute the smoothed density value into Equation (3).

[0037] As an optimal solution of a frame structure optimization method based on the SIMP-PLSM fusion method, using the SIMP-PLSM fusion method to perform topology optimization calculation on the frame geometric model under each working condition further includes:

[0038] Using the Gaussian function as the basis function of the PLSM topology optimization method and restricting the influence range of the Gaussian function on a single node:

[0039]

[0040] where r i is the Euclidean distance between two coordinate points in space:

[0041]

[0042] In the formula, c is the bandwidth coefficient of the Gaussian function, and d m represents the influence range of the basis function at the control point (xi, y i );

[0043] As an optimal solution of a frame structure optimization method based on the SIMP-PLSM fusion method, after establishing the initial input level set function, using the PLSM method to perform secondary topology optimization on the frame geometric model includes:

[0044] The implicit expression of the horizontal input set function is converted into an explicit boundary by using the Heaviside function:

[0045]

[0046] where μ is the coefficient that controls the steepness of the Heaviside function;

[0047] The relationship between the level set function value and the node density is:

[0048] ρ(Φ) = ρ min +(ρ max -ρ min )·H(Φ)(12)

[0049] where ρ min and ρ max represent the lower and upper limits of the relative density of the material, respectively. Take ρ min = 0.01 and ρ max = 1;

[0050] The PLSM topology optimization method uses sensitivity-driven iterative calculation of design variables:

[0051] Calculation of the sensitivity of the objective function:

[0052]

[0053] Calculation of the sensitivity of the constraint conditions:

[0054]

[0055] where:

[0056]

[0057]

[0058]

[0059]

[0060] where C is the structural compliance, G is the volume constraint, V 0 is the total volume of the initial structure, and η is the reserved volume fraction set for optimization;

[0061] In a small space near the boundary, the level set function value of the node is linearly approximated as:

[0062]

[0063] Wherein, L is the distance from the node to the structural boundary, and |▽Φ| is the gradient of the level set function at the structural boundary;

[0064] The maximum gradient of the level set function at the structural boundary is:

[0065]

[0066] Wherein D is the structural dimension and c is the Gaussian function bandwidth coefficient;

[0067] According to Equation (19) and Equation (20), the maximum level set function value near the boundary is obtained Thus, the partial derivative n of the density function corresponding to the maximum level set function value is obtained min , and substitute n min into Equation (16) to calculate the μ value.

[0068] As an optimized scheme of a frame structure optimization method based on the SIMP-PLSM fusion method, the stiffness analysis of the first topology optimization model under each working condition includes:

[0069] Compare the influence degree between every two working conditions to obtain the importance ratio of every two working conditions. The judgment matrix M composed of the importance ratios is:

[0070]

[0071] Wherein, a ij represents the importance ratio of the i-th working condition and the j-th working condition, and m represents the number of working conditions;

[0072] Calculate the eigenvector of the judgment matrix M, and each element in the eigenvector is the weight value of each working condition.

[0073] As an optimized scheme of a frame structure optimization method based on the SIMP-PLSM fusion method, after obtaining the judgment matrix M, it also includes judging the consistency of the judgment matrix M:

[0074]

[0075] In the formula, λ max is the maximum eigenvalue of the judgment matrix, and m is the number of working conditions;

[0076] The consistency ratio of judgment matrices of different orders is:

[0077]

[0078] Wherein, RI is the random consistency index, which is determined according to the number of working conditions;

[0079] When the CR value is less than 0.1, the judgment matrix meets the consistency requirement.

[0080] As a preferred solution of a frame structure optimization method based on the SIMP-PLSM fusion method, after obtaining the final optimized frame model, it further includes:

[0081] Using the finite element software to perform simulation calculations on the final optimized frame model under each working condition, obtaining the stress distribution of the final optimized frame model under each working condition, comparing the stress distribution uniformity and peak values of the frame geometric model and the final optimized frame model, and verifying the performance advantages and disadvantages of the final optimized frame model.

[0082] A frame structure optimization system based on the SIMP-PLSM fusion method includes:

[0083] A model establishment module, used to establish a frame geometric model and define the design domain of the frame geometric model and the first boundary conditions under multiple preset different working conditions;

[0084] A first topology optimization module, used to perform topology optimization calculations on the frame geometric model under each working condition by using the SIMP-PLSM fusion method with topology optimization software, and obtaining the first topology optimization model under each working condition;

[0085] A force analysis module, used to perform stiffness analysis on the first topology optimization model under each working condition, and obtaining the weight value of each working condition according to the stiffness analysis result;

[0086] A second topology optimization module, used to perform weighted average processing on the topology optimization objectives of each working condition according to the weight value of each working condition, and performing re-topology optimization on the frame geometric model by using the SIMP-PLSM fusion method to obtain a frame model after topology optimization under multiple working conditions. As a preferred solution,

[0087] The beneficial effects of the present invention are:

[0088] The present invention provides a frame structure optimization method based on the SIMP-PLSM fusion method, which performs structural optimization on the frame through the SIMP-PLSM fusion method, realizes the lightweight of the frame on the premise of ensuring the frame stiffness, has strong manufacturability, and compared with the traditional single topology optimization method, has better optimization effect and higher optimization efficiency; at the same time, combining multiple working conditions to perform structural optimization on the frame enables the optimized frame to simultaneously meet the requirements of the bending stiffness and torsional stiffness of the frame, and has better practicability and reliability.

[0089] The present invention also provides a frame structure optimization system based on the SIMP-PLSM fusion method, which has a better optimization effect on the frame, can realize the lightweight of the frame while ensuring the frame stiffness, and guarantees the use reliability of the vehicle. Description of the Drawings

[0090] To more clearly illustrate the technical solutions in the embodiments of the present invention, the following will briefly introduce the drawings required for the description in the embodiments of the present invention. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained according to the content of the embodiments of the present invention and these drawings.

[0091] Figure 1 is a flowchart of the frame structure optimization method based on the SIMP-PLSM fusion method provided by the embodiments of the present invention;

[0092] Figure 2 is a schematic diagram of the principle of the frame structure optimization method based on the SIMP-PLSM fusion method provided by the embodiments of the present invention;

[0093] Figure 3 is a density function curve graph provided by the embodiments of the present invention;

[0094] Figure 4 is a partial derivative curve graph of the density function provided by the embodiments of the present invention;

[0095] Figure 5 is a schematic diagram of the gooseneck semi-trailer frame structure provided by the embodiments of the present invention;

[0096] Figure 6 is a schematic diagram of the mesh division of the frame geometric model provided by the embodiments of the present invention;

[0097] Figure 7 is a result graph of the frame optimized by the SIMP topology optimization method under the full-load flat road condition provided by the embodiments of the present invention;

[0098] Figure 8 is a result graph of the frame optimized by the SIMP-PLSM fusion method under the full-load flat road condition provided by the embodiments of the present invention;

[0099] Figure 9 is a result graph of the frame optimized by the SIMP topology optimization method under the braking condition provided by the embodiments of the present invention;

[0100] Figure 10 is a result graph of the frame optimized by the SIMP-PLSM fusion method under the braking condition provided by the embodiments of the present invention;

[0101] Figure 11 is a result graph of the frame optimized by the SIMP topology optimization method under the turning condition provided by the embodiments of the present invention;

[0102] Figure 12 is a result graph of the frame optimized by the SIMP-PLSM fusion method under the turning condition provided by the embodiments of the present invention;

[0103] Figure 13 It is the result diagram of the frame optimized by the SIMP topology optimization method under the full-load rough working condition provided by the embodiment of the present invention;

[0104] Figure 14 It is the result diagram of the frame optimized by the SIMP-PLSM fusion method under the full-load rough working condition provided by the embodiment of the present invention;

[0105] Figure 15 It is the schematic diagram of the frame model after topology optimization under multiple working conditions provided by the embodiment of the present invention;

[0106] Figure 16 It is the schematic diagram of the final optimized frame model after the regular design of the frame model after topology optimization under multiple working conditions provided by the embodiment of the present invention;

[0107] Figure 17 It is the stress distribution diagram of the new frame under the full-load flat road working condition provided by the embodiment of the present invention;

[0108] Figure 18 It is the stress distribution diagram of the new frame under the braking working condition provided by the embodiment of the present invention;

[0109] Figure 19 It is the stress distribution diagram of the new frame under the turning working condition provided by the embodiment of the present invention;

[0110] Figure 20 It is the stress distribution diagram of the new frame under the full-load rough working condition provided by the embodiment of the present invention;

[0111] Figure 21 It is the displacement nephogram of the bending stiffness of the new frame provided by the embodiment of the present invention;

[0112] Figure 22 It is the displacement nephogram of the torsional stiffness of the new frame provided by the embodiment of the present invention;

[0113] Figure 23 It is the 7th order vibration mode diagram of the new frame provided by the embodiment of the present invention;

[0114] Figure 24 It is the 8th order vibration mode diagram of the new frame provided by the embodiment of the present invention;

[0115] Figure 25 It is the 9th order vibration mode diagram of the new frame provided by the embodiment of the present invention;

[0116] Figure 26 It is the 10th order vibration mode diagram of the new frame provided by the embodiment of the present invention;

[0117] Figure 27 It is the 11th order vibration mode diagram of the new frame provided by the embodiment of the present invention;

[0118] Figure 28 It is the 12th order vibration mode diagram of the new vehicle frame provided by the embodiment of the present invention.

[0119] In the figure:

[0120] 1. Side support; 2. Cross beam; 3. Rear frame; 4. Front frame. Specific embodiments

[0121] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It can be understood that the specific embodiments described herein are only used to explain the present invention, rather than limiting the present invention. In addition, it should be noted that for the convenience of description, only the parts related to the present invention are shown in the drawings, rather than all the structures.

[0122] As Figure 1 shown, this embodiment provides a frame structure optimization method based on the SIMP-PLSM fusion method for optimizing the structure of the frame, such as optimizing the structure of the frame of a semi-trailer. The frame structure optimization method based on the SIMP-PLSM fusion method includes the following steps:

[0123] S100: Establish a frame geometric model, and define the design domain of the frame geometric model and the first boundary conditions under multiple preset different working conditions;

[0124] Among them, the four working conditions of the frame include full-load flat road condition, braking condition, turning condition and full-load rough condition.

[0125] Specifically, establish a frame geometric model according to the frame entity structure to be optimized. For example, take the gooseneck semi-trailer frame as the optimization object, then perform mesh division on the frame geometric model, and use finite element software, such as ANSYS, to simulate and calculate the frame geometric model under each working condition to obtain the stress and deformation distributions of the frame geometric model under each working condition, and define the design domain of the frame geometric model according to the stress and deformation distributions. For example, define the cross beam of the frame as the design domain, that is, in the GMSH software, use the "PhysicalVolume" command to define the cross beam part as the "Design" design domain. The subsequent topology optimization is to optimize the structure of the cross beam in the design domain part.

[0126] Exemplarily, when searching for the design domain of the frame geometric model, a finite element software is used to perform mechanical analysis on the frame geometric model to obtain the stress and deformation distribution nephograms of the frame geometric model under each working condition. From the stress and deformation distribution nephograms, it can be known where the frame has large deformation and where it has small deformation. The places with small deformation are used as the design domain. For example, the deformation of the side support of the frame is large, and the maximum deformation of the side support reaches 8.5207 mm under the turning working condition, which is close to the safety limit. Reducing the weight by drilling holes in the side support will definitely lead to an increase in deformation. Therefore, considering using the crossbeam with relatively small stress and deformation as the optimization object to avoid the situation where the stress meets the requirements but the deformation exceeds the safety limit in the final optimization result, that is, taking the crossbeam as the design domain.

[0127] Further, after defining the design domain, in the GMSH software, reasonable material properties are set, such as the material properties shown in Table 1, and the first boundary conditions under four working conditions are defined respectively. The fixed constraint surface is set to "Fixed", and the load application surface is set to "Traction". The specific magnitude and direction of the load are set in the parameter file. After defining the design domain and the first boundary conditions, tetrahedral elements are used to mesh the frame to generate an msh mesh file.

[0128] Table 1 Material property table

[0129]

[0130] The msh mesh file output by GMSH will classify the meshes according to the content defined for each component, which is convenient for reading and setting the finite element model in MATLAB. For the contact positions of each part of the frame, the meshes generated by GMSH will automatically generate co-nodes at these positions, which can effectively simulate the force transmission and deformation between welded parts without the need to define additional contact relationships. Importing the generated msh mesh file into MATLAB can obtain a complete finite element model of the frame.

[0131] S200: Use a topology optimization software to perform topology optimization calculations on the frame geometric model under each working condition using the SIMP-PLSM fusion method to obtain the first topology optimization model under each working condition; that is, as Figure 2 shown, after setting the optimization parameters, single-condition topology optimization is performed; among them, setting the optimization parameters includes setting the geometric parameters, material properties, load conditions, constraint conditions of the frame geometric model, and the setting of design variables in the topology optimization method.

[0132] Specifically, import the msh mesh file output by GMSH into MATLAB for topology optimization. To quickly obtain the force transmission path, the convergence tolerance in the initial optimization stage of SIMP is set to 0.01, and the convergence tolerance in the subsequent secondary topology optimization is set to 0.001; in the SIMP-PLSM fusion method, the minimum density sensitivity n is setmin , maximum expansion coefficient |α i | max , steepness coefficient μ. MATLAB loads the model with the first boundary conditions under four working conditions respectively to obtain the first topology optimization model under each working condition.

[0133] Specifically, in step S200:

[0134] S201: Use the SIMP topology optimization method to perform a first topology optimization on the frame geometric model. Set the sensitivity filtering radius, penalty factor, and reserved volume fraction of the design domain as the second boundary condition in the topology optimization software. Iteratively calculate with the minimum structural compliance as the objective function to obtain the optimized force transmission path model. The force transmission path model has n elements, and each element contains density information, and the element density is ρ n ;

[0135] Among them, the SIMP topology optimization method is to find the optimal material density distribution under the set volume constraint to minimize the overall compliance of the structure. The corresponding mathematical model of SIMP topology optimization can be described as:

[0136] Find: Q=(q 1 ,...,q i ,...q n ) T

[0137]

[0138] s.t.: F = KU

[0139]

[0140] 0 < q min ≤ x i ≤ q max ≤ 1

[0141] Among them, Q is the design variable in the SIMP method, q i contains the relative density values of each element i, representing the relative density value of element i, q max and q max respectively represent the upper and lower limits of the relative density value setting. C is the total compliance value of the structure, F represents the external load, U represents the nodal displacement matrix in the optimization process, K represents the structural stiffness matrix, which is a symmetric matrix, V represents the total volume of the structure in the optimization process, V 0 is the total volume of the initial structure, N represents the total number of elements divided in the structural design domain, u i represents the displacement vector of element i, k i is the stiffness matrix of element i, k 0represents the stiffness matrix of the entity unit, v i represents the volume fraction of element i, η is the reserved volume fraction set by optimization, and p represents the penalty factor.

[0142] The SIMP method function is controlled by the penalty factor, sensitivity filtering radius, and volume constraint. Exemplarily, the filtering radius is set to 2 - 3 times the mesh size, for example, set to 2.4 times, the penalty factor is set to 3, and the reserved volume fraction of the design domain is set to 0.5. The continuum is discretized by finite elements through the SIMP topology optimization method, and the finally obtained topological configuration consists of elements with different densities, that is, the n elements in the force transmission path model optimized by the SIMP topology optimization method all contain density information ρ n 。

[0143] S202: Convert the element density ρ n into the node density ρ i usable in the PLSM topology optimization method to obtain the initial input level set function of the PLSM topology optimization method;

[0144] Specifically, in step S202:

[0145] S2021: According to the following formula (1), convert the element density ρ n into the node density ρ i :

[0146]

[0147] In the formula, M represents the number of elements directly connected to node i;

[0148] In this embodiment, the element density is converted into the node density by inserting pseudocode:

[0149] Initialize the node density and weight counter

[0150] node_density = [0.0] * number_of_nodes

[0151] node_weight = [0] * number_of_nodes

[0152] Traverse the elements to update the cumulative density value and weight value of the nodes

[0153] for element in elements:

[0154] density = element_density[element]

[0155] nodes_in_element = element_connectivity[element]

[0156] for node in nodes_in_element:

[0157] node_density[node] += density

[0158] node_weight[node] += 1

[0159] Calculate the average density of each node

[0160] for node in range(number_of_nodes):

[0161] If node_weight[node] > 0:

[0162] node_density[node] / = node_weight[node]

[0163] Where elements is the information of all elements, each element has a density value, nodes is the information of all nodes, element_connectivity is which nodes each element is connected to, element_density is the density of each element, and node_density is the density of each node.

[0164] S2022: Use the obtained node density values as the initial input of the parameterized level set function in the PLSM topology optimization method to obtain the level set function describing the structure boundary:

[0165]

[0166] In the formula, N is the number of nodes, is the basis function used in the PLSM topology optimization method, and α i (t) represents the expansion coefficient corresponding to the basis function at x at time t i ;

[0167] Where the PLSM topology optimization method implicitly represents the structure boundary through the level set function, and the specific expression is:

[0168]

[0169] In the formula, x is the node coordinate in the structure design domain, Ω is the design domain of the structure, D is the hole domain, is the boundary between the solid region and the hole region, Points within the structural entity region Points on the structural boundary Points within the structural hole region

[0170] Since the relative densities of the elements obtained by the SIMP topology optimization method are all greater than 0, and the level set functions composed of node densities are also all non - negative numbers. According to the definition of the level set method in Equation (25), there is no hole region in the initial level set structure expressed by Equation (2) at this time. Therefore, the initial level set function needs to be "translated" to ensure that the force - transmission path optimized by the SIMP topology optimization method can be correctly extracted. After "translation", the volume of the solid domain with node density greater than 0 satisfies the set volume fraction.

[0171] Shift the level set function downward by ξ until there is a situation where the level set function value is less than 0, and obtain the initial input level set function of the PLSM topology optimization method:

[0172] Φ(t 0 ) = Aα(t) = {ρ 1 - ξ…ρ N - ξ} T (3)

[0173] Where

[0174]

[0175] α(t) = {α 1 (t) … α N (t)} T (5)

[0176] In the formula, A is the basis function matrix composed of basis function values;

[0177] In this embodiment, a Gaussian function is used as the basis function of the PLSM topology optimization method, and the influence range of the Gaussian function on a single node is restricted:

[0178]

[0179] Where r i is the Euclidean distance between two coordinate points in space:

[0180]

[0181] In the formula, x is the point to be calculated during the optimization process, x i is the structural boundary point, c is the bandwidth coefficient of the Gaussian function, and d m represents the influence range of the basis function at the control point (xi, y i ) and is usually set to 2 - 4 times the grid size.

[0182] By restricting the influence range of the Gaussian function on a single node, restricting the influence range of the Gaussian function can effectively reduce the pseudo-oscillation phenomenon in the numerical solution. When the influence range is restricted, the numerical calculation is only performed in a local area, which is beneficial to reducing the computational amount. Moreover, restricting the influence range can better match the actual physical process, avoid the distortion of physical meaning caused by over-smoothing, and ensure the physical interpretability of the results.

[0183] Under the fixed grid, all elements in A are constant values, the matrix A is invertible, and the initial value of the expansion coefficient can be calculated according to the following formula:

[0184] α(t 0 )=A- 1 {ρ 1 -ξ... ρ N -ξ} T (6)

[0185] In this embodiment, the moving distance ξ of the level set function can be determined by the bisection method, and the corresponding pseudocode is as follows:

[0186] Initialize the upper and lower limits of the moving distance

[0187] deffind_ξ(matrix,rows,cols):

[0188] low=0

[0189] high=1

[0190] Define a function to calculate the number of elements greater than 0 in the matrix obtained by subtracting the threshold from the original node density matrix

[0191] defcount_positive_nodes(matrix,rows,cols,ξ):

[0192] count=0

[0193] foriin range(rows):

[0194] forj in range(cols):

[0195] ifmatrix[i][j]-threshold>

[0196] 0:count+=1

[0197] return count

[0198] Define the target retention volume fraction

[0199] target_count=rows*cols*η

[0200] Calculating the moving distance by the bisection method

[0201] while high - low > 1e - 6:

[0202] mid = (low + high) / 2

[0203] count = count_positive_nodes(matrix, rows, cols, mid)

[0204] if count > target_count:

[0205] low = mid

[0206] else:

[0207] high = mid

[0208] return mid

[0209] Among them, matrix is the matrix containing all node density information, rows is the number of rows of the matrix, and cols is the number of columns of the matrix. Since the node density is in the range of 0 to 1, the initial upper and lower limits of ξ are set to 1 and 0.

[0210] After step S202, the force transmission path optimized by the SIMP topology optimization method is transformed into the initial input structure of the PLSM topology optimization method. Since the force transmission path is already close to the optimal topological configuration of the structure at this time, the obtained initial input structure can not only ensure the stability of the optimization process, but also effectively reduce the time required for the PLSM topology optimization method to find the optimal topological structure during the optimization process, significantly improving the optimization efficiency of the PLSM topology optimization method.

[0211] Preferably, between step S2021 and step S2022, it further includes the step of:

[0212] S2023: Converting the element density ρ n into the node density ρ available for the PLSM topology optimization method i After that, it further includes performing density smoothing on the node density ρ i using the bilateral smoothing method:

[0213] The smoothed density value

[0214]

[0215] Among them, W p is the normalization factor:

[0216]

[0217] In the formula, ρ i is the density value of the i-th neighboring node; d pi is the spatial distance between node p and node i; σ s is the standard deviation that controls the influence of the spatial distance, which is usually related to the size of the grid cell and can be selected as 1-2 times the size of the grid cell. For example, when the cell size is 1, σ s takes 1.5, and σ r determines the intensity of spatial smoothing. Usually, based on the requirements of density change, since the range of material density is [0,1], 0.1-0.3 can be selected. For example, take 0.2;

[0218] Substitute the smoothed density value into Equation (3).

[0219] The bilateral smoothing method takes into account both the spatial distance and the difference in pixel values (or density values) to ensure that the edges are not blurred. Its core idea is to calculate the smoothed value of each point through weighted averaging, where the weights depend not only on the distance but also on the similarity of the density values. After obtaining the node density information through the equal-density contour method, since important details or small result features may be lost during the averaging process, the bilateral smoothing method is used to perform smoothing by combining spatial and attribute information, which can retain important edges and details, thus making the topology optimization result more accurate.

[0220] S203: Use the PLSM topology optimization method to perform secondary topology optimization on the frame geometry model after the first topology optimization. Set the minimum density sensitivity n min , the maximum expansion coefficient |α i | max , and the steepness coefficient μ in the topology optimization software. Take the minimum structural compliance as the objective function and the volume constraint as the constraint condition to iteratively calculate the force transmission path model of the PLSM topology optimization method to obtain the first topology optimization model.

[0221] After establishing the initial level set function, use the PLSM topology optimization method to further optimize the structure. During this process, the Heaviside function is used to project the initial input level set function in two-dimensional or three-dimensional space to obtain the geometric shape of the topological structure. The Heaviside function can convert the implicit expression of the initial input level set function into an explicit boundary:

[0222]

[0223] In the formula, μ is the coefficient that controls the steepness of the Heaviside function;

[0224] The empirical formula between the level set function value and the node density is:

[0225] ρ(Φ) = ρ min +(ρ max -ρ min )·H(Φ)(12)

[0226] In the formula, ρ min and ρ max respectively represent the lower and upper limits of the relative density of the material. To avoid the elastic modulus of the material in the hole area being 0 and making the assembled stiffness matrix singular, take ρ min = 0.01, ρ max = 1;

[0227] In this embodiment, the PLSM topology optimization method uses sensitivity-driven design variable iterative calculation, where the design variables are the minimum density sensitivity n min , the maximum value of the expansion coefficient |α i | max , and the steepness coefficient μ. The structure optimized by the SIMP topology optimization method is already close to the optimal topological configuration. In this case, the level set function only makes small changes within the boundary range, and the sensitivity calculation at this time can be simplified and approximately obtained through the chain derivative rule:

[0228] Sensitivity calculation of the objective function:

[0229]

[0230] Sensitivity calculation of the constraint condition:

[0231]

[0232] Among them:

[0233]

[0234]

[0235]

[0236]

[0237] In the formula, C is the structural compliance, G is the volume constraint, V 0 is the total volume of the initial structure, and η is the reserved volume fraction set for optimization;

[0238] It can be seen from formula (13) and formula (14) that both the sensitivity of the objective function and the sensitivity of the constraint condition contain the partial derivative of the node density with respect to the level set function. It can be seen from formula (11) and formula (12) that this partial derivative is controlled by the steepness coefficient μ, which directly affects the sensitivity information of PLSM. The density function curve is as Figure 2As shown. Set the value of μ to 1, and the partial derivative curve of the density function corresponding to Equation (16) is as Figure 3 shown. In the figure represents the maximum level set function value near the boundary, and n min represents the partial derivative of the density function corresponding to the maximum level set function value. From Figure 2 and Figure 3 it can be seen that when μ is set to a relatively large value, the density function is relatively steep, and the partial derivatives of the density function near the structural boundary all approach 0, causing the sensitivity information obtained by the chain rule of differentiation to fail and leading to the topological optimization falling into a local optimum; when μ is set to a relatively small value, the density change of the nodes near the structural boundary is gentle, slowing down the optimization convergence speed. Therefore, a reasonable μ needs to be set to ensure that both the steepness of the density function change and the optimization speed are reasonable, that is, the optimization boundary needs to be effectively controlled to ensure the stability and efficiency of the optimization process. To control the boundary, the allowable minimum partial derivative of the density function n min needs to be determined:

[0239] In a small space near the boundary, for example, within 1 - 3 grid cells near the boundary, the level set function value of the node is linearly approximated as:

[0240]

[0241] where L is the distance from the node to the structural boundary, and |▽Φ| is the gradient of the level set function at the structural boundary;

[0242] The maximum gradient of the level set function at the structural boundary is:

[0243]

[0244] where D is the structural dimension, which is a three-dimensional structure in this embodiment, that is, D is 3; the value range of |α i | max is usually between 0.1 and 5.0 to ensure the interface fineness and the stability of the numerical solution process. For example, |α i | max takes a value of 0.5; c is the Gaussian function bandwidth coefficient, and the bandwidth coefficient is selected according to the grid size, generally in the range of 0.1 - 2.0 times. For example, it takes 0.7 times. The larger the bandwidth coefficient, the greater the influence of the Gaussian function on the surrounding area of the center point, and at the same time, the smaller the difference between two adjacent points of the level set function, and thus the global gradient decreases, which will reduce the optimization efficiency of the PLSM method to a certain extent. The value of c is specifically set according to actual requirements.

[0245] According to Equation (19) and Equation (20), the maximum level set function value near the boundary is obtained Thus, the partial derivative of the density function corresponding to the maximum level set function value n min is obtained, and nmin Substitute into Equation (16) to calculate the value of μ. Obtain n min and the value of μ. When solving and calculating in the topology optimization software, set |α i | max 、n min and the value of μ. For example, take |α i | max value to be 0.5, n min value to be 0.5, and μ value to be 0.4725.

[0246] After performing topology optimization calculations on the frame geometric models under four working conditions through the SIMP-PLSM fusion method, the first topology optimization model under each working condition is obtained, that is, each frame under each working condition corresponds to an optimal topology optimization structure. To obtain the best optimization structure combining the four working conditions, the following steps are also carried out:

[0247] S300: Refer to Figure 1 and Figure 2 again, and use finite element analysis software to perform stiffness analysis on the first topology optimization model under each working condition, and obtain the weight value of each working condition according to the stiffness analysis results;

[0248] Among them, the stiffness analysis includes bending stiffness analysis and torsional stiffness analysis.

[0249] Specifically, step S300 includes the following steps:

[0250] S301: After regularizing and designing the first topology optimization model obtained under each working condition, import it into ANSYS to perform stiffness analysis on it, calculate the bending stiffness and torsional stiffness of the frame under each working condition, and according to the calculation results, sort the importance of each working condition in terms of the bending stiffness of the frame, and sort the importance of each working condition in terms of the torsional stiffness of the frame; Exemplarily, in terms of the bending stiffness of the frame, the importance of each working condition is: full load on flat road > braking > full load on rough road > turning, and in terms of the torsional stiffness of the frame, the importance of the four working conditions is: full load on flat road > braking > turning > full load on rough road.

[0251] S302: Compare the influence degrees of topology optimization on the frame stiffness under the four working conditions pairwise, obtain the importance ratio between every two working conditions, and to convert the decision matrix into a numerical matrix, give the initial importance reference definition between indicators, as shown in Table 2 below:

[0252] Table 2 Factor level table of importance reference definition between indicators

[0253]

[0254]

[0255] Among them, if the relative importance of i to j is between two of the above importance ratios, then a ij Correspondingly, they are 2, 4, 6, 8, 1 / 2, 1 / 4, 1 / 6, 1 / 8.

[0256] According to the sorting of the importance of the bending stiffness and torsional stiffness of the frame under each working condition and Table 2, construct the judgment matrix M composed of importance ratios:

[0257]

[0258] Among them, a ij represents the importance ratio of the i-th working condition to the j-th working condition, and m represents the number of working conditions;

[0259] By comparing two working conditions pairwise, the complexity of considering four working conditions simultaneously is avoided. Combining the judgment matrix to verify the importance relationship of each working condition eliminates the accidental error of the designer's subjective judgment.

[0260] S303: Calculate the eigenvector of the judgment matrix M, and each element in the eigenvector is the weight value of each working condition.

[0261] Preferably, after calculating the eigenvector of the judgment matrix M, perform normalization processing on it to obtain the weight values of each final working condition, so as to improve the data accuracy, thereby improving the accuracy and reliability of the final topology optimization result.

[0262] In this embodiment, before step S303, after obtaining the judgment matrix M, it also includes judging the consistency of the judgment matrix M:

[0263]

[0264] In the formula, λ max is the maximum eigenvalue of the judgment matrix, m is the number of working conditions, which is 4 in this embodiment;

[0265] The consistency ratio of judgment matrices of different orders is:

[0266]

[0267] In the formula, RI is the random consistency index, which is determined according to the number of working conditions and is obtained from Table 3:

[0268] Table 3 Reference values of the random consistency index RI

[0269]

[0270] That is, RI is 0.90. When the CR value is less than 0.1, the judgment matrix meets the consistency requirement.

[0271] S400: Using topology optimization software, according to the weight value of each working condition, the topology optimization objectives of each working condition are weighted and averaged, and the SIMP-PLSM fusion method is used to perform secondary topology optimization on the frame geometric model to obtain the frame model after topology optimization under multiple working conditions; that is, after determining the weight values of each working condition, multi-condition topology optimization is carried out.

[0272] In this embodiment, the linear weighted method is used to perform topology optimization on multiple working conditions. The linear weighted method linearly combines multiple objective functions into a comprehensive objective function:

[0273] The topology optimization objectives under the four working conditions are all to minimize the compliance of the frame structure. The dimensions of the objective functions are the same, and the linear weighted method can be used to solve the multi-condition topology optimization problem. The mathematical expression of its objective function is as follows:

[0274]

[0275] Among them, F represents the load of the structure; ω i is the weight coefficient; f is the overall volume retention rate of the optimized model; C represents the overall flexibility of the structure; U m represents the structural displacement under the mth loading condition; K represents the overall rigidity; V 0 and V * are the volumes of the model before and after optimization respectively; x min is the lower limit value of the relative density of the element, and x e is the relative density of the element.

[0276] When using the SIMP-PLSM fusion topology optimization method to perform multi-condition topology optimization on the frame geometric model, set the weight values of the four working conditions, and other parameter settings are the same as those for single-condition topology optimization. After iterative calculation, the frame model after topology optimization under multiple working conditions is obtained.

[0277] S500: Regularize the frame model according to the production process requirements to obtain the final optimized frame model.

[0278] The frame model obtained by topology optimization is difficult to be directly applied to actual production. Since the generated topology configuration has an irregular shape, directly machining the structure of the design domain according to the optimization results will greatly increase the manufacturing cost. At the same time, the sharp corners in the results are prone to stress concentration, which will reduce the structural safety. Therefore, it is necessary to re-model the frame according to the results. In actual engineering, circular holes, square holes, and oblong holes are mostly used for the blanking treatment of sheet metal parts. For the post-processing of the optimized frame, in this embodiment, the scheme of "more circular holes, fewer square holes and oblong holes" is adopted. At the same time, in order to avoid excessive stress concentration caused by the opening, the right angles of the square holes are changed to rounded corners.

[0279] Such as Figure 2As shown in the figure, in order to verify the effectiveness of the frame structure optimization method based on the SIMP-PLSM fusion method provided in this embodiment and the safety of the optimized frame under various working conditions, that is, to verify the rationality of the final optimized frame model, it includes:

[0280] S600: Use finite element software to perform simulation calculations on the final optimized frame model under each working condition to obtain the stress distribution of the final optimized frame model under each working condition. Compare the stress distribution uniformity and peak values of the frame geometric model and the final optimized frame model to verify the performance advantages and disadvantages of the final optimized frame model. That is, use finite element analysis software to perform static analysis on the final optimized frame model to obtain the stress distribution of the optimized frame, and compare the areas where the maximum stress occurs before and after optimization and the changes in the force structure of the entire vehicle. If the stress distribution in the design domain part of the optimized frame is more uniform and the stress peak value decreases, it means that the final optimized frame model is effective, and the optimization result can be output. That is, the final optimized frame model obtained in step S500 is the new frame. The optimized new frame improves durability and reliability to a certain extent, and at the same time, hole digging and material reduction improve fuel efficiency. If it is unreasonable, re-design the optimization parameters, repeat the above steps, and perform topology optimization again.

[0281] In this embodiment, the frame modal frequency is closely related to its mass and stiffness. When the stiffness and mass change, the modal frequency also changes. Obtain the vibration mode of the final optimized frame model through finite element analysis software, and compare the modal frequencies of each order of vibration modes before and after optimization. If the modal frequency of a certain order of vibration mode increases, it means that the final optimized frame model is effective and the safety performance of the entire vehicle has been improved. The optimized frame can better avoid the excitation frequency range of the road surface and the engine, reducing the risk of resonance.

[0282] Furthermore, in order to verify that the frame structure optimization method based on the SIMP-PLSM fusion method has better optimization effect than the traditional single SIMP method, it further includes:

[0283] Use the SIMP method integrated in ANSYS software to perform topology optimization on the frame geometric model under four working conditions. The penalty factor is set to 3, the filtering radius is set to 2.4 times the mesh size, and the retained volume fraction of the design domain is set to 0.5. Iteratively calculate the single method optimization models corresponding to the four working conditions with the minimum structural compliance as the objective function, and compare the result diagrams and weight reduction of the single method optimization model and the first topology optimization model under each working condition.

[0284] The following further illustrates the frame structure optimization method based on the SIMP-PLSM fusion method provided in this embodiment with examples:

[0285] As Figure 5As shown in the figure, the frame of the gooseneck semi-trailer is taken as the optimization object. The frame of the gooseneck semi-trailer includes a rear border 3, upper wing plates, lower wing plates, cross beams 2, a front border 4, side supports 1, and webs. The total length of the frame is 8610 mm, and the total mass is 1233.024 kg. The lengths of the front border and the rear border are both 2400 mm. The front and rear heights of the webs are 469 mm and 239 mm respectively. A frame geometric model is established according to the structure of the gooseneck semi-trailer frame;

[0286] As Figure 6 shown in the figure, the frame geometric model is meshed using tetrahedral elements, the cross beam is defined as the design domain, and the first boundary condition is defined;

[0287] The mesh model is imported into ANSYS and MATLAB respectively for optimization. ANSYS uses the integrated SIMP method for topology optimization, and the SIMP-PLSM fusion method is used for topology optimization in MATLAB. In both topology optimization methods, the penalty factor is set to 3, the filtering radius is set to 2.4 times the mesh size, the retained volume fraction of the design domain is set to 0.5. In the SIMP-PLSM fusion method, the minimum density sensitivity is set to 0.5, the maximum expansion coefficient is set to 0.5, the steepness coefficient is set to 0.4725, the convergence tolerance in the initial optimization stage of SIMP is set to 0.01, and the convergence tolerance in the subsequent secondary topology optimization is set to 0.001. The frame geometric model is loaded with the first boundary condition under four working conditions respectively, and the optimization effects of the two optimization methods on the frame are analyzed and compared:

[0288] Under the full-load flat road condition, the results obtained by using the SIMP method for topology optimization of the frame are as Figure 7 shown in the figure, and the results obtained by using the SIMP-PLSM fusion method for topology optimization are as Figure 8 shown in the figure. Compared with the SIMP method, the results obtained by the SIMP-PLSM fusion topology optimization method have no gray-scale elements in the structure and the boundaries are smooth. After the frame geometric model is optimized by the fusion topology optimization method, the weight is reduced by 1185.929 kg compared with 1233.024 kg, a reduction of 3.82%. After the frame geometric model is optimized by the SIMP method, the weight is reduced by 3.58%. Although the retained volume fractions set by the two methods are the same, the fusion optimization method introduces additional volume in the preprocessing stage, resulting in an increase in the original volume of the frame geometric model. The relative densities of these additional regions are set to 0 in the subsequent optimization, making the finally optimized removed volume slightly larger than that of the SIMP method.

[0289] Under the braking condition, the results obtained by using the SIMP method for topology optimization of the frame are as Figure 9 shown in the figure, and the results obtained by using the SIMP-PLSM fusion method for topology optimization are as Figure 10As shown in the figure. There are no small-sized structures in the topological configuration generated by the SIMP-PLSM fusion topology optimization method, and the continuity of the overall material distribution is better, which can effectively save the post-processing cost. After the fusion topology optimization method, the weight of the frame geometric model drops to 1184.927 kg, with a weight reduction of 3.9%. After optimizing the frame geometric model using the SIMP method, the weight reduction is 3.61%.

[0290] Under the turning condition, the results obtained by using the SIMP method for topology optimization of the frame are as Figure 11 shown, and the results obtained by using the SIMP-PLSM fusion method for topology optimization are as Figure 12 shown. Under the turning condition, the frame undergoes a certain degree of torsional deformation. As a component to resist torsional deformation, the equivalent stress distribution of the frame crossbeam is asymmetric, and the final result is significantly asymmetric. At the same time, there are no small-sized structures in the crossbeam holes obtained by the SIMP-PLSM fusion optimization method, which is convenient for production and processing. However, the SIMP method obtains many small-sized structures, and the hole-digging and material-removing scheme is complex, which will increase the manufacturing cost. There are no small-sized structures in the topological configuration generated by the SIMP-PLSM fusion topology optimization method, and the continuity of the overall material distribution is better, which can effectively save the post-processing cost. After the fusion topology optimization method, the weight of the frame geometric model drops to 1187.39 kg, with a weight reduction of 3.7%. The weight reduction of the optimized model obtained in ANSYS is 3.55%.

[0291] Under the full-load rough condition, the results obtained by using the SIMP method for topology optimization of the frame are as Figure 13 shown, and the results obtained by using the SIMP-PLSM fusion method for topology optimization are as Figure 14 shown. Under the full-load rough condition, the frame also undergoes a certain degree of torsional deformation. Different from the large deformation under the turning condition, at this time, the frame only generates a large torsional force at the suspended wheel, and the optimization result of the crossbeam at the suspended wheel is asymmetric, while the materials of the other crossbeams are basically symmetrically distributed. After the fusion topology optimization method, the weight of the frame geometric model drops by 48.05 kg, with a weight reduction of 3.9%. After optimizing the model using the SIMP method, the weight reduction is 3.63%.

[0292] The optimized models obtained by using the SIMP method and the SIMP-PLSM fusion method are imported into ANSYS after regular design for stiffness analysis, and the stiffness comparison of the frame before and after optimization is obtained as shown in Table 4 below:

[0293] Table 4 Stiffness Comparison of the Frame Before and After Optimization

[0294]

[0295] As can be seen from the above table, the SIMP-PLSM fusion method is slightly inferior to the SIMP method in terms of bending stiffness, but performs excellently under other working conditions. Since the bending stiffness of the frame is mainly affected by the strength of the upper and lower wing plates and the longitudinal beam, and the optimization design of these components is not carried out, the final change in bending stiffness is small. In terms of torsional stiffness, the torsional resistance tests under turning and full-load rough road conditions show that the stiffness reduction of the optimized models of the SIMP-PLSM fusion method and the SIMP method is small, and the trend is consistent with the actual working conditions. In the full-load flat road condition, the torsional stiffness of the model optimized by the SIMP-PLSM fusion method decreases by 3.592%, which is better than 4.521% of the SIMP method. Considering the changes in both bending and torsional stiffness, the SIMP-PLSM fusion method is more effective in the frame topology optimization.

[0296] According to Table 2 and Table 4, calculate the importance ratio between every two working conditions:

[0297] Table 5 Importance ratio between every two working conditions

[0298]

[0299] The judgment matrix is obtained from Table 5. Calculate the maximum eigenvalue of the judgment matrix as 4.0155, and calculate to get CR = 0.0057 < 0.1. The judgment matrix constructed above meets the consistency requirement.

[0300] The eigenvector corresponding to the maximum eigenvalue of the above judgment matrix is [0.8780, 0.4168, 0.1783, 0.1537] T , and after normalizing it, the final weight values of the four working conditions can be obtained, as shown in Table 6:

[0301] Table 6 Weight values of four working conditions

[0302]

[0303] According to the weight values of the four working conditions in the above table, use MATLAB to perform topology optimization on the frame geometric model again, and obtain the frame model after topology optimization under multiple working conditions, as Figure 15 shown. After multi-condition topology optimization, the mass of the obtained frame is reduced by 47.35 kg, and the overall mass is decreased by 3.84%. In the multi-condition topology optimization, the full-load flat road condition and the braking condition with symmetrically distributed loads have relatively large weight coefficients, and the finally generated topology configuration is basically symmetrically distributed, meeting the requirements of frame stability.

[0304] After obtaining the frame model after topology optimization under multiple working conditions, perform regular design on it to obtain a new frame, as Figure 16 shown. The mass of the redesigned frame is reduced by 43.16 kg, and the overall mass of the frame is decreased by 3.5%.

[0305] The static analysis of the new vehicle frame was carried out using ANSYS software. As Figures 17 to 20 shown, from the stress distribution of the new vehicle frame under four working conditions, it can be seen that the area where the maximum stress of the new vehicle frame appears has not changed compared with the original vehicle frame, and the force-bearing structure of the whole vehicle has not changed significantly after topology optimization. Except that the maximum stress under the full-load rough condition has decreased slightly, the peak stresses in the other working conditions have all increased. Among them, the stress peak in the full-load flat road condition has increased the most, by 7.45 MPa, the peak stress in the braking condition has increased by 3.49 MPa, and the peak stress in the turning condition has increased by 3.61 MPa. However, the overall stress still meets the safety factor requirements. Compared with the original vehicle frame, the stress distribution of the cross beam of the new vehicle frame is more uniform. Since the opening has changed the deformation ability of the cross beam, the stress concentration phenomenon at the contact position between the cross beam and the upper wing plate of the longitudinal beam has been effectively alleviated. The peak stresses of the cross beam under the four working conditions are 251.49 MPa, 240.82 MPa, 246.77 MPa, and 234.32 MPa respectively, which have decreased by 6.7%, 5.1%, 8.6%, and 3.8% compared with the original vehicle frame. The hole-drilling and material reduction not only improve the fuel efficiency of the vehicle frame, but also enhance the durability and reliability of the cross beam to a certain extent.

[0306] The stiffness analysis of the optimized new vehicle frame was carried out, and the corresponding stress distribution is as Figure 21 and Figure 22 shown. The maximum deflection at the left loading point of the optimized vehicle frame is 0.22107 mm, and the maximum deflection at the right loading point is 0.22115 mm. The calculated bending stiffness is 9.452×106 N / m, which is 0.133% lower than that of the original vehicle frame. The deformation at the left loading point of the optimized vehicle frame is 0.77424 mm, and the deformation at the right loading point is 0.71377 mm. At this time, the torsion angle of the vehicle frame is 0.0917°, and the calculated torsion stiffness is 1.014×104 N·m / °, which is only 0.927% lower than that of the original vehicle frame. It can be seen that the SIMP-PLSM fusion method has successfully achieved the lightweight of the vehicle frame on the premise of ensuring little stiffness loss, and effectively improved the mass-stiffness ratio.

[0307] The vibration mode results of the new vehicle frame were analyzed, and the vibration modes of the new vehicle frame are as Figures 23 to 28 shown. From the overall deformation of the vehicle frame, the vibration mode order of the optimized vehicle frame is the same as that of the original vehicle frame. Among them, the modal frequency of the relatively important 7th vibration mode has increased by 4.3% compared with the original vehicle frame, and the modal frequency of the 9th vibration mode has increased by 2.15% compared with the original vehicle frame, and the safety performance of the whole vehicle has been improved. The optimized vehicle frame can better avoid the excitation frequency range of the road surface and the engine, reducing the risk of resonance.

[0308] The frame structure optimization method based on the SIMP-PLSM fusion method provided in this embodiment optimizes the frame structure through the SIMP-PLSM fusion method, realizes the lightweight of the frame while ensuring the stiffness of the frame, has strong manufacturability, and has better optimization effect and higher optimization efficiency compared with the traditional single topology optimization method. At the same time, the frame structure is optimized in combination with multiple working conditions, so that the optimized frame can meet the requirements of the bending stiffness and torsional stiffness of the frame at the same time, and has better practicability and reliability.

[0309] This embodiment also provides a frame structure optimization system based on the SIMP-PLSM fusion method. The frame structure optimization system based on the SIMP-PLSM fusion method includes a model establishment module, a first topology optimization module, a force analysis module and a second topology optimization module. The model establishment module is used to establish a frame geometric model and define the design domain of the frame geometric model and the first boundary conditions under multiple preset different working conditions. The first topology optimization module is used to perform topology optimization calculations on the frame geometric model under each working condition by using topology optimization software with the SIMP-PLSM fusion method to obtain the first topology optimization model under each working condition. The force analysis module is used to perform stiffness analysis on the first topology optimization model under each working condition, and obtain the weight value of each working condition according to the stiffness analysis result. The second topology optimization module is used to perform weighted average processing on the topology optimization objectives of each working condition according to the weight value of each working condition, and perform re-topology optimization on the frame geometric model by using the SIMP-PLSM fusion method to obtain the frame model after topology optimization under multiple working conditions. By adopting this system to implement the above-mentioned frame structure optimization method based on the SIMP-PLSM fusion method, the optimization effect on the frame is better, the lightweight of the frame can be realized while ensuring the stiffness of the frame, and the use reliability of the vehicle is guaranteed.

[0310] Note that the above is only the preferred embodiment of the present invention and the applied technical principle. Those skilled in the art will understand that the present invention is not limited to the specific embodiments described here, and various obvious changes, re-adjustments and substitutions can be made by those skilled in the art without departing from the protection scope of the present invention. Therefore, although the present invention has been described in detail through the above embodiments, the present invention is not limited to the above embodiments. Without departing from the concept of the present invention, more other equivalent embodiments can be included, and the scope of the present invention is determined by the scope of the appended claims.

Claims

1. A frame structure optimization method based on SIMP-PLSM fusion method, characterized in that: include: Establishing a vehicle frame geometric model, and defining a design domain of the vehicle frame geometric model and first boundary conditions under a plurality of preset different working conditions; Using topology optimization software and SIMP-PLSM fusion method to perform topology optimization calculation on the frame geometry model under each working condition, and obtain a first topology optimization model under each working condition; Using finite element analysis software to perform stiffness analysis on the first topology optimization model under each working condition, and obtaining a weight value for each working condition according to the stiffness analysis result; The topology optimization software is used to perform weighted average processing on the topology optimization target of each working condition according to the weight value of each working condition, and the frame geometric model is topologically optimized again by using the SIMP-PLSM fusion method to obtain a frame model after topology optimization under multiple working conditions; The frame model is regularly designed according to the production process requirements to obtain a final optimized frame model.

2. The frame structure optimization method based on SIMP-PLSM fusion method according to claim 1 is characterized in that: The topology optimization calculation of the frame geometry model under each working condition using the SIMP-PLSM fusion method includes: The SIMP topology optimization method is used to perform a topology optimization on the frame geometry model. In the topology optimization software, the sensitivity filter radius, penalty factor, and retained volume fraction of the design domain are set as the second boundary conditions. The optimized force transmission path model is iteratively calculated with the minimum structural flexibility as the objective function. The force transmission path model has n units, each of which contains density information, and the unit density is ρ n ; The cell density ρ n Transformed into the node density ρ that can be used in PLSM topology optimization method i , get the initial input level set function of PLSM topology optimization method; The PLSM topology optimization method is used to perform secondary topology optimization on the frame geometry model after the primary topology optimization, and the minimum density sensitivity n is set in the topology optimization software. min , maximum expansion factor |α i | max , steepness coefficient μ, taking the minimum structural flexibility as the objective function and the volume constraint as the constraint condition, the force transmission path model of the PLSM topology optimization method is iteratively calculated to obtain the first topology optimization model.

3. The frame structure optimization method based on SIMP-PLSM fusion method according to claim 2 is characterized in that: According to the following formula (1), the unit density ρ n Transformed into the node density ρ that can be used in PLSM topology optimization method i : Where M represents the number of units directly connected to node i; The obtained node density value is used as the initial input of the parameterized level set function in the PLSM topology optimization method to obtain the level set function describing the structure boundary: Where N is the number of nodes, is the basis function used by the PLSM topology optimization method, α i (t) represents x at time t i The expansion coefficient corresponding to the basis function at ; The level set function is moved down to the case where the level set function value is less than 0, and the initial input level set function of the PLSM topology optimization method is obtained: Φ(t0)=Aα(t)={ρ1-ξ…ρ N -ξ} T (3) in, α(t)={α1(t) … α N (t)} T (5) Where A is the basis function matrix composed of basis function values; Under a fixed grid, all elements in A are fixed values, the matrix A is reversible, and the initial value of the expansion coefficient can be calculated as follows: α(t0)=A -1 {ρ1-ξ … ρ N -ξ} T (6)。 4. The frame structure optimization method based on SIMP-PLSM fusion method according to claim 3 is characterized in that: The cell density ρ n Transformed into the node density ρ that can be used in the PLSM topology optimization method i After that, it also includes using bilateral smoothing method to calculate the node density ρ i To perform density smoothing: Smoothed density value Among them, W p is the normalization factor: In the formula, ρ i is the density value of the i-th neighboring node; d pi is the spatial distance between node p and node i; σ s is the standard deviation of the control space distance effect, σ r Determines the intensity of spatial smoothing; The smoothed density value Substitute into formula (3).

5. The frame structure optimization method based on SIMP-PLSM fusion method according to claim 3 is characterized in that: The topology optimization calculation of the frame geometry model under each working condition using the SIMP-PLSM fusion method also includes: The Gaussian function is used as the basis function of the PLSM topology optimization method, and the influence range of the Gaussian function on a single node is limited: Among them, r i is the Euclidean distance between two coordinate points in space: Where c is the bandwidth coefficient of the Gaussian function, d m Indicates that the basis function is at the control point (xi,y i )’s impact area.

6. The vehicle frame structure optimization method based on SIMP-PLSM fusion method according to claim 5, characterized in that: After establishing the initial input level set function, performing secondary topology optimization on the frame geometric model using the PLSM method includes: The Heaviside function is used to convert the implicit expression of the initial input level set function into an explicit boundary: In the formula, μ is the coefficient that controls the steepness of the Heaviside function; The relationship between the level set function value and the node density is: p(Φ)=p min +(r max -r min )·H(Φ)(12) Where ρ min and ρ max Respectively represent the lower and upper limits of the relative density of the material, taking ρ min =0.01,ρ max =1; The PLSM topology optimization method uses sensitivity-driven iterative calculation of design variables: Objective function sensitivity calculation: Constraint sensitivity calculation: in: In the formula, C is the structural flexibility, G is the volume constraint, V0 is the total volume of the initial structure, and η is the retained volume fraction set by the optimization; In the tiny space near the boundary, the level set function value of the node is linearly approximated as: Where L is the distance from the node to the structure boundary, is the gradient of the level set function at the structure boundary; The maximum gradient of the level set function at the structure boundary is: Where D is the structural dimension, c is the bandwidth coefficient of the Gaussian function; According to equations (19) and (20), the maximum level set function value near the boundary is obtained: Thus, the partial derivative n of the density function corresponding to the maximum level set function value is obtained min , n min Substitute it into formula (16) to calculate the value of μ.

7. The frame structure optimization method based on SIMP-PLSM fusion method according to claim 1 is characterized in that: The stiffness analysis of the first topology optimization model under each working condition includes: By comparing the influence degree between each two working conditions, the importance ratio of each two working conditions is obtained. The judgment matrix M composed of the importance ratio is: Among them, a ij represents the importance ratio of working condition i to working condition j, and m represents the number of working conditions; The eigenvector of the judgment matrix M is calculated, and each element in the eigenvector is the weight value of each working condition.

8. The vehicle frame structure optimization method based on SIMP-PLSM fusion method according to claim 7, characterized in that: After obtaining the judgment matrix M, the consistency of the judgment matrix M is also judged: Where λ max is the maximum eigenvalue of the judgment matrix, m is the number of working conditions; The consistency ratio of judgment matrices of different orders is: In the formula, RI is the random consistency index, which is determined according to the number of working conditions; When the CR value is less than 0.1, the judgment matrix meets the consistency requirement.

9. The vehicle frame structure optimization method based on SIMP-PLSM fusion method according to claim 1, characterized in that: After obtaining the final optimized frame model, the method further includes: The finite element software is used to simulate and calculate the final optimized frame model under each working condition, and the stress distribution of the final optimized frame model under each working condition is obtained. The stress distribution uniformity and peak value of the frame geometric model and the final optimized frame model are compared to verify the performance of the final optimized frame model.

10. A vehicle frame structure optimization system based on SIMP-PLSM fusion method, characterized in that: include: A model building module, used for building a frame geometric model and defining a design domain of the frame geometric model and a plurality of first boundary conditions under different preset working conditions; A first topology optimization module is used to perform topology optimization calculation on the frame geometry model under each working condition by using topology optimization software and SIMP-PLSM fusion method to obtain a first topology optimization model under each working condition; A force analysis module, used for performing a stiffness analysis on the first topology optimization model under each working condition, and obtaining a weight value of each working condition according to the stiffness analysis result; The second topology optimization module is used to perform weighted averaging of the topology optimization target of each working condition according to the weight value of each working condition, and use the SIMP-PLSM fusion method to perform topology optimization on the frame geometry model again to obtain a frame model after topology optimization under multiple working conditions.

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