A two-stage topology optimization design method for multi-cell energy-absorbing structures in automobiles

Abstract

This invention belongs to the technical field of automotive energy-absorbing structures, specifically relating to a two-stage topology optimization design method for automotive multi-cell energy-absorbing structures. This method can design the configuration and thickness of thin-walled energy-absorbing structures based on given impact load conditions. For a given impact load condition, with the energy absorption value of the automotive multi-cell energy-absorbing structure as the design objective, and under constraints on the total mass and maximum displacement of the automotive multi-cell energy-absorbing structure, the first stage uses the presence or absence of partitions in the automotive multi-cell energy-absorbing structure as the design variable, and obtains the multi-cell configuration with optimal crashworthiness through a discrete topology optimization method based on integer encoding genetic algorithms. The second stage, based on the optimization results of the first stage, uses the unit thickness of the automotive multi-cell energy-absorbing structure as the design variable, and optimizes the unit thickness of the automotive multi-cell energy-absorbing structure using a topology optimization method based on unit energy, ultimately aiming to obtain a highly efficient automotive multi-cell energy-absorbing structure.

Description

Technical Field

[0001] This invention belongs to the field of automotive energy-absorbing structure technology, specifically relating to a two-stage automotive multi-cell energy-absorbing structure topology optimization design method. Background Technology

[0002] The basic structure of a car body is composed of thin-walled components. In a collision, the plastic deformation of these thin-walled energy-absorbing structures dissipates most of the collision energy, while simultaneously transferring the collision load to other parts of the vehicle body to minimize injury to occupants. Studies show that in a head-on collision at 48 km / h, 50%-70% of the collision energy is absorbed and dissipated by thin-walled energy-absorbing structures (thin-walled energy-absorbing cylinders, thin-walled front longitudinal beams, etc.). The deformation mode and energy absorption characteristics of these structures directly determine the acceleration and impact response of the vehicle body during a collision, which directly affects occupant safety. Existing research indicates that cross-sectional configuration is a crucial factor influencing the collision performance of thin-walled structures. Compared to single-cell energy-absorbing structures, multi-cell thin-walled structures offer advantages such as a smoother collision process and greater energy absorption. Metal multi-cell structures have been proven to be highly efficient energy-absorbing structures. Research on the topological configuration of multi-cell structures can further expand the lightweight design space for energy-absorbing structures, demonstrating significant application potential.

[0003] However, current research on thin-walled multicellular structures has the following limitations: First, existing research shows that the cross-sectional topology significantly affects the energy absorption characteristics of thin-walled multicellular structures, but current research mainly focuses on multicellular thin-walled structures with specific topological geometries, and there is relatively little analysis on the impact of cross-sectional topological evolution on the impact resistance of thin-walled multicellular structures; Second, current thin-walled energy-absorbing structure designs are based on the concept of uniform thickness design, but in the actual deformation process of thin-walled energy-absorbing structures, the load-bearing capacity of each part is non-uniform. If the uniform design concept is still adopted, the load-bearing capacity and material utilization rate of each part of the structure are not fully explored, and the impact of material distribution on the impact resistance of thin-walled structures is not considered. Summary of the Invention

[0004] The purpose of this invention is to provide a two-stage topology optimization design method for automotive multi-cell energy-absorbing structures. This method can efficiently and quickly design the topology configuration of energy-absorbing structures. The first step of this method is to optimize the cross-sectional configuration design through a discrete topology optimization algorithm to obtain the optimal multi-cell configuration. The second step is to perform variable thickness design based on the topology optimization method of unit energy to improve the energy absorption characteristics of thin-walled energy-absorbing structures.

[0005] To achieve the above objectives, the present invention employs the following technical solution:

[0006] A two-stage topology optimization design method for automotive multicellular energy-absorbing structures includes the following steps:

[0007] Step 1: Determine the dimensional and mechanical parameters of the automotive multicell energy-absorbing structure to be optimized. The mechanical parameters are determined based on the design requirements of the automotive multicell energy-absorbing structure, including the loading method, load size, material parameters, and initial and boundary conditions for numerical simulation.

[0008] Step 2: Based on the dimensional and mechanical parameters of the aforementioned automotive multi-cell energy-absorbing structure, establish a finite element model using the multi-cell partition of the automotive multi-cell energy-absorbing structure as the design unit;

[0009] Step 3: Based on the established finite element model, construct the mathematical model for the first-stage automotive multi-cell energy-absorbing structure configuration design;

[0010] Step 4: The discrete topology optimization method based on integer encoding genetic algorithm is used to optimize the configuration of the multi-cell energy-absorbing structure of the car to obtain the optimal multi-cell configuration;

[0011] Step 5: Based on the obtained optimal multi-cell configuration, adjust the finite element model using the finite element model mesh elements as design variables;

[0012] Step 6: Based on the adjusted finite element model, construct a mathematical model for the second-stage automotive multicellular energy-absorbing structure variable thickness optimization problem;

[0013] Step 7: Use topology optimization design based on element energy to perform variable thickness optimization design on the adjusted finite element model to determine the optimal thickness design scheme.

[0014] Furthermore, the mathematical model in step 3 is as follows:

[0015]

[0016] Where x = [x1, x2, ..., x n [The following is a list of design variables determined based on the multi-cell partition: EA(x) is the total energy absorbed by the multi-cell energy-absorbing structure of the vehicle, and U(x) represents the displacement of the multi-cell energy-absorbing structure of the vehicle under a given load condition; U...] * M is the maximum allowable displacement in the optimization problem. * To determine the mass of the initial multicellular energy-absorbing structure of the vehicle before optimization, w is the mass fraction, and M(x) is the allowable mass of the multicellular energy-absorbing structure of the vehicle before optimization, which is related to the mass fraction w. Taking a mass fraction w = 0.3 as an example, M(x) must be less than or equal to 0.3 times the mass of the initial multicellular energy-absorbing structure of the vehicle before optimization; design variables x1, x2, ..., x n It can be 0 or 1, where 1 indicates that the multi-cell energy-absorbing structure partition of the car exists, and 0 indicates that the partition does not exist.

[0017] Furthermore, the specific implementation process of step 4 is as follows:

[0018] Step 4.1: Set the population size, maximum number of iterations, and convergence condition for the integer encoding genetic algorithm, and create a random initial population. The convergence condition is reaching the maximum number of iterations.

[0019] Step 4.2: Update the corresponding finite element model of the multicellular energy-absorbing structure of the car based on the corresponding chromosomes in the population. Perform finite element simulation on the established finite element model using LS-DYNA software. Obtain the target value and constraint value of the energy-absorbing structure from the result file after finite element analysis using Matlab and LS-PrePost software. Apply a static objective penalty function to chromosomes that violate the constraints. Apply a penalty, where S→∞, q ​​is the number of constraints satisfied, l is the total number of constraints, and g... i (x) is the i-th constraint function.

[0020] Step 4.3: Evaluate the objective function and determine whether it meets the convergence condition. If the convergence condition is met, proceed to step 4.4. Otherwise, create a new population using the roulette wheel selection strategy, the two-point crossover strategy, and the single-point mutation strategy, and repeat steps 4.2-4.3.

[0021] Step 4.4: Output the optimal design scheme and convert it into the optimal multicell configuration.

[0022] Furthermore, step 5 is implemented as follows: Based on the obtained optimal multi-cell configuration, first determine whether the automotive multi-cell energy-absorbing structure is designed with varying thickness along the axial direction or along the circumferential direction of the cross-section. Then, according to the thickness design range and mesh division, determine the number of design variables and the element number and quantity contained in each design variable. The design with varying thickness along the axial direction uses each row of elements or every few rows of elements as a design variable; the design with varying thickness along the circumferential direction of the cross-section uses each column of elements or every few columns of elements as a design variable.

[0023] Furthermore, the mathematical model in step 6 is as follows:

[0024]

[0025] Where E i For the design objective, represents the strain energy of the i-th design variable, and N represents the number of design variables; U max U represents the maximum displacement of the element node; * It is the maximum allowable displacement for the optimization problem, m. i M is the quality of the i-th design variable; * It is the total mass of the design constraints; x i It is the thickness of the i-th design variable.

[0026] Furthermore, the specific implementation process of step 7 is as follows:

[0027] Step 7.1: Based on the optimization results of the first stage, specify the initial design variable thickness and determine the convergence condition. The convergence condition is reaching the maximum number of iterations or the change in the objective function reaching a given value. The change in the objective function is calculated according to the following formula:

[0028]

[0029] Where g is a positive number, ε is the convergence tolerance, and g is usually 5. error represents the average change of the objective function in the 10 iterations before the k-th iteration, and its value can be adjusted according to the optimization case.

[0030] Step 7.2: Perform finite element simulation using LS-DYNA software. Use Matlab and LS-PrePost software together to obtain the necessary data for design variables, such as strain energy, thickness, and mass, from the finite element analysis results file. Process the extracted data, calculate the sensitivity of the design variables, and apply the formula... Calculate the design variable strain energy density.

[0031] Step 7.3: To reduce oscillations during the iteration process, the strain energy density of the i-th design variable in the current k-th iteration is updated by the weighted sum of the previous three iterations:

[0032] Step 7.4: According to the formula Update the design variable thickness, Δx k It is the change in thickness at the k-th iteration, Δx 0 It is a positive number that limits the thickness change during each iteration. and These are the maximum and minimum values ​​of strain energy density among all design variables; α c This is a control threshold. During the iteration process, the control threshold α... c Adjustments can be made as needed based on the following process:

[0033] 7.4.1: Take α min =min[α i ], α max =max[α i ];

[0034] 7.4.2: Calculate α c =(α min +α max ) / 2;

[0035] 7.4.3: Update design variable x i And calculate the total mass of the current structure ∑m i If ∑mi <M * Update α max =α c Otherwise update α min =α c ;

[0036] 7.4.4: Repeat 7.4.2 to 7.4.3 until the quality convergence condition is met:

[0037]

[0038] Where τ is the convergence tolerance value, the size of which can be defined according to the optimization case.

[0039] Step 7.5: Determine if the convergence condition is met. If it is met, terminate the optimization; otherwise, repeat steps 7.2-7.5.

[0040] Step 7.6: Output the optimal variable thickness design scheme.

[0041] Compared with the prior art, the technical solution of the present invention has the following beneficial effects:

[0042] This invention provides a two-stage topology optimization design method for automotive multi-cell energy-absorbing structures. The first stage obtains the multi-cell cross-sectional configuration with optimal crashworthiness, and the second stage, based on the optimization results of the first stage, obtains the optimal variable thickness design scheme. This scheme can realize the topology optimization design of automotive multi-cell energy-absorbing structures according to specific design requirements, thus enabling the design of optimal variable thickness energy-absorbing multi-cell structures under different operating conditions and achieving excellent energy absorption performance. Attached Figure Description

[0043] Figure 1 This is a flowchart of the present invention;

[0044] Figure 2(a) is a schematic diagram of the energy-absorbing multi-cell structure of a car;

[0045] Figure 2(b) is a schematic diagram of the cross-section of the energy-absorbing multi-cell structure of the automobile;

[0046] Figure 3 This is a schematic diagram of the design variables for the first stage of topology configuration optimization.

[0047] Figure 4 To optimize the topology configuration for the first stage;

[0048] Figure 5 Schematic diagram of the second stage of variable thickness optimization

[0049] Figure 6 This is the optimal configuration for the second stage. Detailed Implementation

[0050] The method proposed in this invention will now be described using the design of the automotive multi-cell energy-absorbing structure scheme shown in Figures 2(a) and 2(b) as examples. In this embodiment, the energy absorption of the automotive multi-cell energy-absorbing structure is the design objective, and the greater the better.

[0051] Step 1: Based on the multi-cell energy-absorbing structure shown in Figure 2(a) and Figure 2(b), establish a finite element model with multi-cell partitions as design units. The tube length H = 250 mm, the cross-sectional dimensions L × L = 90 × 90 mm, and the initial thickness of the partition T = 1 mm. Each partition of the multi-cell thin-walled structure is regarded as a design variable. Considering the symmetry of the structure, a 1 / 8 symmetric model is used for optimization, and the number of design variables is 15.

[0052] Step 2: Construct a mathematical model for the first-stage configuration optimization problem of the multicellular energy-absorbing structure of an automobile;

[0053]

[0054] Where x = [x1, x2, ..., x 15 [These are] design variables, a total of 15. EA(x) is the total energy absorbed by the automotive multicell energy-absorbing structure, and U(x) represents the displacement of the automotive multicell energy-absorbing structure under a given load condition, which must be less than or equal to 135mm. M * To optimize the mass of the initial multicellular energy-absorbing structure of the car, with a mass fraction w = 0.3, M(x) must be less than or equal to 0.3 times the mass of the initial multicellular energy-absorbing structure of the car before optimization; design variables x1, x2, ..., x 15 It can be 0 or 1, where 1 indicates that the multi-cell energy-absorbing structure partition of the car exists, and 0 indicates that the partition does not exist.

[0055] Step 3: Use an integer-encoded genetic algorithm to perform discrete topological optimization on the multi-cell energy-absorbing structure of the car to obtain the optimal multi-cell cross-section configuration, with a population size of 100. Optimization ends once the maximum number of iterations reaches 50. The chromosomes in the population are converted into the topological structure of the multi-cell energy-absorbing structure. Based on the corresponding chromosomes, the corresponding finite element model of the multi-cell tube is updated. Finite element simulation is performed on the established finite element model using LS-DYNA software. The total energy absorption, total mass, and displacement of the energy-absorbing structure are obtained from the finite element analysis results file using a combination of Matlab and LS-PrePost software. The objective function is evaluated to determine if the convergence condition is met. If the termination condition is met, the best result is output and converted into the optimal multi-cell configuration. Otherwise, a new population is created using roulette wheel selection, two-point crossover, and single-point mutation strategies, and the above process is repeated. The resulting optimal multi-cell car configuration is shown below. Figure 4 .

[0056] Step 4: Based on the obtained optimal multicell cross-sectional configuration, perform variable thickness design along the circumferential direction, as shown in the schematic diagram below. Figure 5 As shown. The thickness variation range of the variable thickness design is (0.8, 1.2). Considering the symmetry of the forces on the multi-cell structure, the number of design variables is 28, and the initial thickness is taken as 1.0 mm.

[0057] The mathematical model in step 5 is as follows:

[0058]

[0059] In the formula E i The value of m represents the strain energy of the i-th design variable, and N represents the number of design variables, with a total of 28 design variables; i M is the quality of the i-th design variable; * It is the total mass of the automotive multicellular structure with its initial thickness before the start of the second phase of optimization; x i It is the thickness of the i-th design variable.

[0060] Step 6 uses LS-DYNA software for finite element analysis. After the analysis, Matlab and LS-PrePost software are used to extract the strain energy of each design variable from the finite element analysis results file, and then use the formula... To calculate the strain energy density of the design variables and reduce oscillations during the iteration process, the strain energy density of the i-th design variable in the current k-th iteration is updated by weighted sum of the previous three iterations. According to the formula Update the design variable thickness and determine if the objective function meets the convergence condition. If it does, terminate the optimization; otherwise, repeat the above steps. The optimal configuration is as follows. Figure 6 As shown.

[0061] The above description is merely a preferred embodiment of the present invention, but the design concept of the present invention is not limited thereto. Any non-substantial modifications made to the present invention by those skilled in the art within the scope of the technology disclosed in the present invention using this concept shall be deemed as an infringement of the protection scope of the present invention.

Claims

1. A two-stage topology optimization design method for a multi-cell energy-absorbing structure in automobiles, characterized in that, Includes the following steps: Step 1: Determine the dimensional and mechanical parameters of the automotive multicell energy-absorbing structure to be optimized. The mechanical parameters are determined based on the design requirements of the automotive multicell energy-absorbing structure, including the loading method, load size, material parameters, and initial and boundary conditions for numerical simulation. Step 2: Combining the dimensional and mechanical parameters of the automotive multi-cell energy-absorbing structure, establish a finite element model using the multi-cell partition of the automotive multi-cell energy-absorbing structure as the design unit; Step 3: Based on the established finite element model, construct the mathematical model for the first-stage automotive multi-cell energy-absorbing structure configuration design; The mathematical model for the first-stage automotive multi-cell energy-absorbing structure configuration design is as follows: in, EA(x) is the total energy absorbed by the multi-cell energy-absorbing structure of the vehicle, which is a design variable determined based on the multi-cell partition. This represents the displacement of the multicellular energy-absorbing structure of a vehicle under a given load condition. It is the maximum allowable displacement in the optimization problem. To optimize the mass of the initial multicellular energy-absorbing structure of the vehicle, w represents the mass fraction. The mass of the permissible multicellular energy-absorbing structure for a car is related to the mass fraction w; design variables x1, x2, ..., x n The value can be 0 or 1, where 1 indicates that the multi-cell energy-absorbing structure partition of the car exists, and 0 indicates that the partition does not exist; Step 4: The discrete topology optimization method based on integer encoding genetic algorithm is used to optimize the configuration of the multi-cell energy-absorbing structure of the car to obtain the optimal multi-cell configuration; Step 5: Based on the obtained optimal multi-cell configuration, adjust the finite element model using the finite element model mesh elements as design variables; Step 6: Based on the adjusted finite element model, construct a mathematical model for the second-stage automotive multicellular energy-absorbing structure variable thickness optimization problem; The mathematical model for the second-stage optimization problem of variable thickness of multicellular energy-absorbing structures in automobiles is as follows: in The strain energy represents the i-th design variable, and N represents the number of design variables; Represents the maximum displacement of the element node; It is the maximum allowable displacement in the optimization problem. It is the quality of the i-th design variable; It is the total mass of the design constraints; It is the thickness of the i-th design variable; Step 7: Use topology optimization design based on element energy to perform variable thickness optimization design on the adjusted finite element model to determine the optimal thickness design scheme.

2. The topology optimization design method for a two-stage automotive multi-cell energy-absorbing structure according to claim 1, characterized in that, The specific implementation process of step 4 is as follows: Step 4.1: Set the population size, maximum number of iterations, and convergence condition for the integer encoding genetic algorithm, and create a random initial population. The convergence condition is reaching the maximum number of iterations. Step 4.2: Update the corresponding finite element model of the multicellular energy-absorbing structure of the car based on the corresponding chromosomes in the population. Perform finite element simulation on the established finite element model using LS-DYNA software. Obtain the target value and constraint value of the energy-absorbing structure from the result file after finite element analysis using Matlab and LS-PrePost software. Apply a static objective penalty function to chromosomes that violate the constraints. A penalty is applied, where S→∞, q ​​is the number of constraints satisfied, and l is the total number of constraints. It is the i-th constraint function; Step 4.3: Evaluate the objective function and determine whether it meets the convergence condition. If the convergence condition is met, proceed to step 4.4; otherwise, create a new population using the roulette wheel selection strategy, the two-point crossover strategy, and the single-point mutation strategy, and repeat steps 4.2-4.

3. Step 4.4: Output the optimal design scheme and convert it into the optimal multicell configuration.

3. The topology optimization design method for a two-stage automotive multi-cell energy-absorbing structure according to claim 1 or 2, characterized in that: The specific implementation process of step 5 is as follows: Based on the obtained optimal multi-cell configuration, first determine whether the automotive multi-cell energy absorption structure is designed with varying thickness along the axial direction or with varying thickness along the circumferential direction of the cross section. Then, according to the thickness design range and mesh division, determine the number of design variables and the unit number and quantity contained in each design variable. The variable thickness design along the axial direction uses each row of units or every few rows of units as a design variable; the variable thickness design along the circumferential direction of the cross section uses each column of units or every few columns of units as a design variable.

4. The topology optimization design method for a two-stage automotive multi-cell energy-absorbing structure according to claim 1 or 2, characterized in that: The specific implementation process of step 7 is as follows: Step 7.1: Based on the optimization results of the first stage, specify the initial design variable thickness and determine the convergence condition. The convergence condition is reaching the maximum number of iterations or the change in the objective function reaching a given value. The change in the objective function is calculated according to the following formula: Where g is a positive number. It is the convergence tolerance, where error represents the average change of the objective function in the 10 iterations prior to the k-th iteration; Step 7.2: Perform finite element simulation using LS-DYNA software. Use Matlab and LS-PrePost software together to obtain the required data for strain energy, thickness, and mass of the design variables from the finite element analysis results file. Process the extracted data, calculate the sensitivity of the design variables, and apply the formula... Calculate the design variable strain energy density; Step 7.3: To reduce oscillations during the iteration process, the strain energy density of the i-th design variable in the current k-th iteration is updated by the weighted sum of the previous three iterations: ; Step 7.4: According to the formula Update the design variable thickness. It is the change in thickness during the k-th iteration. It is a positive number that limits the thickness change during each iteration. and These are the maximum and minimum values ​​of strain energy density among all design variables; To control the threshold; Step 7.5: Determine if the convergence condition is met. If it is met, terminate the optimization; otherwise, repeat steps 7.2-7.

5. Step 7.6: Output the optimal variable thickness design scheme.

5. The topology optimization design method for a two-stage automotive multi-cell energy-absorbing structure according to claim 3, characterized in that: The specific implementation process of step 7 is as follows: Step 7.1: Based on the optimization results of the first stage, specify the initial design variable thickness and determine the convergence condition. The convergence condition is reaching the maximum number of iterations or the change in the objective function reaching a given value. The change in the objective function is calculated according to the following formula: Where g is a positive number, This is the convergence tolerance, where error represents the average change in the objective function during the 10 iterations prior to the k-th iteration. Step 7.2: Perform finite element simulation using LS-DYNA software. Use Matlab and LS-PrePost software together to obtain the required data for strain energy, thickness, and mass of the design variables from the finite element analysis results file. Process the extracted data, calculate the sensitivity of the design variables, and apply the formula... Calculate the design variable strain energy density; Step 7.3: To reduce oscillations during the iteration process, the strain energy density of the i-th design variable in the current k-th iteration is updated by the weighted sum of the previous three iterations: ; Step 7.4: According to the formula Update the design variable thickness. It is the change in thickness during the k-th iteration. It is a positive number that limits the thickness change during each iteration. and These are the maximum and minimum values ​​of strain energy density among all design variables; To control the threshold; Step 7.5: Determine if the convergence condition is met. If it is met, terminate the optimization; otherwise, repeat steps 7.2-7.

5. Step 7.6: Output the optimal variable thickness design scheme.

6. The topology optimization design method for a two-stage automotive multi-cell energy-absorbing structure according to claim 4, characterized in that: In step 7.4, during the iteration process, the control threshold is... Make timely adjustments according to the following process: Step 7.4.1: Take , ; Step 7.4.2: Calculation ; Step 7.4.3: Update design variables And calculate the total mass of the current structure. ;if ,renew Otherwise update ; Step 7.4.4: Repeat steps 7.4.2 to 7.4.3 until the quality convergence condition is met. in This is the convergence tolerance value.

7. The topology optimization design method for a two-stage automotive multi-cell energy-absorbing structure according to claim 5, characterized in that: In step 7.4, during the iteration process, the control threshold is... Make timely adjustments according to the following process: Step 7.4.1: Take , ; Step 7.4.2: Calculation ; Step 7.4.3: Update design variables And calculate the total mass of the current structure. ;if ,renew Otherwise update ; Step 7.4.4: Repeat steps 7.4.2 to 7.4.3 until the quality convergence condition is met. in This is the convergence tolerance value.

8. The topology optimization design method for a two-stage automotive multi-cell energy-absorbing structure according to claim 4, characterized in that: In step 7.1, g is set to 5.

9. The topology optimization design method for a two-stage automotive multi-cell energy-absorbing structure according to claim 5, characterized in that: In step 7.1, g is set to 5.

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