Frame structure design method for material and thickness collaborative optimization under multiple working conditions

Abstract

The invention discloses a frame structure design method for material and thickness collaborative optimization under multiple working conditions, and the method comprises the steps: constructing a frame structure subregion cellular automaton model, and employing an internal and external loop iteration mechanism to achieve the optimal distribution solution of the structure material and quality under multiple working conditions. The outer cycle sets target cost and target quality for the inner cycle to provide optimization guidance and construct a combined target field variable function, and the inner cycle drives dynamic updating of cellular thickness and materials under multiple working conditions based on a material and thickness collaborative updating strategy and guides cellular field variables to approach target field variables, so that the structural performance is remarkably improved. In order to break through the algorithm efficiency bottleneck, the global search capability and convergence speed of the algorithm are effectively enhanced through the strategy of parallel point adding and search area expanding, and the method is particularly suitable for optimization design of a frame structure with a large number of materials and thickness design variables under the constraint of multiple working conditions. And an efficient and reliable technical path is provided for lightweight design and performance optimization of the frame structure.

Description

Technical Field

[0001] This invention belongs to the field of lightweight and safe design technology for frame structures, specifically involving a frame structure design method for co-optimization of materials and thickness under multiple working conditions. Background Technology

[0002] With the increasing demands for lightweight and safety in frame structures from industries such as automotive and construction, the coordinated optimization of material selection and thickness distribution has become a key means to improve the overall performance of frame structures. The problem of co-optimizing materials and thickness involves a large number of discrete variables and is characterized by multi-condition coupling and strong correlations between variables. Traditional optimization methods cannot effectively balance computational efficiency and optimization accuracy, especially when dealing with integrated constraints under multiple conditions, easily falling into local optima. While current mainstream surrogate model optimization methods reduce computational costs through approximate modeling, they face the "curse of dimensionality" in high-dimensional design spaces. Machine learning-based surrogate models, due to insufficient generalization ability, struggle to accurately capture the implicit correlations between design variables under complex loads, thus limiting the reliability of optimization results.

[0003] Hybrid Cellular Automata (HCA) methods effectively circumvent the gradient dependency problem of traditional methods through a heuristic search mechanism driven by local rules. However, existing HCA algorithms mostly focus on optimization scenarios with a single material type or thickness parameter, lacking a collaborative optimization mechanism for material and thickness parameters, and exhibiting insufficient adaptability to various operating conditions, leading to global configuration schemes deviating from the Pareto optimal front. These problems severely restrict the optimization design and engineering application of frame structures, urgently requiring new technological breakthroughs. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides a frame structure design method that coordinates material and thickness optimization under multiple working conditions, enabling the efficient design of frame structures with a large number of material and thickness variables.

[0005] The present invention achieves the above-mentioned technical objectives through the following technical means.

[0006] A frame structure design method for co-optimization of materials and thickness under multiple working conditions:

[0007] Construct a finite element model of the framework structure, and build a sub-region cellular automaton model based on the finite element model;

[0008] Set constraint functions and constraint boundaries for the frame structure under different working conditions, and define optimization variables: material variables, thickness variables, and field variables;

[0009] Outer loop: Call simulation software to perform dynamic collision simulation analysis and stiffness simulation analysis to obtain information about the current frame structure, including the thickness of all cells, materials, field variables and constraint violations; based on the constraint violations at the current design point, use a parallel strategy of bisection method and penalty function method to update the target mass and target cost of the frame structure under different working conditions, and use an arbitrary and step-parallel update strategy to construct the target field variable function for the inner loop;

[0010] Inner loop: Update each "step interval" in the inner loop [id] i-1 id i The field variables for controlling quality and the field variables for controlling cost are used for the collaborative update rules of cell material and thickness. Based on the target quality and target cost, the cell thickness and material under different working conditions are updated through the collaborative update rules of cell material and thickness, and the final cell thickness and material are determined according to the working condition adaptive allocation rules.

[0011] The inner loop converges based on its convergence condition. If it does not converge, the loop returns to the inner loop; otherwise, it exits the inner loop. The global loop converges based on its convergence condition. If it does not converge, the loop returns to the outer loop; otherwise, the optimization result is output for designing the framework structure.

[0012] Furthermore, the arbitrary target field variable function is:

[0013]

[0014] in, The target field variable of the "arbitrary interval" i in the kth outer loop and the hth inner loop.

[0015] Furthermore, the collaborative update rule for the cell material and thickness is as follows:

[0016] Define a candidate material library and assign mechanical properties of the material library to the cells based on the current cell material;

[0017] The local control rules based on cell thickness and density update the thickness and density of the current cell, and update the nominal flow stress of the current cell according to the cell flow stress update rules.

[0018] By comparing the actual density of each material in the candidate material library, the material type that is closest to the updated current cell density is selected as the candidate material type for the current cell.

[0019] The flow stress of all material grades is compared among the candidate material types. Finally, the material grade that is closest to the nominal flow stress of the current cell after the update is selected as the selected material for the current cell, and the cell material information is assigned. The thickness of the current cell is the updated thickness.

[0020] Furthermore, the adaptive allocation rule for the working condition determines the final cell thickness and material, specifically as follows:

[0021] Based on the response level of each component under different operating conditions, the weights for different operating conditions are adjusted in real time according to the final weighting coefficients:

[0022]

[0023] in, Let J be the field variable of the j-th cell in the i-th sub-region under the lc-th operating condition during the k-th outer loop. Let λ be the mean of the field variables of the lc-th platform, and λ2 represent the dynamic adjustment coefficient for component importance;

[0024] Weight These are used as coefficients for the cell material grade and cell thickness under each working condition, respectively, to update the cell material grade and cell thickness under each working condition into a final set of materials and thicknesses.

[0025] Furthermore, the final weighting coefficients Where λ1 represents the dynamic adjustment coefficient for constraint violation. ω represents the relative weight under the k-th outer loop lc condition. base_lc The basic weights for each operating condition.

[0026] Furthermore, the relative weights under the k-th outer loop lc condition in, This represents the constraint violation amount under the lc-th operating condition.

[0027] Furthermore, the constraint violation quantity under the lcth operating condition in, Let be the response value of the i-th constraint function under the lc-th working condition of the k-th outer loop. Let n be the constraint boundary of the i-th constraint function under the lc-th working condition. lc Let lc be the number of constraint functions under each of the lc operating conditions.

[0028] Furthermore, in order to more accurately regulate the coordinated updating of cell material and thickness variables in the next iteration by the local control rules for cell thickness and density updates, an adaptive correction strategy for cell field variables is used to update field variables under different working conditions. Specifically, the field variable under the collision condition is the internal energy density, and the field variable under the stiffness condition is the strain energy density.

[0029] Furthermore, under collision conditions, the formula for the adaptive correction strategy of the intracellular energy density field variable is as follows:

[0030]

[0031] in, Let be the yield strength of the cellular material of the j-th cell in the i-th subregion during the k-th outer layer cycle and the h-th inner layer cycle. Let be the tensile strength of the cellular material of the j-th cell in the i-th subregion during the k-th outer layer cycle and the h-th inner layer cycle. Let be the cell material density of the j-th cell in the i-th sub-region during the k-th outer layer cycle and the h-th inner layer cycle. Let be the elastic modulus of the cellular material of the j-th cell in the i-th subregion during the k-th outer layer cycle and the h-th inner layer cycle. This is an estimate of the maximum elastic strain energy density of the current cell. This is an estimate of the plastic strain energy density of the current cell. This is the field variable of the current cell.

[0032] Furthermore, under stiffness conditions, the formula for the adaptive correction strategy for updating the cellular strain energy density is:

[0033]

[0034] The beneficial effects of this invention are as follows:

[0035] (1) This invention introduces the binary search method and the penalty function method as target cost and quality update methods in the outer loop, forming a parallel point addition strategy and expanding the search area, which effectively improves the search efficiency and global convergence ability of the algorithm.

[0036] (2) The present invention uses an update strategy based on a combination of step and arbitrary target field variable functions in the outer loop, which can more flexibly adapt to the field variable distribution requirements under complex working conditions. This not only reduces the waste of computing resources, but also significantly improves the efficiency and accuracy of structural optimization and enhances the robustness of the algorithm.

[0037] (3) The frame structure thickness and material synergistic optimization of the present invention breaks the limitations of a single optimization method, realizes the synergistic gain of thickness and material, and achieves the dual improvement of cost reduction and weight reduction.

[0038] (4) This invention seeks to balance the structural performance under various working conditions by using an adaptive weight allocation rule, adapts to the optimization needs of material thickness distribution differences under different working conditions, and achieves a multi-dimensional leap in performance indicators such as impact resistance and stiffness. Attached Figure Description

[0039] Figure 1 This is a block diagram of a frame structure design method for co-optimization of materials and thickness under multiple working conditions, as described in this invention.

[0040] Figure 2 This is a schematic diagram of the step-type target field variable function of the present invention;

[0041] Figure 3 This is a schematic diagram of the arbitrary target field variable function of the present invention;

[0042] Figure 4 This is a schematic diagram of the finite element model of the side collision of the present invention;

[0043] Figure 5 This is a schematic diagram of the finite element model of the side column collision of the present invention;

[0044] Figure 6 This is a schematic diagram of the finite element model of the top compressive working condition of the present invention;

[0045] Figure 7 This is a schematic diagram of the finite element model of the bending stiffness condition of the present invention;

[0046] Figure 8 This is a schematic diagram of the finite element model of the torsional stiffness condition of the present invention;

[0047] Figure 9 This is a schematic diagram of the measurement points at the B-pillar chest and pelvic positions according to the present invention.

[0048] Figure 10(a) is a cost iteration curve of the method of the present invention;

[0049] Figure 10(b) is a graph showing the quality iteration process of the method of the present invention;

[0050] Figure 11(a) is a cost iteration history curve of the MOBO algorithm in an embodiment of the present invention;

[0051] Figure 11(b) is a graph showing the quality iteration history of the MOBO algorithm in an embodiment of the present invention.

[0052] Figure 12 The Pareto front curves of the method and MOBO algorithm of this invention are shown below.

[0053] Figure 13 This is a comparison diagram of the vehicle body material distribution before and after optimization according to the present invention;

[0054] Figure 14 This is a comparison diagram of the vehicle body thickness distribution before and after optimization for this invention. Detailed Implementation

[0055] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, but the scope of protection of the present invention is not limited thereto.

[0056] A frame structure design method for co-optimization of materials and thickness under multiple operating conditions is proposed, based on a sub-region hybrid cellular automata algorithm. The material and thickness co-optimization method consists of inner and outer loops. Before executing the outer loop, a finite element model and the definition of the cellular automata are required. The outer loop mainly obtains cell (in this example, the components of the frame structure) information through finite element simulation analysis, defines the target mass and target cost for the inner loop, and constructs the target field variable function. The inner loop updates the cell thickness and material under different operating conditions according to the target mass and cost provided by the outer loop through the cell material and thickness co-update rule, and determines the final cell thickness and material according to the operating condition adaptive allocation rule. This process drives the cost and mass of the inner loop to converge asymptotically to the target value of the outer loop, while guiding the cellular field variables to approach the target field variables.

[0057] like Figure 1 As shown, a frame structure design method for co-optimization of materials and thickness under multiple working conditions is described in the following process: Figure 1 As shown, the specific steps include:

[0058] S1. Construct the finite element model of the frame structure under multiple working conditions required for optimization, build the sub-region cellular automaton model and define the cell number;

[0059] S1.1, The geometric model of the frame structure to be optimized is meshed using finite element preprocessing software, and each component is assigned corresponding properties and materials. The model connection, boundary conditions and load conditions are defined. Based on the above steps, finite element models of the frame structure under various load conditions are established.

[0060] S1.2, Based on the finite element model of the frame structure, construct a one-dimensional cellular automaton model of the sub-region and define the cell number;

[0061] The discrete design space of the finite element model is divided into l sub-regions Ω. i (i = 1, 2, ..., l), each subregion Ω i From a one-dimensional cellular automata model and cell state Description of a one-dimensional cellular automata model Composed of the current cell and its neighboring cells (each cell corresponds to a component of the finite element model), using Let Ω represent the cell state of the i-th sub-region, where Ω is the i-th sub-region. i The state of the j-th cell within is shown by equation (1):

[0062]

[0063] In the formula, The i-th subregion Ω iThe material grade variable and thickness variable of the j-th cell within the unit are given. For the i-th subregion Ω i The local field variables of the j-th cell are calculated using the formula shown in equation (2):

[0064]

[0065] in, For the i-th subregion Ω i The internal energy or strain energy of the nth cell within the unit; The i-th subregion Ω i The thickness and surface area of ​​the nth cell within the unit cell; For the i-th subregion Ω i The set of neighboring cells of the j-th cell, the number of cells in the set is

[0066] S2, set constraint functions (design conditions to be met, designed according to specific requirements) and constraint boundaries (upper and lower limits of the constraint functions) under multiple working conditions, and define optimization variables including material variables, thickness variables and field variables (the field variable is internal energy density under collision conditions, and the field variable is strain energy density under stiffness conditions).

[0067] S3, enter the outer loop and perform the following steps:

[0068] S3.1, call the simulation software to carry out dynamic collision simulation analysis and stiffness simulation analysis, and obtain the information of the current cell, including the thickness, material, field variables and constraint violation amount of all cells (the difference between the response value and the constraint boundary under the corresponding condition constraint after finite element analysis).

[0069] S3.2, based on the constraint violation amount of the current design point (i.e., the target frame structure design, the initial loop is the initial frame structure design), the target quality and target cost of the frame structure under different working conditions are updated using a parallel strategy of bisection method and penalty function method, which is used for the inner loop; the parallel strategy of bisection method and penalty function method is as follows: based on the current design point, new design points generated by bisection method and penalty function respectively are used as design point candidates (candidate schemes). The response values ​​of the candidate points are analyzed by finite element method. If all candidate points are infeasible solutions (frame structure designs that do not meet all constraints), the solution with the smallest constraint violation amount is selected as the design point for the next iteration. If there is a feasible solution among the candidate points (frame structure designs that meet all constraints), the solution closest to the target cost and target quality among the feasible solutions is selected as the design point for the next iteration.

[0070] The binary search goal update rule is as follows: Taking quality update as an example, when the design point is a feasible solution, the outer loop decreases the target quality; when the design point is an infeasible solution, the outer loop increases the target quality; until one of two adjacent design points is a feasible solution and the other is an infeasible solution, the finite step size binary search method will continue to search for feasible solutions within the quality range of these two design points.

[0071] The specific steps are as follows:

[0072] S3.2.1, perform finite element simulation analysis at the initial point, and denote the initial mass of the frame structure within the discrete design space as M. *(0) If the design point is a feasible solution, the target mass M obtained in the first iteration update is... *(1) As shown in equation (3):

[0073] M *(1) =M *(0) -VM (3)

[0074] If the design point is an infeasible solution, the updated quality is as shown in equation (4):

[0075] M *(1) =M *(0) +VM (4)

[0076] Here, VM represents a predefined quantity of quality change.

[0077] S3.2.2, repeat S3.2.1. When one of two adjacent design points is a feasible solution and the other is an infeasible solution, continue to update the quality within the quality interval between these two different design points. With each iteration, the VM will be reduced to half of the quality change in the previous iteration. The VM is updated using equation (5):

[0078]

[0079] In the formula, p represents the number of iterations of the finite-step bisection method. and Defined as the iteration threshold of the finite step size bisection method, and

[0080] S3.2.3, when When the finite step size bisection method is terminated.

[0081] Penalty function update rule (taking cost update as an example): Based on the degree of constraint violation ΔC at the current design point in the outer loop. *(k) Update the target cost C of the k-th outer loop. *(k) .

[0082] S3.3, the target field variable function is constructed using an arbitrary and step-type parallel update strategy. A schematic diagram of the step-type target field variable function is shown below. Figure 2 As shown, the construction process of the step-type target field variable function is existing technology, and its specific form is as follows:

[0083]

[0084] in, The "step interval" in the k-th outer loop and the h-th inner loop [id] i-1 ,id i The target field variables within ]

[0085] A schematic diagram of arbitrary target field variable functions is shown below. Figure 3 As shown, the details are as follows:

[0086] S3.3.1, divide the arbitrary interval of the field variable based on the cell index (each cell is a separate interval).

[0087] S3.3.2, construct the Gaussian process regression model (GPR) of field variable (FV) with cost / quality and field variable with constraints, as shown in formula (7):

[0088]

[0089] Where FV is the field variable, It is a Gaussian process regression model of field variables and cost / quality. It is a Gaussian process regression model with field variables and the j-th constraint function, μ f (FV) and These are the mean values ​​of the objective function and the j-th constraint function, respectively, and k is the mean value of k. f (FV,FV * )and These are the covariance functions of the objective function and the j-th constraint function, respectively.

[0090] S3.3.3, with the minimization of structural cost and quality as the objective function and the performance of the finite element model as the constraint, the field variable optimization problem is constructed as shown in equation (8):

[0091]

[0092] Among them, cost *(k) and mass *(k) Let C represent the structural cost and structural mass in the k-th outer loop, respectively. *(k) and M *(k) These represent the target cost and target quality defined in the k-th outer loop, respectively.

[0093] S3.3.4, the non-dominated sorting genetic algorithm NSGA-II is used to optimize the field variable FV (i.e., to solve equation (8)) to obtain the target field variable of the "arbitrary interval" i in the k-th outer loop and the h-th inner loop. The field variables whose cost is closest to the target cost, whose quality is closest to the target quality, and which satisfy the constraints are selected as arbitrary target field variable functions, and the arbitrary target field variables are constructed as shown in equation (9):

[0094]

[0095] S4, enter the inner loop and perform the following steps:

[0096] S4.1, Set the basic weight ω for each working condition. base_lc .

[0097] S4.2, according to equations (10) and (11), update the field variables of control quality and control cost for each "step interval" in the inner loop respectively (this is the prior art):

[0098]

[0099] Among them, M *(k) and C *(k) M represents the target quality and target cost obtained from the k-th outer loop update, respectively; (h,k) and C (h,k) Let these represent the current quality and current cost obtained after the collaborative update of material and thickness in the k-th outer loop and the h-th inner loop, respectively. The target field variable represents the control cost of the k-th outer loop and the h-th inner loop. This represents the target field variable for controlling the quality of the k-th outer loop and the h-th inner loop.

[0100] S4.3, this invention introduces a density variable as an important parameter for controlling material selection, and regulates it using a field variable that controls mass; based on the cell material and thickness collaborative update rule, the cell material and cell thickness are updated under collision and stiffness conditions, resulting in a set of cell material and cell thickness solutions for each condition. The cell material and thickness collaborative update rule is as follows:

[0101] S4.3.1, Define the candidate material library, represented as (for prior art):

[0102]

[0103] Where, ρ s E represents the density of the s-th material in the candidate material library. s σ represents the elastic modulus of the s-th material in the candidate material library.ys σ represents the yield strength of the s-th material in the candidate material library. us This represents the tensile strength of the s-th material in the candidate material library. denoted as the flow stress of the s-th material in the candidate material library, l is the number of material grades, and n is the hardening index.

[0104] Assigning mechanical properties from the material library to cells based on current cellular materials:

[0105]

[0106] in, Let represent the density, elastic modulus, yield strength, tensile strength, and flow stress of the j-th cell in the i-th subregion during the k-th outer layer cycle and the h+1-th inner layer cycle, respectively.

[0107] S4.3.2, based on the local control rules for updating cell thickness and density (these rules are prior art and include the content of S4.2), the thickness and density of the current cell are updated, and the nominal flow stress of the current cell is updated according to the cell flow stress update rules (prior art).

[0108] S4.3.3, by comparing the actual density ρ of each material in the candidate material library. s The material type that is closest to the updated current cell density (S4.3.2) is selected as the candidate material type for the current cell.

[0109] S4.3.4: Compare the flow stress of all material grades among the candidate material types, and finally select the material grade that is closest to the nominal flow stress of the current cell after the update (S4.3.2) as the selected material of the current cell, and assign material information to the cell. The thickness of the current cell is the thickness updated in S4.3.2.

[0110] S4.4, the final cell material and thickness are determined based on the adaptive weight allocation rule for operating conditions. The specific steps are as follows:

[0111] S4.4.1, Based on S4.1, determine the basic weight ω for each working condition. base_lc .

[0112] S4.4.2, the formula for constraint violation under a single working condition is as follows:

[0113]

[0114] in, This represents the constraint violation amount under the lc-th operating condition. Let be the response value of the i-th constraint function under the lc-th working condition of the k-th outer loop. Let n be the constraint boundary of the i-th constraint function under the lc-th working condition. lc Let lc be the number of constraint functions under each working condition;

[0115] S4.4.3, Dynamically generate relative weights based on constraint violation quantities:

[0116]

[0117] in, This represents the relative weight under the k-th outer loop lc condition.

[0118] S4.4.4, Based on the relative weight coefficients, the final weight coefficients for each working condition are adaptively generated: Where λ1 represents the dynamic adjustment coefficient for constraint violation (empirical value, e.g., 0.5).

[0119] S4.4.5, Based on the response level of each component under different operating conditions, the weights of different operating conditions are adjusted in real time according to the final weight coefficients:

[0120]

[0121] in, Let J be the field variable of the j-th cell in the i-th sub-region under the lc-th operating condition during the k-th outer loop. λ is the mean of the field variables of the lc-th platform, and λ2 represents the dynamic adjustment coefficient of component importance.

[0122] Weights in S4.4.6 and S4.4.5 These are used as coefficients for the cell material grade and cell thickness under each working condition, respectively, to update the cell material grade and cell thickness under each working condition into a final set of materials and thicknesses.

[0123] S4.4.7, Based on the final materials and thickness, calculate the current mass and current cost of the frame structure:

[0124]

[0125] Among them, C (h+1,k) and M (h+1,k) Let $\mathbf$ represent the cost and $\mathbf$ of the $j$-th cell in the $i$-th subregion during the $k$-th outer loop and the $h+1$-th inner loop, respectively. Let be the final material price of the j-th cell in the i-th sub-region during the k-th outer cycle and the (h+1)-th inner cycle. Let be the final material density of the j-th cell within the i-th sub-region during the k-th outer layer cycle and the (h+1)-th inner layer cycle. Let be the thickness of the j-th cell within the i-th sub-region. Let be the area of ​​the j-th cell within the i-th subregion.

[0126] In step S4.5, to enable more precise control of the coordinated updating of material and thickness variables in the next iteration (S4.3.2), an adaptive correction strategy for cellular field variables is proposed based on the elastoplastic material property curves. This strategy is used to update field variables under different working conditions (internal energy density under collision conditions and strain energy density under stiffness conditions).

[0127] Under collision conditions, the adaptive correction strategy formula for the intracellular energy density field variable is as follows:

[0128]

[0129] Under stiffness conditions, the formula for the adaptive correction strategy of cellular strain energy density update is:

[0130]

[0131] in, Let be the yield strength of the cellular material of the j-th cell in the i-th subregion during the k-th outer layer cycle and the h-th inner layer cycle. Let be the tensile strength of the cellular material of the j-th cell in the i-th subregion during the k-th outer layer cycle and the h-th inner layer cycle. Let be the cell material density of the j-th cell in the i-th sub-region during the k-th outer layer cycle and the h-th inner layer cycle. Let be the elastic modulus of the cellular material of the j-th cell in the i-th subregion during the k-th outer layer cycle and the h-th inner layer cycle. This is an estimate of the maximum elastic strain energy density of the current cell. This is an estimate of the plastic strain energy density of the current cell. This is the field variable of the current cell.

[0132] S4.6, determine whether the inner loop has converged based on the inner loop convergence condition. If it has not converged, return to S4.2. If it has converged, exit the inner loop and execute S4.7. The convergence condition of the inner loop is shown in equation (20):

[0133] |M (h,k) -M *(k) |+|C (h,k) -C *(k) |<ε1 or k1≥k 1max (20)

[0134] In the formula, M (h,k) and C (h,k)These are the structural quality and cost obtained from k iterations and h inner iterations, respectively. ε1 is the quality convergence factor (typically taken as 0.001), and k1 represents the number of iterations in the inner loop. 1max This indicates the maximum number of iterations in the inner loop.

[0135] S4.7, determine whether the global convergence is achieved based on the global convergence condition: if the convergence condition is not met, return to S3; if the global convergence condition is met, the material and thickness co-optimization method converges and the optimization result is output.

[0136] The material and thickness co-optimization method converges if any one of the following three convergence conditions is met:

[0137] (1) The number of iterations k of the outer loop (i.e. the number of finite element simulation analyses) exceeds the predefined maximum number of iterations k. max .

[0138] (2) When the number of times an infeasible solution appears, p, is greater than the initially set maximum number of iterations for consecutive occurrences of infeasible solutions. Furthermore, the current design point is still considered an "infeasible solution".

[0139] (3) When the design variable, nominal flow stress, and thickness variation are very small, that is, when the variation is satisfied... in, and Let N and ε2 represent the nominal flow stress and thickness of the j-th cell in the i-th subregion during the k-th outer layer cycle, respectively. N represents the total number of cells, and ε2 is the global convergence factor (typically taken as 0.001).

[0140] S5 uses the optimization results output by S4.7 as a benchmark to design the framework structure.

[0141] Example

[0142] Taking the vehicle body frame as an example, collision conditions (side impact, side pole impact, and top compression) and stiffness conditions (bending stiffness and torsional stiffness) are introduced. The method of this invention is used to collaboratively optimize the thickness and material of the vehicle body frame. The convergence and efficiency of the method are verified by comparing it with the MOBO optimization algorithm. The finite element models of the vehicle body frame under the five conditions in this embodiment are as follows:

[0143] Side impact scenario: In accordance with the regulations for occupant protection in side impacts of automobiles (GB 20071-2006), the moving deformable barrier vehicle weighs 950 kg and impacts the target vehicle perpendicularly at an initial speed of 50 km / h. Figure 4 As shown, the contact algorithm used between the moving barrier vehicle and the vehicle being collided with is surface-to-surface contact.

[0144] Side pole impact scenario: In accordance with the regulations for occupant protection in side pole collisions of automobiles (GB / T 37337—2019), a rigid pole is deployed and impacts the target vehicle perpendicularly at an initial speed of 32 km / h. Figure 5 As shown.

[0145] Top compression test: In accordance with the regulations for "Roof Compression Strength of Passenger Cars" (GB 26134-2010), a rigid pressure plate is used to apply a load to the test vehicle at a speed of 5 mm / s. The load displacement must be greater than or equal to 127 mm. The roof compression strength rating is evaluated by the ratio of the peak load measured within the 127 mm displacement range to the vehicle weight (curb weight; in this invention, the actual vehicle weight is 1421 kg). Figure 6 As shown.

[0146] Bending stiffness condition: The boundary conditions of the finite element model for the bending stiffness condition are set according to the loading conditions of the bending stiffness test. The translational degrees of freedom in the X, Y, and Z directions of the center points of the front left and right shock absorber towers and the translational degree of freedom in the Z direction of the center points of the rear left and right shock absorber towers are constrained. A force of 1668 N (approximately the weight of a single normal occupant) is applied to the R point of each front seat. Similarly, a force of 5004 N is applied to the three rear seats in the Z direction. Figure 7 As shown.

[0147] Torsional stiffness condition: The boundary conditions of the finite element model for the torsional stiffness condition are set according to the loading conditions required by the torsional stiffness test: constraining the translational degrees of freedom in the Z direction of the center point of the front anti-collision beam, the translational degrees of freedom in the X, Y, and Z directions of the center point of the left rear shock absorber tower, and the translational degrees of freedom in the X and Z directions of the center point of the right rear shock absorber tower. Apply forces of equal magnitude but opposite direction in the Z direction, with a magnitude of 1000 N, to the center points of the left and right front suspensions. Figure 8 As shown.

[0148] Under combined collision and stiffness conditions, the B-pillar, sill, doors, and roof crossbeams are the main energy-absorbing structures in side and pole impacts, while the A-pillar, upper side beam, and seat crossbeams are used to transfer impact loads. In top compression, the roof crossbeam and upper side beam must have sufficient strength to prevent structural collapse. Meanwhile, the overall torsional and bending stiffness of the vehicle body are closely related to core components such as the A-pillar, B-pillar, sill, and longitudinal beams. Therefore, this embodiment defines the material grade and thickness of 34 parts from 14 key structural components, including the A-pillar, B-pillar, sill, upper side beam, doors, front and rear longitudinal beams, seat crossbeams, and roof crossbeam, as design variables. The candidate material library information for these material variables is shown in Table 1. Based on the topological connection characteristics of the vehicle body structure, a sub-regional cellular automaton model is defined for the body beam skeleton, and cells are numbered sequentially from smallest to largest according to the principles of inside to outside, front to back, and bottom to top.

[0149] Table 1. Candidate Material Library Information

[0150]

[0151] In this embodiment, the objective function is to minimize the total cost and total mass of 34 parts. Considering the passenger safety, under the side collision condition, the constraints are the chest intrusion amount d1(Mat,t) corresponding to the B-pillar, the chest intrusion velocity v1(Mat,t) corresponding to the B-pillar, the pelvic intrusion amount d2(Mat,t) corresponding to the B-pillar, and the pelvic intrusion velocity v2(Mat,t) corresponding to the B-pillar. Under the side pole collision condition, the constraints are the chest intrusion amount d3(Mat,t) corresponding to the B-pillar, the pelvic intrusion amount d4(Mat,t), the chest intrusion amount d5(Mat,t) corresponding to the door, and the pelvic intrusion amount d6(Mat,t) corresponding to the door. Here, the chest position of the B-pillar refers to point A on the inner panel of the B-pillar, which is parallel to the passenger's chest position, and the pelvic position of the B-pillar refers to point B on the inner panel of the B-pillar, which is parallel to the passenger's pelvic position. Figure 9 As shown; under the top compressive condition, SWR is used as the constraint; under the stiffness condition, the bending stiffness K is used. b and torsional stiffness K t As a constraint function, in order to meet the requirements of the "Occupant Protection in Side Collision of Automobiles" (GB 20071-2006) regulations, the corresponding objective function is shown in equation (21).

[0152]

[0153] Where, x L As the lower bound of the design variable, x U To design an upper limit for variables.

[0154] In this embodiment, the optimization design problem of equation (19) is solved simultaneously using the method of this invention and the MOBO algorithm. The initial sample size of MOBO is set to 8, and the maximum number of iterations for both methods is set to 50. Each iteration adopts a parallel scheme, updating 4 sample points each time. The optimization ends when both methods converge. The optimization method proposed in this invention significantly improves the material distribution of the vehicle body beam frame. As shown in Table 2, after optimization, the method of this invention achieves reasonable material reinforcement in the key load-bearing areas, while scientifically thinning the material in non-critical parts. This optimization strategy not only effectively reduces the weight of the vehicle body and achieves the lightweight goal, but also further improves the overall structural performance by optimizing the material distribution.

[0155] Table 2 Comparison of vehicle frame material distribution before and after optimization

[0156]

[0157]

[0158] Table 3 Comparison of efficiency and accuracy of the method of this invention and the MOBO algorithm.

[0159]

[0160] Table 3 compares the efficiency and accuracy of the two algorithms. Figures 10(a) and 10(b) show the cost and mass iteration curves of the optimization method of this invention, respectively. Figures 11(a) and 11(b) show the cost and mass iteration curves of the MOBO algorithm, respectively. The figures show that the optimization method of this invention converges after 13 iterations, finding the optimal solution in the 6th iteration, while the MOBO algorithm converges after 50 iterations, finding the optimal solution in the 25th iteration. This indicates that the optimization method proposed in this invention has stronger search efficiency and faster convergence speed. After optimization using the method proposed in this invention, the total cost of 34 body parts is reduced to 1265.3 yuan, a decrease of 3.42% compared to the initial design, and the total mass is reduced to 101.9 kg, a decrease of 5.82%. In contrast, MOBO's optimization ability is insufficient, with the total cost increasing to 1733.75 yuan, an increase of 32.34%, and the mass increasing to 127.52 kg, an increase of 17.86%. Figure 12 As shown, by comparing the Pareto front distributions of the method of this invention and the MOBO algorithm, it can be found that although the MOBO algorithm can approximately converge to the Pareto front, its optimization performance has obvious bottlenecks. In contrast, the method of this invention not only breaks through the search boundary limitations of traditional algorithms, but also achieves a better synergistic balance between the two optimization objectives of quality and cost, fully verifying that the method has a superior global optimization capability when dealing with multi-objective, high-dimensional complex optimization problems.

[0161] Table 4 shows a comparison of the vehicle body beam frame performance before and after optimization using the two algorithms. The method of this invention significantly improves the vehicle body's energy absorption and structural protection performance. In side impact conditions, the maximum intrusion at the B-pillar chest and pelvic positions decreased by 35.97% and 36.66% respectively compared to the initial design; the intrusion velocity at the B-pillar chest and pelvic positions decreased by 8.31% and 16.39% respectively; in side pole impact conditions, the optimized intrusion at key B-pillar and door positions improved by 13%–29%; in top compression conditions, the ratio of peak load to vehicle weight was reduced from the initial 4.2 to 3.7, controlling the structural stiffness distribution while meeting regulatory requirements; in stiffness conditions, the bending stiffness increased to 16209.77 N / mm, and the torsional stiffness increased to 5539.83 N·m / deg.

[0162] Table 4. Percentage performance improvement before and after optimization

[0163]

[0164] For the MOBO algorithm, in the side impact test, the maximum intrusion at the B-pillar chest and pelvic positions decreased by 50.63% and 43.90% respectively compared to the initial design. After optimization, the intrusion velocities at the chest and pelvic positions decreased by 43.90% and 17.59% respectively. In the side pole impact test, the optimized intrusion at the critical B-pillar position improved by approximately 37%, while the improvement at the critical door position was between 18% and 22%, indicating good crashworthiness after optimization. However, in the top compression test, the peak load to vehicle weight ratio increased to 5.6. In the stiffness test, the body bending stiffness increased to 16118.23 N / mm, and the torsional stiffness increased to 6145.1 N·m / deg. Some indicators show that the MOBO algorithm is slightly better than the optimization method proposed in this invention, but the mass and cost of the body beam frame increased after optimization using the MOBO algorithm. A schematic diagram of the material and thickness distribution of the body beam frame before and after optimization using the method of this invention is shown below. Figure 13 and Figure 14 As shown, under the coordinated optimization strategy of materials and thickness, the structural role and performance potential of each component under different platform conditions were fully explored. The optimization results not only effectively reduced the cost and weight of the whole vehicle, but also ensured collision safety and structural stiffness.

[0165] In summary, the optimization method proposed in this invention achieves a good balance between cost, quality, and structural performance, exhibiting higher algorithm stability and engineering applicability. It is particularly suitable for dual-objective, strongly constrained collaborative optimization scenarios involving collision safety and structural stiffness.

[0166] The embodiments described above are preferred embodiments of the present invention, but the present invention is not limited to the above embodiments. Any obvious improvements, substitutions or modifications that can be made by those skilled in the art without departing from the essence of the present invention shall fall within the protection scope of the present invention.

Claims

1. A frame structure design method for co-optimization of materials and thickness under multiple working conditions, characterized in that: Construct a finite element model of the framework structure, and build a sub-region cellular automaton model based on the finite element model; Set constraint functions and constraint boundaries for the frame structure under different working conditions, and define optimization variables: material variables, thickness variables, and field variables; Outer loop: Call simulation software to perform dynamic collision simulation analysis and stiffness simulation analysis to obtain information about the current frame structure, including the thickness of all cells, materials, field variables and constraint violations; based on the constraint violations at the current design point, use a parallel strategy of bisection method and penalty function method to update the target mass and target cost of the frame structure under different working conditions, and use an arbitrary and step-parallel update strategy to construct the target field variable function for the inner loop; Inner loop: Update each "step interval" in the inner loop [id] i-1 id i The field variables for controlling quality and the field variables for controlling cost are used for the collaborative update rules of cell material and thickness. Based on the target quality and target cost, the cell thickness and material under different working conditions are updated through the collaborative update rules of cell material and thickness, and the final cell thickness and material are determined according to the working condition adaptive allocation rules. The inner loop converges based on its convergence condition. If it does not converge, the loop returns to the inner loop; otherwise, it exits the inner loop. The global loop converges based on its convergence condition. If it does not converge, the loop returns to the outer loop; otherwise, the optimization result is output for designing the framework structure.

2. The frame structure design method for multi-condition material and thickness synergistic optimization according to claim 1, characterized in that, The arbitrary target field variable function is: in, The target field variable of the "arbitrary interval" i in the kth outer loop and the hth inner loop.

3. The frame structure design method for multi-condition material and thickness synergistic optimization according to claim 1, characterized in that, The collaborative update rule for cell material and thickness is as follows: Define a candidate material library and assign mechanical properties of the material library to the cells based on the current cell material; The local control rules based on cell thickness and density update the thickness and density of the current cell, and update the nominal flow stress of the current cell according to the cell flow stress update rules. By comparing the actual density of each material in the candidate material library, the material type that is closest to the updated current cell density is selected as the candidate material type for the current cell. The flow stress of all material grades is compared among the candidate material types. Finally, the material grade that is closest to the nominal flow stress of the current cell after the update is selected as the selected material for the current cell, and the cell material information is assigned. The thickness of the current cell is the updated thickness.

4. The frame structure design method for multi-condition material and thickness synergistic optimization according to claim 1, characterized in that, The adaptive allocation rule for the working condition determines the final cell thickness and material, specifically as follows: Based on the response level of each component under different operating conditions, the weights for different operating conditions are adjusted in real time according to the final weighting coefficients: in, Let J be the field variable of the j-th cell in the i-th sub-region under the lc-th operating condition during the k-th outer loop. Let λ be the mean of the field variables of the lc-th platform, and λ2 represent the dynamic adjustment coefficient for component importance; Weight These are used as coefficients for the cell material grade and cell thickness under each working condition, respectively, to update the cell material grade and cell thickness under each working condition into a final set of materials and thicknesses.

5. The frame structure design method for multi-condition material and thickness synergistic optimization according to claim 4, characterized in that, Final weighting coefficients Where λ1 represents the dynamic adjustment coefficient for constraint violation. ω represents the relative weight under the k-th outer loop lc condition. base_lc The basic weights for each operating condition.

6. The frame structure design method for multi-condition material and thickness synergistic optimization according to claim 5, characterized in that, Relative weights under the kth outer loop lc condition in, This represents the constraint violation amount under the lc-th operating condition.

7. The frame structure design method for multi-condition material and thickness synergistic optimization according to claim 6, characterized in that, Constraint violation amount under the lcth operating condition in, Let be the response value of the i-th constraint function under the lc-th working condition of the k-th outer loop. Let n be the constraint boundary of the i-th constraint function under the lc-th working condition. lc Let lc be the number of constraint functions under each of the lc operating conditions.

8. The frame structure design method for multi-condition material and thickness synergistic optimization according to claim 3, characterized in that, In order to more accurately regulate the coordinated updating of cell material and thickness variables in the next iteration by the local control rules for cell thickness and density updates, an adaptive correction strategy for cell field variables is used to update field variables under different working conditions. Specifically, the field variable under the collision condition is the internal energy density, and the field variable under the stiffness condition is the strain energy density.

9. The frame structure design method for multi-condition material and thickness synergistic optimization according to claim 8, characterized in that, Under collision conditions, the adaptive correction strategy formula for the intracellular energy density field variable is as follows: in, Let be the yield strength of the cellular material of the j-th cell in the i-th subregion during the k-th outer layer cycle and the h-th inner layer cycle. Let be the tensile strength of the cellular material of the j-th cell in the i-th subregion during the k-th outer layer cycle and the h-th inner layer cycle. Let be the cell material density of the j-th cell in the i-th sub-region during the k-th outer layer cycle and the h-th inner layer cycle. Let be the elastic modulus of the cellular material of the j-th cell in the i-th subregion during the k-th outer layer cycle and the h-th inner layer cycle. This is an estimate of the maximum elastic strain energy density of the current cell. This is an estimate of the plastic strain energy density of the current cell. This is the field variable of the current cell.

10. The frame structure design method for multi-condition material and thickness synergistic optimization according to claim 9, characterized in that, Under stiffness conditions, the formula for the adaptive correction strategy of cellular strain energy density update is:

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