Nonlinear robust topology optimization method for anti-explosion stiffened structure

Abstract

The application provides a kind of anti-explosion stiffened structure nonlinear robust topology optimization method, first to the anti-explosion stiffened structure to be optimized, according to the design requirement, determine the noise factor and fluctuation, select the appropriate taguchi design envelope, then establish the corresponding finite element model based on taguchi design envelope, construct anti-explosion stiffened structure nonlinear robust topology optimization design mathematical model, with design variable strain energy density signal-to-noise ratio as sensitivity, nonlinear robust topology optimization design is carried out using energy-based topology optimization algorithm, to determine the stiffened position of anti-explosion stiffened structure. The application deeply considers the influence of the uncertainty of design parameters on the topology optimization design of anti-explosion stiffened structure in the process of nonlinear topology optimization design, improves the reliability of design results to the uncertainty of design parameters, and ensures the safety of design.

Description

Technical Field

[0001] This invention belongs to the field of explosion-proof reinforced structure technology, specifically relating to a nonlinear robust topology optimization method for explosion-proof reinforced structures. Background Technology

[0002] Research on protective structures is crucial for protecting personnel and facilities from blast damage. As a commonly used type of protective structure, stiffened plates have been widely applied in civilian and military fields, such as ship hulls, offshore structures, box girders, oil and gas storage tanks, and explosion-proof vehicle flooring. Compared to flat plates, stiffened plates with reinforcing ribs are considered more effective in improving load-bearing capacity and are lighter in weight. However, most research on the blast-proof performance of stiffened structures focuses on a few given stiffened plate structures, which are generally devised based on experience, and the topologies considered are relatively simple. How to design stiffening topologies to achieve better blast-proof results remains a rather challenging problem for designers.

[0003] Furthermore, practical engineering problems often involve numerous uncertainties, such as material properties and geometric dimensions. These parameters frequently exhibit random fluctuations, and if the product design is sensitive to these fluctuations, the product design quality may deviate from the design objectives. Significant fluctuations can severely impact the stability of product quality. Robust design, by rationally designing parameter combinations, can improve design robustness and reduce fluctuations while simultaneously finding the optimal target value. However, the computational efficiency of current robust algorithms remains significantly lower than that of deterministic topology optimization, limiting their practical engineering applications. Therefore, research into highly efficient robust topology optimization algorithms is still necessary. To efficiently solve nonlinear topology optimization design problems with uncertainties in engineering, this patent develops a nonlinear robust topology optimization method based on the Taguchi method for explosion-proof stiffened plates. Summary of the Invention

[0004] The purpose of this invention is to provide a nonlinear robust topology optimization method for explosion-proof reinforced structures, which can efficiently and quickly design the topology configuration of explosion-proof reinforced structures.

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

[0006] A nonlinear robust topology optimization method for explosion-proof reinforced structures includes the following steps:

[0007] Step 1: Determine the dimensional and mechanical parameters of the explosion-proof reinforced structure: The mechanical parameters are the load magnitude, noise factor and fluctuation, material parameters and numerical simulation initial and boundary conditions determined according to the design requirements of the explosion-proof reinforced structure.

[0008] Step 2: Based on the noise factors and fluctuations, determine the number of noise factors and the number of levels. Use the Latin square sampling method to determine the Taguchi design surface. Based on the number of experiments in the Taguchi design surface and the dimensional and mechanical parameters of the explosion-proof reinforced structure, establish corresponding finite element models of the same number. Each finite element model is the same except for the noise factor parameters listed in the Taguchi design surface.

[0009] Step 3: Based on the established finite element model, construct a robust topology optimization design mathematical model for the explosion-proof reinforced structure, and use the design variable strain energy density signal-to-noise ratio as the sensitivity for nonlinear robust topology optimization design.

[0010] Step 4: Using a topology optimization algorithm based on element energy, combined with LS-DYNA, LS-PrePost and Matlab software, nonlinear robust topology optimization design is performed based on the topology optimization mathematical model in Step 3 and the finite element model of the explosion-proof reinforced structure in Step 2 to determine the reinforcement location of the explosion-proof reinforced structure.

[0011] Step 5: Determine whether the design result meets the application scenario requirements; if not, repeat step 4 until the requirements are met, and finally output the optimal design solution.

[0012] Furthermore, the mathematical model in step 3 is as follows:

[0013]

[0014] In the formula, SNR i The signal-to-noise ratio of strain energy density for the i-th design variable is represented by N, where N represents the number of design variables, Q is the number of finite element models determined based on the Taguchi design surface, and m is the number of finite element models. ij M represents the mass of the i-th design variable in the j-th finite element model. * To optimize the total mass of the initial explosion-proof reinforced structural stiffener, w represents the mass fraction, and x... i This represents the presence or absence of the i-th element; 0 indicates deletion of the i-th element, and 1 indicates retention of the i-th element. The design variable, strain energy signal-to-noise ratio (SNR), is... i This is an indicator used to measure product robustness. This invention aims to maximize the target by selecting the signal-to-noise ratio with large amplitude characteristics for calculation, and its specific representation is as follows: Where α ij This represents the strain energy density of the i-th design variable in the j-th finite element model. The strain energy density can be expressed by the formula... Obtained, of which E ij Let represent the strain energy of the i-th design variable in the j-th finite element model.

[0015] Furthermore, the specific implementation process of step 4 is as follows:

[0016] Step 4.1: For the explosion-proof reinforced structure to be optimized, specify the initial thickness as a design variable. Determine the convergence condition, which 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:

[0017]

[0018] Where g is a positive number, ε is the convergence tolerance (typically g is 5), and error is the error rate.

[0019] This represents the average change in the objective function over the 10 iterations prior to the k-th iteration. The specific value can be adjusted based on the optimization case.

[0020] Step 4.2: In each iteration, finite element simulations are performed using LS-DYNA software based on the Taguchi design surface. Using Matlab and LS-PrePost software, the necessary data for each design variable, such as strain energy, thickness, and mass, are obtained from the finite element analysis results file. The extracted data is then processed to calculate the strain energy density. After completing all finite element analyses based on the Taguchi design surface, the obtained data is used to calculate the strain energy density signal-to-noise ratio (SNR) value for each design variable in each iteration, according to the SNR formula.

[0021] Step 4.3: To reduce oscillations during the iteration process, the strain energy density signal-to-noise ratio of the i-th design variable in the current k-th iteration is updated by weighting the sum of the first three iterations.

[0022] Step 4.4: According to the formula Update the design variable thickness;

[0023] Where, 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; SNR c To control the threshold, the threshold SNR is controlled during the iteration process. c Adjustments can be made as needed based on the following process:

[0024] 4.4.1: Obtain SNR min =min[SNR] i SNR max =max[SNR i ];

[0025] 4.4.2: Calculate SNR c=(SNR) min +SNR max ) / 2;

[0026] 4.4.3: Update design variable x i And calculate the total mass of the current structural design variables. if Update SNR max =SNR c Otherwise update SNR min =SNR c ;

[0027] 4.4.4: Repeat steps 4.4.2 to 4.4.3 until the quality convergence condition is met:

[0028]

[0029] Where τ is the convergence tolerance value, the size of which can be defined according to the optimization case.

[0030] Step 4.5: Determine if the convergence condition is met. If it is met, terminate the optimization; otherwise, repeat steps 4.2-4.5.

[0031] Step 4.6: Output the optimal design scheme.

[0032] Compared with the prior art, the technical solution of the present invention has the following beneficial effects:

[0033] (1) In the process of nonlinear topology optimization design, this scheme takes into account the impact of the uncertainty of design parameters on the nonlinear topology optimization design of explosion-proof reinforced structure, improves the reliability of design results to the uncertainty of design parameters, and ensures the safety of design.

[0034] (2) The method is simple and flexible, and can effectively handle the nonlinear robust topology optimization problem of explosion-proof reinforced structure, significantly shorten the design cycle and development cost of explosion-proof reinforced structure, and greatly improve the performance robustness of explosion-proof reinforced structure. Attached Figure Description

[0035] Figure 1 This is a flowchart of the present invention;

[0036] Figure 2 Schematic diagram of the design domain and dimensions for the explosion-proof reinforced structure;

[0037] Figure 3 The optimal reinforcement form is determined through nonlinear robust topology optimization for explosion-proof reinforced structures. Detailed Implementation

[0038] Now Figure 2The method proposed in this invention will be illustrated using the design of the explosion-proof reinforced structure shown as an example. In this embodiment, the research object is a reinforced plate under explosive load, and the main research objective is to optimize the arrangement of the reinforcing ribs in the reinforced plate.

[0039] Step 1: The front panel of the explosion-proof reinforced plate has a square shape with dimensions L×L=300mm×300mm, and the thickness of the plate and reinforcing ribs is T=1mm. Numerical simulation of the reinforced plate is performed using the explicit nonlinear processor LS-DYNA. The reinforced plate is completely fixed on all four sides. Under impact load, the effective area of ​​the reinforced plate is 300mm×300mm, and the material used for the reinforced plate is 304 stainless steel. The CONWEP algorithm is used to simulate the explosion load. In the numerical simulation, the shape of the explosion load is set to spherical, and the detonation distance is 100mm. The detonation point is located 100mm above the center point of the reinforced plate. Assuming the coordinates of the center point of the reinforced plate are (0,0,0), the coordinates of the detonation point are (0,0,100).

[0040] Step 2: The noise factor is the distribution along the x-axis of the detonation point of a single variable explosive. Assuming that the variation range of all noise factors is (0±7.5), Latin square sampling is used to sample the noise factors. The specific Taguchi design surface is shown in Table 1. Based on the determined Taguchi design surface, five finite element models are established by combining the dimensional and mechanical parameters of the explosion-proof reinforced structure. Each finite element model is the same except for the noise factor parameters listed in the Taguchi design surface.

[0041] Table 1. Taguchi Design Exterior

[0042]

[0043] Step 3: Based on the established finite element model, construct a robust topology optimization design mathematical model for the explosion-proof reinforced structure, using the signal-to-noise ratio of the design variable strain energy density as the sensitivity.

[0044]

[0045] In the formula, SNR i The signal-to-noise ratio of strain energy density represents the i-th design variable, and the specific calculation method is as follows: Where α ij This represents the strain energy density of the i-th design variable in the j-th finite element model. Q is the number of finite element models determined based on the Taguchi design surface; in this case, there are 5. Each iteration performs finite element analysis on the 5 established finite element models, then extracts the necessary data such as strain energy, thickness, and mass for each design variable. The extracted data is processed to calculate the strain energy density, and then the signal-to-noise ratio of the design variable strain energy density is calculated. The number of design variables is 10000; m ijM is the mass of the i-th design variable in the j-th finite element model; * To optimize the total mass of the initial explosion-proof reinforced structural stiffeners; x i It is the thickness of the i-th design variable, with a mass fraction w of 0.5.

[0046] Step 4: Using a topology optimization algorithm based on element energy, combined with LS-DYNA, LS-PrePost and Matlab software, nonlinear robust topology optimization design is performed based on the topology optimization mathematical model in Step 3 and the finite element model of the explosion-proof reinforced structure in Step 2 to determine the reinforcement location of the explosion-proof reinforced structure.

[0047] Step 5: Determine if the design result meets the application scenario requirements; if not, repeat step 4 until the requirements are met. The final optimal design solution is as follows: Figure 3 As shown.

Claims

1. A nonlinear robust topology optimization method for explosion-proof reinforced structures, characterized in that, Includes the following steps: Step 1: Determine the dimensional and mechanical parameters of the explosion-proof reinforced structure: The mechanical parameters are the load magnitude, noise factor and fluctuation, material parameters and numerical simulation initial and boundary conditions determined according to the design requirements of the explosion-proof reinforced structure. Step 2: Based on the noise factors and fluctuations, determine the number of noise factors and the number of levels. Use the Latin square sampling method to determine the Taguchi design surface. Based on the number of experiments in the Taguchi design surface and the size and mechanical parameters of the explosion-proof reinforced structure, establish corresponding finite element models of the same number. Each finite element model is the same except for the noise factor parameters listed in the Taguchi design surface. Step 3: Based on the established finite element model, construct a nonlinear robust topology optimization design mathematical model for the explosion-proof reinforced structure, and use the signal-to-noise ratio of the design variable strain energy density as the sensitivity for nonlinear robust topology optimization design. The mathematical model for the nonlinear robust topology optimization design of the explosion-proof reinforced structure is as follows: In the formula Represents the signal-to-noise ratio of strain energy density for the i-th design variable, where N represents the number of design variables. The number of finite element models is determined based on the exterior design of Taguchi. This represents the quality of the i-th design variable in the j-th finite element model. To optimize the total mass of the initial explosion-proof reinforced structural stiffeners, w represents the mass fraction. This represents the presence or absence of the i-th unit; 0 means deleting the i-th unit, and 1 means keeping the i-th unit. Design variable strain energy density signal-to-noise ratio It is a metric used to measure product robustness, calculated using the signal-to-noise ratio (SNR) characteristic of large-scale applications, and its specific representation is as follows: ,in Let represent the strain energy density of the i-th design variable in the j-th finite element model; Step 4: Using a topology optimization algorithm based on element energy, combined with LS-DYNA, LS-PrePost and Matlab software, nonlinear robust topology optimization design is performed based on the topology optimization mathematical model in Step 3 and the finite element model of the explosion-proof reinforced structure in Step 2 to determine the reinforcement position of the explosion-proof reinforced structure. Step 5: Determine whether the design result meets the application scenario requirements; if not, repeat step 4 until the requirements are met, and finally output the optimal design solution.

2. The nonlinear robust topology optimization method for explosion-proof reinforced structures as described in claim 1, characterized in that, The specific implementation process of step 4 is as follows: Step 4.1: For the explosion-proof reinforced structure to be optimized, specify the initial thickness as a design variable 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, and error represents the average change of the objective function during the g iterations before the k-th iteration. The specific value can be adjusted according to the optimization case. Step 4.2: In each iteration, based on the Taguchi design surface, the established finite element model is sequentially simulated using LS-DYNA software. Using Matlab and LS-PrePost software, strain energy, thickness, and mass data for each design variable are obtained from the finite element analysis results file. The extracted data is then processed to calculate the strain energy density. After completing all finite element analyses based on the Taguchi design surface, the obtained data is combined with the signal-to-noise ratio formula to calculate the strain energy density signal-to-noise ratio value for each design variable in each iteration. Step 4.3: To reduce oscillations during the iteration process, the strain energy density signal-to-noise ratio of the i-th design variable in the current k-th iteration is updated by the weighted sum of the current iteration and the previous two iterations. ; Step 4.4: 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 4.5: Determine if the convergence condition is met. If it is met, terminate the optimization; otherwise, repeat steps 4.2-4.

5. Step 4.6: Output the optimal design scheme.

3. The nonlinear robust topology optimization method for explosion-proof reinforced structures as described in claim 2, characterized in that, In step 4.4, during the iteration process, the control threshold is... Make timely adjustments according to the following process: Step 4.4.1: Take , ; Step 4.4.2: Calculation ; Step 4.4.3: Update design variables And calculate the total mass of the current structural design variables. ;if ,renew Otherwise update ; Step 4.4.4: Repeat steps 4.4.2 to 4.4.3 until the quality convergence condition is met. in This is the convergence tolerance value.

4. A nonlinear robust topology optimization method for explosion-proof reinforced structures as described in claim 2 or 3, characterized in that, In step 4.1, g is set to 5.

5. A nonlinear robust topology optimization method for explosion-proof reinforced structures as described in claim 1, 2, or 3, characterized in that, The strain energy density is obtained through the formula Obtain, among which Let represent the strain energy of the i-th design variable in the j-th finite element model.

6. The nonlinear robust topology optimization method for explosion-proof reinforced structures as described in claim 4, characterized in that, The strain energy density can be expressed by the formula Obtain, among which Let represent the strain energy of the i-th design variable in the j-th finite element model.

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