Failure safety topological optimization design method under dynamic load

Abstract

The invention provides a failure safety topology optimization design method under a dynamic load. The method comprises the following steps: step 1, defining a design domain and design parameters of a structure; 2, performing transient dynamic analysis on the structure; 3, calculating to obtain an equivalent static load of the dynamic load; 4, performing failure safety topological optimization design on the model under the equivalent static load; the maximum flexibility of the minimization structure under the local failure condition is taken as an optimization target; carrying out optimization iteration on the design variable unit density by using a moving asymptote method until the internal loop failure safety topological optimization process is finished; and 5, according to the design variable updated after the failure safety topological optimization, judging whether an outer circulation convergence condition is met or not. According to the method, the possible local failure condition of the structure is fully considered in the design process, and the performance of the structure under the local failure condition is improved; the dynamic load under the original working condition is converted into the static load through the equivalent static load method, and the calculation efficiency of the optimization process is effectively improved.

Description

Technical Field

[0001] The present invention relates to the technical field of mechanical engineering, and particularly relates to a failure-safe topology optimization design method under dynamic loads. Background Art

[0002] Optimization design methods include size optimization, shape optimization, and topology optimization. Among them, topology optimization can change the material distribution in the design domain according to the constraint conditions and objective function, obtain the optimal material distribution under this working condition, and at the same time achieve weight reduction and performance optimization of the structure. Common topology optimization methods include the homogenization method, the variable density method, the progressive optimization method, etc. At present, topology optimization is mostly applied to the structural optimization under static loads.

[0003] For the structures of transportation equipment, there are many dynamic load conditions such as impact and vibration. Under such working conditions, the structure is prone to local failure, seriously affecting the structural performance. For the structure under dynamic load conditions, due to the complexity of the load conditions, the equivalent static load method is a method of converting the dynamic load received by the structure into an equivalent static load. The equivalent static load obtained by this method can make the structure produce the same displacement as the original dynamic load, thus simplifying the solution of the problem.

[0004] Failure-safe topology optimization, based on topology optimization design, introduces the possible local failure conditions of the structure into the design, so as to ensure that the structure can still guarantee its performance under local failure conditions and achieve safe redundancy design. Failure-safe topology optimization, based on topology optimization design, introduces the possible local failure conditions of the structure into the design, so as to ensure that the structure can still guarantee its performance under local failure conditions and achieve safe redundancy design.

[0005] The invention patent with publication number CN201610807923 discloses an equivalent static load method dynamic response topology optimization method for improving the bidirectional progressive method. The improved bidirectional progressive method is applied to the equivalent static load method, which improves the optimization calculation efficiency and simplifies the optimization process. However, the safety redundancy of the optimized structure is small. If the structure undergoes local failure under dynamic loads, the structural safety will face challenges. The invention patent with publication number CN202410168312 discloses a multi-phase material structure dynamic topology optimization method based on the equivalent static load method. The equivalent static load method is used to replace the time variable with a static variable, and the multi-phase material structure dynamic topology optimization problem is transformed into a multi-phase material structure static topology optimization model under multiple working conditions, effectively improving the calculation efficiency. The optimized structure has better dynamic performance. However, the optimized structure still has the problem of small safety redundancy.

[0006] The utility model patent with publication number CN202323032059 discloses an offshore wind turbine jacket with failure-safe design. The failure area is set in the design domain, and the dynamic performance of the optimized structure before and after failure in the failure area and the static performance of the optimized structure are analyzed. The optimized structure of the wind turbine jacket with failure-safe design is obtained, so that the optimized design structure can still maintain good stability when partial damage occurs. However, the structural design is mainly optimized for the arrangement of the connecting rods, and the topological optimization method is not used. The optimization results obtained still have room for optimization.

[0007] Compared with structures subjected to static loads, structures subjected to dynamic loads are more likely to experience local failures. Therefore, it is necessary to consider failure-safe design in the optimization of dynamic load structures to ensure their performance in the event of local failures to prevent greater losses and provide more safety redundancy. Summary of the invention

[0008] The content of the present invention is to fully consider the possible local failure of the structure under the structural dynamic load condition, improve the performance of the structure when local failure occurs under the dynamic load, and realize the lightweight structure of the carrier equipment.

[0009] The present invention discloses a method for optimizing a fail-safe topology design under dynamic load, and the method comprises the following steps:

[0010] Step 1, define the design domain and design parameters of the structure;

[0011] Step 2, perform transient dynamic analysis on the structure;

[0012] Step 3, according to the control equation, calculate the equivalent static load of the dynamic load;

[0013] Step 4: Perform failure-safe topology optimization design on the model under equivalent static load;

[0014] The following steps are involved:

[0015] Step 41, designing a fail-safe topology optimization model;

[0016] Step 42, using a damage group method to divide the local failure conditions of the cantilever beam;

[0017] Step 43, taking minimizing the maximum flexibility of the structure under local failure as the optimization goal;

[0018] Step 44, obtaining the sensitivity of the optimization target, and using the moving asymptote method to iteratively optimize the design variable unit density until the inner loop failure safety topology optimization process is completed;

[0019] Step 5: Determine whether the outer loop convergence condition is satisfied according to the updated design variables after the fail-safe topology optimization.

[0020] Further, in Step 1, the structure is a cantilever beam, one end of the cantilever beam is fixed, and a dynamic load is applied to the midpoint of the other end. During the design process, the boundary of the end where the dynamic load is applied is set as the non-failure region.

[0021] Further, in Step 2, a transient dynamic analysis is performed on the structure, and the dynamic control equation is:

[0022]

[0023] x represents the unit density of the design variable; M(x) represents the structural mass matrix, C(x) represents the structural damping matrix, K(x) represents the structural stiffness matrix. The three matrices are related to the unit density and change with the change of the unit density. F(t) represents the dynamic load applied to the structure, u represents the displacement, represents the acceleration, represents the velocity.

[0024] Further, in Step 3, the equivalent static load of the dynamic load is:

[0025]

[0026] where K(x) is the structural stiffness matrix, is the displacement at the i-th moment under the dynamic load;

[0027] Take the displacements at n moments to calculate n groups of equivalent static loads, and then take the average of the obtained n groups of data to get a final group of equivalent static loads:

[0028]

[0029] F eq is the finally obtained equivalent static load;

[0030] Apply the obtained equivalent static load to the original model for subsequent topology optimization design.

[0031] Further, in Step 41, the optimization model is described as:

[0032] Find x = [x1, x2,..., x N

[0033] min f = max c i (x)i = 1…m

[0034] s.t. V / V0 ≤ v0

[0035] x​min ≤ x ≤ 1

[0036] Ku = F eq

[0037] where x represents the unit density of the design variable; N represents the number of units; f represents the objective function: the maximum flexibility of the structure under local failure, c i (x) represents the flexibility of the structure under the i-th local failure scenario, m represents the number of local failure scenarios, v0 represents the optimized volume fraction constraint, and the ratio of the volume of the finally optimized structure to the volume before optimization should be less than this value; x min represents the minimum unit density; K is the stiffness matrix of the structure; F eq is the equivalent static load.

[0038] Furthermore, in step 42, the definition of the local failure scenario is:

[0039]

[0040] E i represents the elastic modulus of element i, E min represents the elastic modulus of the failure zone, ρ i represents the pseudo-density of element i, p represents the material interpolation penalty factor, N represents the design domain, F represents the local failure area, and E0 represents the material elastic modulus;

[0041] For the elements in the failure area, the method of damage population is used to divide the local failure situation of the cantilever beam. The square damage is tiled across the entire design domain, and the damage areas do not overlap with each other; and on this basis, more possible damages are considered. The damage is translated along the diagonal direction, and the horizontal and vertical translation distances are L / 2, where L is the preset size of local failure, and the local damage outside the damage domain is removed.

[0042] Furthermore, in step 43, minimizing the maximum flexibility under local failure is the optimization goal:

[0043] min: f = max c(x)

[0044] f represents the objective function, that is, the maximum flexibility of the structure under local failure, and c(x) represents the flexibility of the structure; using the KS function in the aggregation function, the optimization objective function is transformed into:

[0045]

[0046] where γ is the regularization parameter, and γ is selected f0 is the equivalent series of flexibility, c i (x) is the flexibility of the structure under the i-th local failure scenario.

[0047] Further, in step 44, the sensitivity of the objective function is as follows:

[0048]

[0049] where

[0050] The moving asymptote method is used to optimize and iterate the element density of the design variables, and failure-safe topology optimization design is carried out on the model with the equivalent static load applied. The local failure scenarios defined in step 41 are applied to the structure, and the compliance sensitivity information under each failure scenario is obtained. Thus, the sensitivity of the optimization objective function is obtained, realizing the failure-safe topology optimization design of the structure, enhancing the redundancy of the structure, and ensuring a certain stiffness under local failure scenarios.

[0051] Further, in step 44, after optimization, it is judged whether the updated design variables meet the convergence condition. Here, the convergence condition is that the change value of the compliance before and after the structure optimization is less than 0.1%. The updated element density is applied to the original structure to obtain the optimized new structure, and the compliance of the structure is recalculated. The compliance of the structure is as follows:

[0052] c(x) = U T K(x)U

[0053] where U is the displacement and K(x) is the structural stiffness matrix, which is related to the element density.

[0054] The compliance of the structure under the element density after this topology optimization update is compared with the compliance of the structure under the element density before this topology optimization update. If the change value of the compliance of the structure after this optimization and before this optimization is less than 0.1%, the inner-loop failure-safe topology optimization process is terminated.

[0055] Further, in step 5, according to the updated element density of the design variables, it is judged whether the optimization meets the outer-loop convergence condition. Here, the convergence condition is that the change value of the compliance between the structure when constructing the equivalent static load and the optimized structure under the equivalent static load is less than 0.1%. The element density updated in step 4 is applied to the original structure to obtain the optimized new structure, and the dynamics analysis of the structure is carried out again. If the change value of the compliance between the optimized structure and the structure when constructing the equivalent static load is greater than 0.1%, return to step 2, re-perform the dynamics analysis based on the updated structure, construct a new equivalent static load, and carry out the failure-safe topology optimization design in step 4 under the new equivalent static load; if the change value of the compliance between the optimized structure and the structure when constructing the equivalent static load before optimization is less than 0.1%, the outer-loop failure-safe topology optimization process under static and dynamic loads is terminated, and the obtained result is the optimal dynamic load failure-safe topology optimization result.

[0056] The beneficial effects achieved by the present invention are as follows:

[0057] The present invention improves the performance of the structure under dynamic load conditions. During the design process, the possible local failure conditions of the structure are fully considered, and the performance of the structure under local failure conditions is improved; by using the equivalent static load method, the dynamic load under the original conditions is converted into a static load, effectively improving the calculation efficiency of the optimization process. According to the optimized structure of the present invention, it has strong stiffness under dynamic load. When local failure occurs, its structure can still maintain performance, with small stiffness loss and high safety redundancy. Description of the Drawings

[0058] Figure 1 is the flowchart of the failure-safe topology optimization design method implemented under dynamic load in the present invention;

[0059] Figure 2 is the division of geometric parameters, boundary conditions, and design domain of the structure in the embodiment of the present invention;

[0060] Figure 3 is the demonstration of the local failure structure;

[0061] Figure 4 is the distribution of the local failure area of the structure in the embodiment of the present invention;

[0062] Figure 5 is the topology optimization design under dynamic load;

[0063] Figure 6 is the failure-safe topology optimization design under dynamic load with the damage size L = 0.005 m;

[0064] Figure 7 is the optimization result of the cantilever beam with a preset local damage size of 0.02 m in the present invention. Detailed Implementation Manner

[0065] The following will further describe the present invention in combination with specific embodiments, and the advantages and features of the present invention will become clearer with the description. However, these embodiments are exemplary and do not constitute any limitation to the scope of the present invention. Those skilled in the art should understand that without departing from the spirit and scope of the present invention, the details and forms of the technical solution of the present invention can be modified or replaced, but these modifications and replacements all fall within the protection scope of the present invention.

[0066] As Figure 1 shown, the present invention provides a topology optimization design method considering failure-safety under dynamic load. This method reasonably plans the distribution of materials in the design domain according to the possible local failure conditions in the design domain and considering the constraint conditions set in the optimization problem, so as to achieve the safety redundancy design of the structure and improve the dynamic performance of the structure and its performance under local failure conditions.

[0067] The method includes the following steps:

[0068] Step 1: Define the design domain and design parameters of the structure;

[0069] Figure 2 This is an embodiment of the present invention. In this embodiment, the design domain of the structure is a cantilever beam with a length of 0.18 m and a width of 0.06 m. The left end of the cantilever beam is fixed, and a dynamic load is applied to the midpoint of the right end, and the load magnitude is Since a load is applied to the right boundary, the right boundary is set as a non-failure domain during the design process as shown in the blue area in the figure, that is, the right boundary region will not fail in the failure-safe topology optimization.

[0070] Step 2: As Figure 1 shown, start the optimization design. Enter the outer loop to perform structural dynamics analysis and the establishment of equivalent static loads. Perform transient dynamics analysis on the structure, and the dynamic control equation is as follows:

[0071]

[0072] x represents the unit density of the design variable; M(x) represents the structural mass matrix, C(x) represents the structural damping matrix, K(x) represents the structural stiffness matrix. The three matrices are related to the unit density and change with the change of the unit density. F(t) represents the dynamic load applied to the structure, u represents the displacement, represents the acceleration, represents the velocity.

[0073] Step 3: According to the control equation, the displacement at the i-th moment under the dynamic load can be obtained According to this displacement, the equivalent static load of the dynamic load can be calculated as:

[0074]

[0075] where K(x) is the structural stiffness matrix and is related to the unit density.

[0076] It can be seen from this that in order to optimize the dynamic performance of the structure throughout the process, the displacements at n moments can be taken to calculate n groups of equivalent static loads, and then the average value of the obtained n groups of data can be taken to obtain a final group of equivalent static loads

[0077]

[0078] Apply the obtained equivalent static load to the original model for subsequent topology optimization design, and the structure is transformed from the original optimization problem under dynamic load into a static mechanics problem.

[0079] Step 4: Replace the dynamic load of the original structure with an equivalent static load, and perform failure-safe topology optimization design on the model with the equivalent static load applied;

[0080] The optimization objective is to minimize the maximum compliance of the structure under local failure conditions, and to achieve the failure-safe optimization design of the structure. The specific steps are as follows:

[0081] Step 41, design the failure-safe topology optimization model;

[0082] The optimization problem is described as:

[0083] Find x = [x1, x2,..., x N

[0084] min f = max c i (x)i = 1…m

[0085] s.t. V / V0 ≤ v0

[0086] x min ≤ x ≤ 1

[0087] Ku = F eq

[0088] x represents the unit density of the design variable; N represents the number of units; f represents the objective function: the maximum compliance of the structure under local failure conditions, c i (x) represents the compliance of the structure in the i-th local failure scenario, m represents the number of local failure scenarios, v0 represents the volume fraction constraint of the optimization, and the ratio of the volume of the finally optimized structure to the volume before optimization should be less than this value; x min represents the minimum unit density; K is the stiffness matrix of the structure; F eq is the equivalent static load.

[0089] Step 42, it is necessary to define each local failure scenario and introduce it into the optimization design;

[0090] To achieve the failure-safe topology optimization design, it is first necessary to define each local failure scenario and introduce it into the optimization design. The definition of the local failure scenario is shown in the following formula:

[0091]

[0092] E i represents the elastic modulus of element i, E min represents the elastic modulus of the failure region, ρ i represents the pseudo-density of element i, p represents the material interpolation penalty factor, N represents the design domain, F represents the local failure region, and E0 represents the material elastic modulus.

[0093] ​As can be seen from the formula, for the elements outside the failure region in the design domain, their elastic modulus is related to the element density; for the elements in the failure region, their elastic modulus will be equal to E min , in the finite element analysis, the failure region will show a state where there is no material, that is, local failure occurs in this region resulting in material loss, such as Figure 3 shown.

[0094] In the embodiment, the preset size of the local failure is L, which represents the square damage with side length L considered in the optimization design process. Here, the method of damage population is used to divide the local failure situation of the cantilever beam. First, the square damage is tiled over the entire design domain without overlapping damage regions. On this basis, considering more possible damages, the damage is translated along the diagonal direction, and the horizontal and vertical translation distances are L / 2. The local damages outside the damage domain are removed. The schematic diagram of the damage division is shown in Figure 4 shown.

[0095] Step 43, taking the minimization of the maximum compliance of the structure under local failure as the optimization goal;

[0096] From the description of the local failure scenario, it can be seen that there are multiple local failure situations in the structure. In the embodiment, the optimization goal is to minimize the maximum compliance of the structure under local failure, which can be expressed as:

[0097] min: f = max c i (x)i = 1…m

[0098] The objective function f is a discrete function, and it is difficult to directly optimize and solve it. It needs to be transformed into a continuous function to achieve subsequent optimization and solution. As an important tool in structural optimization, the aggregation function can be used to approximate the max function, and it itself has the characteristic of being differentiable, which is very suitable for the transformation of the objective function here. The KS function in the aggregation function is used here, and the objective function will be transformed into:

[0099]

[0100] where γ is the regularization parameter, and its value determines the approximation degree of the approximate function to the maximum value in the original dataset. The larger the value, the greater the peak weight of the function, but too large a value will lead to oscillations in the optimization iteration process. The recommended value here is where f0 is the same order series of compliance.

[0101] Step 44, obtaining the sensitivity of the optimization goal, and using the moving asymptote method to optimize and iterate the design variable element density until the internal loop failure-safe topology optimization process ends;

[0102] For the objective function, its sensitivity is:

[0103]

[0104] After calculating the sensitivity information, the moving asymptote method is used to optimize and iterate the element density of the design variables to achieve Figure 1 the optimization loop process in the inner loop. The failure-safe topology optimization design is carried out on the model with the equivalent static load applied. The local failure scenarios defined in step 41 are applied to the structure to obtain the compliance sensitivity information under each failure scenario. From this, the sensitivity of the optimization objective function is obtained, realizing the failure-safe topology optimization design of the structure, enhancing the redundancy of the structure, and enabling it to maintain a certain stiffness under local failure scenarios.

[0105] After the optimization design is achieved, it is judged whether the updated design variables meet the convergence condition. Here, the convergence condition is that the change value of the compliance before and after the structural optimization is less than 0.1%. The updated element density is applied to the original structure to obtain the optimized new structure, and the compliance of the structure is recalculated. The compliance of the structure is as follows:

[0106] c(x) = U T K(x)U

[0107] where U is the displacement and K(x) is the structural stiffness matrix, which is related to the element density. The compliance of the structure under the element density after this topology optimization update is compared with the compliance of the structure under the element density before this topology optimization update. If the change value of the compliance of the structure after this optimization and the structure before optimization is less than 0.1%, the inner loop failure-safe topology optimization process is terminated.

[0108] Step 5: After achieving the failure-safe topology optimization, the element density of the design variables updated in the inner loop is obtained. From this, the structural optimization design under this equivalent static load is obtained, and one outer loop is achieved.

[0109] According to the updated element density of the design variables, it is judged whether the optimization meets the outer loop convergence condition. Here, the convergence condition is that the change value of the compliance between the structure when constructing the equivalent static load and the structure optimized under the equivalent static load is less than 0.1%. The element density updated in step 4 is applied to the original structure to obtain the optimized new structure, and the dynamic analysis of the structure is carried out again. If the change value of the compliance of the structure after optimization and the structure when constructing the equivalent static load is greater than 0.1%, return to step 2, re-perform the dynamic analysis based on the updated structure, construct a new equivalent static load, and carry out the failure-safe topology optimization design in step 4 under the new equivalent static load; if the change value of the compliance of the structure after optimization and the structure when constructing the equivalent static load before optimization is less than 0.1%, the failure-safe topology optimization process under dynamic and static loads in the outer loop is terminated, and the obtained result is the optimal dynamic load failure-safe topology optimization result.

[0110] Figure 5 The dynamic load topology optimization design results are given. Figure 6 、 Figure 7 The dynamic load fail-safe topology optimization design results obtained according to the above steps are given and will be elaborated below.

[0111] Figure 6 The optimization results of a cantilever beam with a preset local damage size of 0.005 m by this method are given. The target volume fraction is 40% in the design domain. Through finite element calculation, it can be obtained that Figure 6 when the structure has a square damage with a side length of 0.005 m as set in the optimization design, the maximum flexibility of the structure is 0.00829, Figure 5 the maximum flexibility of the structure is 0.0151. It can be seen that under the dynamic load fail-safe topology optimization, when the structure has a square damage with a side length of 0.005 m, the maximum flexibility value decreases by 45.1%, and the ability of the structure to resist failure is significantly improved. This comparison illustrates the importance of performing fail-safe topology optimization.

[0112] Figure 7 The optimization results of a cantilever beam with a preset local damage size of 0.02 m by this method are given. The target volume fraction is Figure 2 40% in the design domain. Through finite element calculation, it can be obtained that Figure 7 when the structure has a square damage with a side length of 0.02 m as set in the optimization design, the maximum flexibility of the structure is 0.0117, Figure 5 the maximum flexibility of the structure is 0.112, Figure 6 the maximum flexibility of the structure is 0.184. Figure 7 When the structure has a square damage with a side length of 0.02 m, its maximum flexibility value Figure 5 decreases by 89.5% compared with the Figure 6 structure and decreases by 93.6% compared with the

[0113] The above are only the specific steps of the present invention and do not constitute any limitation to the protection scope of the present invention; all technical solutions formed by equivalent transformation or equivalent substitution fall within the scope of the protection of the present invention; the parts not elaborated in detail in the present invention belong to the well-known technologies of those skilled in the art.

Claims

1. A failure-safe topology optimization design method under dynamic loads, characterized in that The failure-safe topology optimization design method under dynamic loads includes the following steps: Step 1: Define the design domain and design parameters of the structure; Step 2: Conduct transient dynamic analysis on the structure; Step 3: Calculate the equivalent static load of the dynamic load according to the control equation; Step 4: Conduct failure-safe topology optimization design on the model under the equivalent static load; It includes the following steps: Step 41: Design the failure-safe topology optimization model; Step 42: Use the method of damage population to divide the local failure situation of the cantilever beam; Step 43: Take the minimization of the maximum flexibility of the structure under local failure as the optimization objective; Step 44: Obtain the sensitivity of the optimization objective, and use the moving asymptote method to optimize and iterate the element density of the design variables until the inner-loop failure-safe topology optimization process ends; Step 5: Judge whether the updated design variables after failure-safe topology optimization meet the outer-loop convergence condition.

2. The failure-safe topology optimization design method under dynamic load according to claim 1, wherein In Step 1, the structure is a cantilever beam, one end of the cantilever beam is fixed, and a dynamic load is applied to the midpoint of the other end. During the design process, the boundary of the end where the dynamic load is applied is set as the area where no failure occurs.

3. The failure-safe topology optimization design method under dynamic load according to claim 1, wherein In Step 2, conduct transient dynamic analysis on the structure. The dynamic control equation is: x represents the unit density of the design variable; M(x) represents the structural mass matrix, C(x) represents the structural damping matrix, K(x) represents the structural stiffness matrix. The three matrices are related to the unit density and change with the change of the unit density. F(t) represents the dynamic load applied to the structure, u represents the displacement, represents the acceleration, represents the velocity.

4. The failure-safe topology optimization design method under dynamic load according to claim 1, characterized in that, In Step 3, the equivalent static load of the dynamic load is: where K(x) is the stiffness matrix of the structure, is the displacement at the i-th moment under dynamic load; Take the displacements at n moments to calculate n groups of equivalent static loads, and then take the mean of the obtained n groups of data to get a final group of equivalent static loads: F eq is the finally obtained equivalent static load; Apply the obtained equivalent static load to the original model for subsequent topology optimization design.

5. The failure-safe topology optimization design method under dynamic load according to claim 1, wherein In Step 41, the optimization model is described as: Find x=[x1,x2,...,x N ​ min f = max c i (x) i = 1…m s.t.V / V0≤v0 x min 0 ≤ x ≤ 1 Ku = F eq where \(x\) represents the unit density of the design variable; \(N\) represents the number of units; \(f\) represents the objective function: the maximum flexibility of the structure under local failure, \(c\) i \((x)\) represents the flexibility of the structure in the \(i\)th local failure scenario, \(m\) represents the number of local failure scenarios, \(v_0\) represents the optimized volume fraction constraint, and the ratio of the volume of the finally optimized structure to the volume before optimization should be less than this value; \(x\) min represents the minimum value of the unit density; \(K\) is the stiffness matrix of the structure; \(F\) eq is the equivalent static load.

6. The failure-safe topology optimization design method under dynamic load according to claim 1, characterized in that In Step 42, the definition of the local failure scenario is: E i Denotes the elastic modulus of element i, E min Denotes the elastic modulus of the failure zone, ρ i Denotes the pseudo-density of element i, p represents the material interpolation penalty factor, N represents the design domain, F represents the local failure region, and E0 represents the material elastic modulus; For the elements in the failure area, use the method of damage population to divide the local failure situation of the cantilever beam. Tile the square damage evenly over the entire design domain, and the damage areas do not overlap with each other; and on this basis, consider more possible damages, translate the damage along the diagonal direction, and the horizontal and vertical translation distances are L / 2, where L is the preset size of local failure, and remove the local damages that exceed the damage domain.

7. The failure-safe topology optimization design method under dynamic loads according to claim 1, characterized in that In Step 43, the minimization of the maximum flexibility under local failure is taken as the optimization objective: min:f=max c(x) f represents the objective function, that is, the maximum flexibility of the structure under local failure, and c(x) represents the flexibility of the structure; use the KS function in the aggregation function to transform the optimization objective function into: where γ is the regularization parameter, and the selection of γ f0 is the same order series of flexibility, c i (x) is the flexibility of the structure under the i-th local failure scenario.

8. The failure-safe topology optimization design method under dynamic loads according to claim 1, characterized in that In Step 44, the sensitivity of the objective function is: Among them, Use the moving asymptote method to optimize and iterate the element density of the design variables, perform failure-safe topology optimization design on the model with equivalent static loads applied, apply the local failure scenarios defined in step 41 to the structure, and obtain the compliance sensitivity information under each failure scenario. Thus, the sensitivity of the optimization objective function is obtained, realizing the failure-safe topology optimization design of the structure, enhancing the redundancy of the structure, and enabling it to still maintain a certain stiffness under local failure scenarios.

9. The failure-safe topology optimization design method under dynamic loads according to claim 8, characterized in that, In Step 44, judge whether the updated design variables after optimization meet the convergence condition. Here, the convergence condition is that the change value of the flexibility of the structure before and after optimization is less than 0.1%. Apply the updated element density to the original structure to obtain the optimized new structure, and recalculate the flexibility of the structure. The flexibility of the structure is as follows: c(x) = U T K(x)U Where U is the displacement, and K(x) is the structural stiffness matrix, which is related to the element density; Compare the flexibility of the structure under the element density after this topology optimization update with the flexibility of the structure under the element density before this topology optimization update. If the change value of the flexibility of the structure after this optimization and the structure before optimization is less than 0.1%, then end the inner-loop failure-safe topology optimization process.

10. The failure-safe topology optimization design method under dynamic load according to claim 1, characterized in that In step 5, according to the updated design variable element density, it is judged whether the optimization meets the outer loop convergence condition. Here, the convergence condition is that the change value of the flexibility between the structure when constructing the equivalent static load and the optimized structure under the equivalent static load is less than 0.1%. Apply the updated element density in step 4 to the original structure to obtain the optimized new structure, and re - conduct the dynamic analysis of the structure. If the change value of the flexibility between the optimized structure and the structure when constructing the equivalent static load is greater than 0.1%, then return to step 2, re - conduct the dynamic analysis based on the updated structure, construct a new equivalent static load, and perform the failure - safe topology optimization design in step 4 under the new equivalent static load; if the change value of the flexibility between the optimized structure and the structure when constructing the equivalent static load before optimization is less than 0.1%, then end the failure - safe topology optimization process under the dynamic and static loads of the outer loop, and the obtained result is the optimal dynamic load failure - safe topology optimization result.

Images