Explosion impact resistant structure optimization method considering material damage

Abstract

The invention belongs to the technical field of aerospace, underwater explosion and topological optimization, and particularly relates to an anti-explosion impact structure optimization method considering material damage, which comprises the following steps of: firstly, acquiring a dynamic response field of a structure through accurate nonlinear dynamic response analysis, judging a failure block and failure time of the structure according to the dynamic response field, and finishing displacement field repair; decoupling the response of the nonlinear dynamics in each time step into a series of linear statics responses; structural sensitivity calculation is carried out in a linear statics framework, and optimization design is realized through flexibility minimization under a statics equivalent working condition; and through repeated iteration and execution of accurate nonlinear dynamic response analysis and the equivalent statics optimization process, the optimization design of the anti-explosion impact structure is finally completed. According to the invention, a user can be helped to quickly explore and obtain a novel structure with high rigidity, light weight and excellent impact resistance in a wide design space.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of aerospace, underwater explosion and topology optimization, and particularly relates to an anti-explosion impact structure optimization method considering material damage. BACKGROUND

[0002] Anti-explosion impact structures and related vibration protection structures for reducing or blocking the effects of explosions and impacts have important applications in weapon ammunition, engineering blasting, aerospace, etc. During the launch of a space launch vehicle, the separation of each stage of the rocket or the satellite-rocket is usually completed by using explosive bolts. When the explosive bolts are initiated, in addition to the high-frequency impact load caused by the shearing of the bolts, a low-frequency vibration impact load (periodic band vibration impact) is also generated by the impact of the sheared bolts on the protective structure.

[0003] In addition to the aerospace field, such structures are also crucial in ship and underwater protection systems. Submarines face threats from weapons such as mines, depth charges, and torpedoes during underwater navigation. After the explosion of underwater explosives, the shock wave propagates rapidly and gradually attenuates from the explosion center outward. At the same time, the gas cloud formed by the explosion products undergoes multiple expansion, contraction, and oscillation processes, and is accompanied by the generation of millisecond secondary pressure waves. When the shock wave and pressure wave encounter the submarine surface, reflection, refraction, and diffraction phenomena occur, resulting in three typical damage modes: plastic large deformation of the submarine hull, hole breaking, and bending deformation of the overall structure vibration of the cabin.

[0004] To effectively respond to the above explosion and impact loads, advanced numerical simulation and optimization methods are essential. With the significant improvement of computer computing power and the continuous progress of numerical algorithms, the finite element method has been extended from static problems in elasticity to complex scenarios such as fluid dynamics, heat conduction, material nonlinearity, and multi-physical field coupling. However, traditional structure optimization methods still face many challenges when dealing with such problems: implicit topology optimization can optimize material distribution, but it has problems such as ambiguous boundary description and numerical instability; explicit methods have clear geometric boundaries, but it is difficult to effectively handle complex topologies such as filled structures. Moreover, when a ship structure encounters a shock wave generated by an underwater explosion load, it will produce complex nonlinear dynamic responses in a very short time, which belongs to a strong nonlinear dynamics problem. For nonlinear dynamics topology optimization problems, due to the complexity of sensitivity calculation and high cost of finite element analysis, traditional gradient-based optimization algorithms have significant limitations in computational efficiency and convergence stability.

[0005] In the face of the problems existing in the traditional structure optimization method, the mobile variable component method (MMC) as an advanced explicit topology optimization method solves the problems of the traditional optimization technology (such as the variable density method) such as fuzzy boundary description, strong grid dependence and difficult engineering of the results. The MMC method takes a 'component' with clear geometric parameter description as a design primitive, and realizes the evolution of the structure topology by controlling the movement, deformation and overlap of the component. In order to further process the strong nonlinear dynamic topology optimization problem, the equivalent static load method (ESLM) is introduced, and the core idea is to decouple the transient nonlinear dynamic response and equivalent to multiple sets of linear static load working conditions through theoretical mapping. By establishing the mapping relationship between the dynamic displacement field and the static load field, the ESLM significantly simplifies the sensitivity analysis process while ensuring the analysis accuracy, avoids the complex nonlinear finite element calculation, and greatly improves the optimization efficiency, supports the rapid iterative design of the anti-impact structure.

[0006] Based on the above method, the application provides an anti-explosion impact structure optimization method considering material damage. SUMMARY

[0007] The purpose of the application is to provide an anti-explosion impact structure optimization method considering material damage, which combines the efficient analysis capability of the equivalent static load method with the clear geometric expression capability of the mobile variable component method, aiming to provide a powerful and efficient design tool for engineers and researchers. The application can help users quickly explore and obtain new structure configurations with high stiffness, lightweight and excellent impact resistance in a wide design space.

[0008] The technical scheme adopted by the application is as follows: An anti-explosion impact structure optimization method considering material damage. First, the dynamic response field of the structure is obtained through accurate nonlinear dynamic response analysis, and the structure is judged for failure block and failure time according to the dynamic response field, to determine the weakening area and the final failure unit, and to complete the displacement field repair. On this basis, the equivalent mapping relationship between the dynamic displacement field and the static load field is established, and the nonlinear dynamic response at each time step is decoupled into a series of linear static responses. Under the premise of ensuring the consistency of the displacement field, the original problem of a series of nonlinear conditions is transformed into linear conditions, and then the structure sensitivity is calculated in the linear static framework, and the optimization design is realized through the flexibility minimization of the static equivalent working condition; through repeated iteration of the accurate nonlinear dynamic response analysis and the above equivalent static optimization process, the optimization design of the anti-explosion impact structure is finally realized.

[0009] In step 1, first, the equilibrium equation of the finite element method of nonlinear dynamics analysis is solved to obtain the nonlinear dynamic displacement vector : where subscript represents nonlinear analysis, is a design variable; is a mass matrix, is a stiffness matrix, is a damping matrix, is a nonlinear dynamic acceleration vector, is a nonlinear dynamic velocity vector, is time, is the number of time steps in the nonlinear dynamic analysis; The step 1 constructs a "failure-guided adaptive correction optimization strategy"; by judging the failure time and identifying the failure area, the material is weakened in the failure area, and the optimizer is guided to strengthen the material at this place; The failure-guided adaptive correction optimization strategy is based on the built-in tensile failure model based on hydrostatic pressure in Abaqus / Explicit; the failure criterion is based on the hydrostatic pressure stress of the element integration point When the value exceeds the critical value of the tensile strength of the material , the element is considered to be failed; the failure condition can be described by the following formula: ; The core logic of the failure-guided adaptive correction optimization strategy includes the following three key steps: Step a: failure block and failure time judgment; after the completion of each outer loop of nonlinear dynamic analysis, the algorithm will find the first failure time, and gradually check the connectivity, rigid body check and calculate the active node failure ratio; when performing connectivity judgment, the algorithm has two built-in connectivity judgment strategies: general connected component method and double connected component method; after connectivity check, if there is no connection to the fixed node, it is marked as failed; if connected to the fixed node, it is judged whether it is in rigid body balance, and if not, it is failed; if it is in rigid body balance, it is not failed; finally, the failure time range is determined and the failure time is judged, that is, the failure node ratio exceeds the set threshold; Step b: determine the weakening area and the final failure element; in order to reinforce the known weak area or guide the structure to reconstruct the force transmission mode, the algorithm defines the final determined cumulative failure area and its surrounding circle of elements as "weakening area"; in the following static optimization inner loop, the material stiffness of all elements located in the weakening area will be forced to be a smaller value; since the stiffness contribution of this area is low, the optimizer will naturally tend to increase material reinforcement at this place or construct new force transmission path reconstruction elsewhere to achieve adaptive repair of weak links; Step c: displacement field repair; this algorithm has two built-in repair methods: scattered interpolation method repair and stiffness matrix division method repair; scattered interpolation method repair uses the built-in function scatteredInterpolant of Matlab to repair the existing unrepaired displacement field based on natural neighbor interpolation; the stiffness matrix division method repair is based on the physical assumption that "the failed nodes are not stressed", and the displacement field is repaired through an auxiliary static analysis; the specific steps are as follows: Step c1: all node degrees of freedom (DoFs) are divided into two categories: "known displacement degrees of freedom" connected to the intact structure and "unknown displacement degrees of freedom" separated due to element failure ; Step c2: auxiliary linear stiffness matrix is constructed based on intact elements , and is divided into blocks according to the above classification , , , ; Step c3: according to the force balance equation , the equation for unknown degrees of freedom is established: ; Step c4: apply the "failed nodes are not stressed" assumption, i.e. , to solve the unknown displacement: ; Finally, the solved is combined with the known to form a physically coordinated and complete displacement field, completing the displacement field repair; In step 2, after obtaining the nonlinear dynamic displacement vector , the equivalent static load of each time step is calculated: Where subscript represents linear analysis, is the equivalent static load vector of the nonlinear displacement at time step s, is the linear stiffness matrix; since the number of ESLs is equal to the number of time steps, there is a strict one-to-one correspondence between the symbols and ; The equivalent static load obtained from equation (11) will be used in multi-condition linear static response optimization; in the optimization process of multi-condition linear static response, the generated at each time step will be used as the external force of linear static analysis and participate in subsequent iterative calculations; as shown in the following equation: According to formula (11), the linear static displacement ; from formula (11) and formula (12), even if there is a large plastic deformation , under the action of linear static displacement field is exactly the same as the nonlinear dynamic displacement field ; However, in the linear static response optimization process, as the optimization progresses, if the structure changes after optimization, and ; the nonlinear displacement field after optimization and the linear displacement field after optimization will differ; in addition, since the target analysis system is a nonlinear system, while the actual optimization is optimized as a linear system, which makes the sensitivities of the two systems different; to solve this problem, the ESL method compensates for these differences by repeatedly optimizing the process in a loop until the convergence criteria are met; this loop process is called "outer loop", which will be described in detail in the next section; when the optimization process converges, these differences have been verified to be zero.

[0010] In step 3, by introducing the equivalent static load method ESLM, the complex transient nonlinear dynamic problem is decoupled and equivalent to a series of linear static problems; The nonlinear dynamic response optimization of the equivalent static load ESL contains two calculation domains of the analysis domain and the design domain; in the analysis domain, the structure response data is obtained by nonlinear dynamic analysis; in the design domain, the equivalent static load ESL is input as an equivalent external force load to the linear static optimization model to drive design updates; the updated design parameters will be reimported into the analysis domain for dynamic analysis, thus forming an iterative feedback mechanism, and this closed-loop process is called outer loop; the outer loop continues to execute until the convergence criteria are met; The flow of the equivalent static load method is as follows: Step 31: set the initial number of outer loop cycles ; design variables ; a small threshold value of the convergence criteria ; Step 31: use to perform nonlinear dynamic analysis; thus, the nonlinear dynamic displacement field ; Step 33: use formula to calculate ; Step 34: linear static response optimization, inner loop optimization, according to the following content; In formula (13c), the external force vector ESL consisting of the ESL obtained in equation (11); the number of external forces is the same as the number of time steps, and these external forces are used as a plurality of load conditions in the linear optimization process; denotes the total number of design variables; Step 35: when go to step 6; when go to step 36 if the following conditions are met: the optimization is ended to obtain the final optimization result ; if not, go to step 26; Step 36: update the design variables and go to step 32; The above details the structure optimization process using equivalent static load for nonlinear dynamic response; first, a complete nonlinear transient dynamic analysis needs to be performed to accurately obtain the time history response of the structure under given dynamic load; the real nonlinear displacement field of the structure at the key time point is extracted; then, based on the real displacement field, the equivalent static load that can produce the same displacement field at that time is calculated; then, the equivalent static load is applied as an external load to the linear model of the same structure, and the structure optimization is performed using the moving deformable component method in the linear model framework, the design variables are updated, and the whole process is repeated until the preset convergence criterion is met. The step 4 is specifically: after obtaining the minimum flexibility design under the static equivalent working condition in step 3, the design is submitted to the nonlinear dynamic response of step 1, and steps 1, 2 and 3 are executed again, and finally the optimization design of the explosion impact resistant structure is completed.

[0011] The technical effects obtained by the application are: In the application: (1) by introducing the equivalent static load method (ESLM), the complex transient nonlinear dynamic problem is decoupled and equivalent to a series of linear static problems, effectively solving the calculation efficiency problem of strong nonlinear dynamic topology optimization. (2) The moving deformable component method (MMC) is used as an explicit topology optimization framework, and the component with clear geometric parameters is used as the design variable, realizing the high-definition geometric boundary of the optimization result and good engineering implementability. (3) In the optimization process, the damage failure mechanism of the material under the explosion impact load is innovatively introduced, so that the optimization result not only meets the lightweight and high stiffness requirements, but also significantly improves the damage resistance of the structure under extreme load, thereby enhancing the reliability and impact resistance of the design scheme. (4) The high-efficiency calculation capability of ESLM and the clear geometric expression capability of MMC are organically integrated to form a special optimization tool for explosion impact resistant structure design, which has the dual advantages of calculation efficiency and result quality, and can help designers quickly explore the optimal or near-optimal structure configuration with high performance and high engineering practicability in a wide design space. Attached Figure Description

[0012] Figure 1 This is a schematic diagram of the structural topology configuration of the present invention under different component layouts and component sizes; Figure 2 This is a schematic diagram of the two-dimensional linear widening component of the present invention; Figure 3 This is a schematic diagram illustrating the operation of the equivalent static load method of the present invention; Figure 4 This is an optimized flowchart of the equivalent static load method of the present invention; Figure 5 This is a flowchart of the adaptive correction optimization strategy for failure guidance in this invention. Figure 6 This is a schematic diagram of the structural load constraint of the present invention; Figure 7 This invention describes the initial MMC component layout and optimization results under a 10KN impact load. Figure 8 These are the objective function, total structural volume violation, and iterative curves of the structural dynamic response under a 10KN impact load according to the present invention.

[0013] Figure 9 This invention describes the initial MMC component layout and optimization results under a 20KN impact load. Figure 10 This is a schematic diagram of the failure of structural units under the optimized 20KN impact load of this invention; Figure 11 These are the iterative curves of the objective function, total structural volume violation, and structural dynamic response under a 20KN impact load according to this invention. Detailed Implementation

[0014] To make the objectives and advantages of this invention clearer, the invention will be specifically described below with reference to embodiments. It should be understood that the following text is merely used to describe one or more specific embodiments of the invention and does not strictly limit the scope of protection specifically claimed by the invention.

[0015] like Figure 1 As shown, an optimization method for an explosion-resistant structure considering material damage includes step 1: First, the dynamic response field of the structure is obtained through precise nonlinear dynamic response analysis, and the failure blocks and failure times of the structure are determined accordingly to identify the weakened region and the final failure unit, and the displacement field is repaired. Step 2: Based on this, establish the equivalent mapping relationship between the dynamic displacement field and the static load field, and decouple the nonlinear dynamic response at each time step into a series of linear static responses; Step 3: Under the premise of ensuring the consistency of the displacement field, a series of nonlinear conditions of the original problem are converted into linear conditions, and then the structural sensitivity calculation is carried out in the linear statics framework, and the optimization design is realized through the flexibility minimization under the equivalent statics working condition; Step 4: Through repeated iteration, the precise nonlinear dynamic response analysis and the equivalent statics optimization process are executed, and finally the optimization design of the explosion-resistant impact structure is completed.

[0016] In the application, the topological optimization method based on the mobile deformable component framework realizes the method of "flexibility minimization" in the "flexibility minimization under the equivalent statics working condition to realize the optimization design" in step 3.

[0017] The topological optimization method based on the mobile deformable component framework takes components with explicit geometric parameter description as the base element of topological optimization, describes each component through a topological description function, and forms the final topology of the structure through the movement, deformation, intersection and coverage of the components. Moreover, the components contain feature size information, and the size control of the structure can be easily realized by controlling the size of the components. As shown in Figure 1 Different component layouts and component sizes will cause significant changes in the structure topology. Figure 1 In the application, Figure 1 a is a topological configuration 1; Figure 1 b is a topological configuration 2; Figure 1 c is a topological configuration 3; Figure 1 d is a topological configuration 4; Fig. 1 is a schematic diagram of structure topological configurations under different component layouts and component sizes For different problems, different component forms can be used for description. Taking a two-dimensional variable-width component as an example, the topological description function (Topology description function, TDF) of the i-th component can be expressed as: wherein represents half of the component length; The profile of the component is controlled (different shaped components correspond to different functions), and in this paper, a linear variable-width description form is selected, and the , the component schematic diagram is shown in Figure 2 . represents the conversion relationship between the coordinates in the local coordinate system and the coordinates in the global coordinate system . wherein is the center point coordinate of the component in the global coordinate system; represents the rotation angle of the component. According to formula (1) and formula (2), the i-th component is The design variables for each component are .

[0018] Figure 2 Schematic diagram of a two-dimensional linear widening component; as shown Figure 2 As shown, for a single component, its topology description function value is relevant across the entire design domain. It can be divided into the following three cases: in The symbol represents a discrete point in the design domain. This refers to the TDF mentioned earlier. , , They represent the first The topological description function of the entire structure can be expressed as: (The text then goes on to describe the internal, boundary, and external spaces occupied by each component.) in Indicates by The area shared by all components, that is, the solid part of the structure, and has Therefore, it is obvious that... .

[0019] In summary, the layout within the design domain of the model... After each component, the topology description function value of the mesh node under each component is calculated. They will receive The boundary description corresponding to each component, for After taking the maximum value, the final topological boundary is obtained by all components. Therefore, the structural design under the MMC framework has a clear and explicit topological boundary. Given all the parameters describing a component, its boundary is determined by the topological description function. The only certainty is that, compared to the variable density method, MMC does not require the use of grayscale units to extract geometric boundaries; any boundary point... All can be directly from The explicit representation completely avoids the boundary blurring and extraction difficulties caused by grayscale diffusion.

[0020] After obtaining the geometric boundary explicitly defined by the topological description function, subsequent finite element analysis can be performed. In the finite element analysis, planar four-node bilinear structured elements are used to uniformly discretize the design domain. When using a substitute model material for finite element analysis, Young's modulus... Calculate using the following formula: In the formula The Young's modulus of the material. For the global topology description function In the The first unit The TDF value at each node represents the entity domain characterized by the node. A positive value indicates that the node has material, while a negative value indicates that the node has no material. The Heaviside function, representing smoothing, is shown in equation (7). This work uses a regularized form. to replace , The format is as follows: In the formula These are regularization parameters used to control... The length of the transition region. For a small positive number (e.g.) This is used to avoid possible singularities in the overall stiffness matrix.

[0021] Represents all components Take the maximum value. This is to ensure analytical sensitivity. Because it is differentiable, the KS function is used here to approximate the operation of the maximum value, and its specific form is as follows: In the formula For a large positive number, such as taking Thus, it was passed. The topological description of the structure was obtained. Therefore, the optimization formula for the structural flexibility minimization problem based on the topology optimization method using the Movable Deformable Component (MMC) framework can be expressed as: In the above formula Allowed values ​​for design variables; For KS function ( (for larger positive numbers) For the Heaviside function, For the overall structure in units TDF function values ​​at the four nodes; are positive numbers and .

[0022] In this invention, the equivalent static load method is used: Equivalent Static Loads (ESL) is a special set of static loads, which is constructed based on the equivalence principle between static and dynamic analysis. Specifically, it is defined as: when a set of loads is applied to the structure, the displacement field obtained by static analysis can be exactly the same as the displacement response at each discrete time node in the nonlinear dynamic analysis. Next, we will introduce the calculation process of ESL based on the concept of "displacement equivalence".

[0023] In step 1, "obtain the dynamic response field of the structure through accurate nonlinear dynamic response analysis": Specifically, first, solve the equilibrium equation of the finite element method of nonlinear dynamic analysis to obtain the nonlinear dynamic displacement vector where the subscript represents nonlinear analysis, is the design variable. is the mass matrix, is the stiffness matrix, is the damping matrix, is the nonlinear dynamic acceleration vector, is the nonlinear dynamic velocity vector, is time, is the number of time steps in nonlinear dynamic analysis.

[0024] In step 2, "on this basis, establish the equivalent mapping relationship between the dynamic displacement field and the static load field, decouple the response of nonlinear dynamics at each time step into a series of linear static responses"; Specifically, after obtaining the nonlinear dynamic displacement vector , calculate the equivalent static load at each time step: where the subscript represents linear analysis, is the nonlinear displacement at time step s, is the linear stiffness matrix; Since the number of ESL is equal to the number of time steps, there is a strict one-to-one correspondence between the symbols and .

[0025] The equivalent static load obtained from equation (11) will be used in multi-condition linear static response optimization; In the optimization process of multi-condition linear static response, the generated at each time step will be used as the external force of linear static analysis and participate in the subsequent iterative calculation. For example, the following equation:​ According to formula (11), linear static displacement can be obtained . It can be seen from formula (11) and formula (12) that even if larger plastic deformation appears in the nonlinear analysis , the linear static displacement field under the action of is exactly the same as the nonlinear dynamic displacement field Figure 3 . As shown in

[0026] Figure 3 The schematic diagram of the effect of the equivalent static load method, wherein Figure 3 a is a schematic diagram of the original load structure; Figure 3 b is a schematic diagram of the original load displacement field; Figure 3 c is a schematic diagram of the equivalent static load; However, in the linear static response optimization process, as the optimization progresses, if the structure changes after optimization, and is not recalculated, the nonlinear displacement field after optimization will be different from the linear displacement field after optimization. In addition, since the target analysis system is a nonlinear system, and the actual optimization is optimized as a linear system, the sensitivities of the two systems are different. To solve this problem, the ESL method compensates for these differences by repeatedly cycling the optimization process until the convergence criteria are met. This cycle is called the "outer loop", which will be described in detail in the next section. When the optimization process converges, these differences have been verified to be zero.

[0027] In step 3: "Under the premise of ensuring the consistency of the displacement field, a series of nonlinear conditions of the original problem are converted into linear conditions, and then the structural sensitivity calculation is carried out in the linear statics framework, and the optimization design is realized through the flexibility minimization of the static equivalent working condition". Specifically, the nonlinear dynamic response structure optimization process of the topological optimization method based on the ESL method and the MMC framework The nonlinear dynamic response optimization based on equivalent static load (ESL) includes two calculation domains of analysis domain and design domain. In the analysis domain, the structural response data is obtained through nonlinear dynamic analysis; in the design domain (inner loop), ESL is input as an equivalent external load to the linear static optimization model to drive design updates. The updated design parameters will be reimported into the analysis domain for dynamic analysis, thereby forming an iterative feedback mechanism. This closed-loop process is called "outer loop". The outer loop continues to execute until the convergence criteria are met, and the overall process is shown in Figure 4 .

[0028] Figure 4Optimization flowchart of equivalent static load method The specific main steps are as follows: Step 1: Set initial outer loop number of cycles ; design variables ; small threshold of convergence criterion .

[0029] Step 2: Perform nonlinear dynamic analysis using . Thus, the nonlinear dynamic displacement field is obtained.

[0030] Step 3: Calculate using equation .

[0031] Step 4: Perform linear static response optimization (inner loop) according to the following.

[0032] In equation (13c), the vector of external forces is composed of the ESL obtained in equation (11). The number of external forces is the same as the number of time steps, and these external forces are used as multiple loading conditions in the linear optimization process. denotes the total number of design variables. In actual optimization, the selected external forces can be filtered according to the total strain of the structure under nonlinear dynamic response. For example, only the external forces at the discrete time points near the maximum value of strain energy are selected, or only the external forces at the discrete time points where the strain energy is greater than , and then the linear static response optimization is carried out according to the selected external forces.

[0033] Step 5: When go to Step 6. When if the following conditions are met: and , then the optimization is ended, and the final optimization result is obtained. If not, go to Step 6.

[0034] Step 6: Update the design variables and go to Step 2.

[0035] ​The above content details the application of equivalent static load in the nonlinear dynamic response structure optimization process. First, a complete nonlinear transient dynamic analysis needs to be performed to accurately obtain the time history response of the structure under the action of a given dynamic load. The real nonlinear displacement field of the structure at the key time point is extracted. Subsequently, based on this real displacement field, the equivalent static load that can produce the same displacement field at that time is calculated. Then, this equivalent static load is applied as an external load to the linear model of the same structure, and the moving deformable component method is used to optimize the structure in the linear model framework, update the design variables, and repeat the entire process until the preset convergence criteria are met.

[0036] In step 1, "and based on this, failure block and failure time judgment is performed on the structure to determine the weakening area and final failure unit, and displacement field repair is completed", specifically, the present application, failure-guided adaptive correction optimization strategy: When dealing with structural dynamic failure problems, a serious challenge is that the structure topology evolves over time. In theory, this means that when performing equivalent static load conversion, each time step should be based on its corresponding, partially failed structure model. However, this would result in the establishment of an equivalent model for each different structure at each time, resulting in huge computational costs and uncertainties.

[0037] To effectively handle material dynamic failure behavior while ensuring computational efficiency and optimization stability, this work innovatively proposes and implements a "failure-guided adaptive correction optimization strategy". The core advantage of this strategy is that it has minimal modifications to the traditional ESLM framework. This strategy identifies the failure time and failure area, and through the weakening of the failure area, it guides the optimizer to strengthen the material in this area.

[0038] This strategy is based on the built-in hydrostatic pressure-based tensile failure model in Abaqus / Explicit. Its failure criterion is based on the hydrostatic pressure stress of the element integration point When this value exceeds the critical value of the material's tensile strength , the element is considered to have failed. The failure condition can be described by the following formula: The overall optimization flowchart of this strategy is shown in Figure 5 , and its core logic includes the following three key steps: Failure block and failure time determination: After the completion of each outer loop of nonlinear dynamic analysis, the algorithm will find the first failure time and check the connectivity, rigid body check and calculate the active node failure ratio step by step. When performing connectivity determination, the algorithm has two built-in connectivity determination strategies: general connected component method and double connected component method. After connectivity check, if there is no connection to the fixed node, it is marked as failure. If connected to the fixed node, continue to judge whether the rigid body is in balance, if not, it is failure; if the rigid body is in balance, it is not failure. Finally, determine the failure time range and judge the failure time (the failure node ratio exceeds the set threshold).

[0039] Determination of weakened area and final failure unit: In order to reinforce the known weak area or guide the reconstruction of the force transmission mode of the structure, the algorithm defines the final determined cumulative failure area and the surrounding ring of units as a "weakened area". In the next static optimization inner loop, the material stiffness of all units located in this weakened area will be forced to be a smaller value. Since the stiffness contribution of this area is low, the optimizer will naturally tend to increase the material here (reinforcement) or build new force transmission paths elsewhere (reconstruction) in order to reduce the overall flexibility of the structure, thereby achieving adaptive repair of weak links.

[0040] Displacement field repair: Unit failure may cause its nodes to separate from the main structure, resulting in unrealistic large displacement under the action of inertia, which will seriously affect the accuracy of ESLM calculation. To solve this problem, the algorithm has two built-in repair methods: scattered interpolation method repair and stiffness matrix division method repair. The scattered interpolation method repair uses the built-in function scatteredInterpolant of Matlab to perform natural neighbor interpolation repair based on the existing un-repaired displacement field. The stiffness matrix division method repair is based on the physical assumption that "failed nodes are not forced", and repairs the displacement field through an auxiliary static analysis. The specific steps are as follows: Divide all node degrees of freedom (DoFs) into two categories: "known displacement freedom" connected to the intact structure and "unknown displacement freedom" separated due to unit failure .

[0041] Based on the intact unit, an auxiliary linear stiffness matrix is constructed , and it is divided into blocks according to the above classification , , , .

[0042] According to the force balance equation , the equation for the unknown freedom is established: .

[0043] Apply the "failure node is not forced" assumption, that is , the unknown displacement is solved: .

[0044] Finally, the solved is combined with the known to form a physically consistent, complete displacement field to ensure the effectiveness of subsequent ESL calculations. Figure 5 is an optimization flow chart of the failure-guided adaptive correction optimization strategy.

[0045] Numerical examples of the present application: In this section, an impact load MBB beam impact resistance optimization example will be shown. Through the impact resistance optimization design of the MBB beam structure, the effectiveness of the method is verified. The material properties selected in the optimization are set in Abaqus according to Table 1.

[0046]

[0047] 10KN impact load optimization In the MBB beam impact resistance optimization example, the rectangular beam is 2m long, 1m wide and 0.01m thick. The x-direction displacement of the left section of the beam is constrained, and the y-direction displacement of the right lower corner vertex is constrained. A half-cycle sinusoidal impact load with an amplitude of 10KN is applied to the left upper corner vertex of the beam. The structural load constraint schematic is shown in Figure 6 . Figure 6 Structural load constraint schematic In this example, the initial MMC initial component layout is set as shown in Figure 7 (a). There is no element failure in the initial and subsequent optimization process of the structure. After 47 outer loop iterations, the optimization result converges, and the convergence result is shown in Figure 7 (b).

[0048] Figure 7 Initial MMC initial component layout and optimization result; in the optimization process, 40% of the final volume constraint is set, and Abaqus / Explicit is used for finite element nonlinear dynamics solution. The target function, structure total volume violation and structure dynamics response iteration curve in the optimization process is shown in Figure 8 . Figure 8 Target function, structure total volume violation and structure dynamics response iteration curve under 10KN impact load 20KN impact load optimization, in the MBB beam impact resistance optimization example, the rectangular beam is 2m long, 1m wide and 0.01m thick. The x-direction displacement of the left section of the beam is constrained, and the y-direction displacement of the right lower corner vertex is constrained. A half-cycle sinusoidal impact load with an amplitude of 20KN is applied to the left upper corner vertex of the beam. The structural load constraint schematic is shown in Figure 6 .

[0049] Figure 9 20KN impact load optimization of initial component layout and optimization results, in this example, as shown in Figure 9 (a) set the initial MMC initial component layout. In this example, the unit has failure condition. As shown in Figure 10 , the figure shows the failure of the unit in different outer loop iteration steps. Among them, green represents the unit that has not failed in finite element simulation, and red represents the unit that has failed in finite element simulation. After 54 outer loop iterations, the optimization result converges, at this time there is no unit failure, and the convergence result MMC component layout is shown in Figure 9 (b).

[0050] Figure 10 Structural unit failure condition diagram, in the optimization process, set the final volume constraint of 40%, and use Abaqus / Explicit for finite element nonlinear dynamics solution. Finally, the objective function, structure total volume violation and structure dynamics response iteration curve in the optimization process are shown in Figure 11 . Figure 11 20KN impact load objective function, structure total volume violation and structure dynamics response iteration curve; The above only is the preferred embodiment of the present application, it should be pointed out that, for the ordinary skilled in the art, without departing from the principles of the present application, can also make a number of improvements and refinements, these improvements and refinements should also be considered as the protection scope of the present application. The structure, device and operation method not specifically described and explained in the present application, if no special description and limitation, are implemented according to the conventional means in the art.

Claims

1. A method for blast-resistant structure optimization considering material damage, characterized in that: The method comprises the following steps: Step 1: First, the dynamic response field of the structure is obtained through accurate nonlinear dynamic response analysis, and the failure block and failure time of the structure are judged based on the dynamic response field, so as to determine the weakening area and the final failure unit, and to complete the displacement field repair; Step 2: On this basis, an equivalent mapping relationship between the dynamic displacement field and the static load field is established, and the nonlinear dynamic response at each time step is decoupled into a series of linear static responses; Step 3: Under the premise of ensuring the consistency of the displacement field, a series of nonlinear conditions of the original problem are converted into linear conditions, and then the structural sensitivity is calculated in the linear static framework, and the optimization design is realized through the flexibility minimization of the equivalent static load method (ESLM); Step 4: Through repeated iteration of the accurate nonlinear dynamic response analysis and the above equivalent static optimization process, the optimization design of the explosion-resistant structure is finally completed.

2. The method for optimizing a structure against blast effects taking into account material damage according to claim 1, characterized in that: In the first of said step 1, the equilibrium equation of the finite element method of the nonlinear dynamic analysis is solved to obtain a nonlinear dynamic displacement vector : wherein the subscript denotes the nonlinear analysis, is the design variable; is the mass matrix, is the stiffness matrix, is the damping matrix, is the nonlinear dynamic acceleration vector, is the nonlinear dynamic velocity vector, is the time, is the number of time steps in the nonlinear dynamic analysis; In step 1, the "failure-guided adaptive correction optimization strategy" is constructed; by judging the failure time and identifying the failure area, the material is strengthened in the failure area through weakening, so as to guide the optimizer to strengthen the material in the failure area; The failure-guided adaptive correction optimization strategy is based on a hydrostatic pressure-based tensile failure model built-in Abaqus / Explicit; the failure criterion thereof is based on the hydrostatic pressure stress of an element integration point When the value exceeds the critical value of the tensile strength of the material , the element is considered to fail; the failure condition can be described by the following formula: 。 3. The method for optimizing a structure against blast effects considering material damage according to claim 2, characterized in that: The core logic of the failure-guided adaptive correction optimization strategy includes the following three key steps: Step a: failure block and failure time judgment; After each nonlinear dynamic analysis in the outer loop is completed, the algorithm will find the first failure time, and then gradually check the connectivity, rigid body check and calculate the active node failure ratio; when checking the connectivity, the algorithm has two built-in connectivity judgment strategies: general connected component method and double connected component method; if there is no connection to the fixed node after the connectivity check, it is marked as failure; if it is connected to the fixed node, it is judged whether it is in rigid body balance, if not, it is failure; if it is in rigid body balance, it is not failure; finally, the failure time range is determined and the failure time is judged, that is, the failure node ratio exceeds the set threshold; Step b: determine the weakening area and the final failure unit; in order to strengthen the known weak area or guide the reconstruction of the structure, the algorithm defines the final determined cumulative failure area and the surrounding units as a "weakening area"; in the following static optimization inner loop, the material stiffness of all units in the weakening area will be forced to be a smaller value; because the stiffness contribution of this area is low, the optimizer will naturally tend to increase material reinforcement here or build new force transmission paths to reconstruct, so as to realize the adaptive repair of the weak link; Step c: displacement field repair; this algorithm has two repair methods: scattered point interpolation method repair and stiffness matrix division method repair; the scattered point interpolation method repair uses the built-in function of Matlab to perform natural neighbor interpolation repair based on the existing un-repaired displacement field; the stiffness matrix division method repair is based on the physical assumption that "the failure node is not forced", and the displacement field is repaired through an auxiliary static analysis; the specific steps are as follows: Step cl: All nodal degrees of freedom (DoFs) are classified into two categories: "known displacement DoFs" connected to the intact structure and "unknown displacement DoFs" disconnected due to element failure ; Step c2: Constructing the linear stiffness matrix based on intact element , and partitioned into blocks according to the above classification , , , ; Step c3: Establish equation for unknown degrees of freedom according to force balance equation , for unknown degrees of freedom: ; Step c4: Apply the "failed nodes not force" assumption, i.e. , to solve for the unknown displacement: ； Finally, the solved known combination, forming a physically coordinated, complete displacement field, complete displacement field repair.

4. The method of claim 1, wherein: In step 2, the nonlinear dynamic displacement vector After that, the equivalent static load at each time step is calculated: where the subscript denotes linear analysis, is the nonlinear displacement is the equivalent static load vector at time step s, is the linear stiffness matrix; since the number of ESLs is equal to the number of time steps, there is a strict one-to-one correspondence between and ; Equivalent static load obtained from equation (11) will be used in the multi-condition linear static response optimization; in the process of multi-condition linear static response optimization, the generated at each time step will be involved in the subsequent iterative calculation as the external force of linear static analysis; as follows: According to equation (11), the linear static displacement ; from equations (11) and (12), it is known that even in the case of a large plastic deformation , the linear static displacement field under the action of is identical to the nonlinear dynamic displacement field ; However, in the process of linear static response optimization, if the structure changes after optimization and is not recalculated, the problem may arise. This can lead to differences between the optimized nonlinear displacement field and the optimized linear displacement field. Furthermore, since the target analysis system is a nonlinear system, while the actual optimization treats the system as a linear system, there are differences in the sensitivity of the two systems. To solve this problem, the ESL method compensates for these differences by continuously iterating the optimization process until the convergence criterion is met. This iterative process is called the "outer loop". When the optimization process converges, these differences have been verified to be zero.

5. The method for optimizing a structure against blast effects considering material damage according to claim 4, characterized in that: In step 3, the equivalent static load method (ESLM) is introduced to decouple the complex transient nonlinear dynamic problem into a series of linear static problems; The nonlinear dynamic response optimization of ESL comprises two calculation domains, an analysis domain and a design domain. In the analysis domain, the structural response data are obtained through nonlinear dynamic analysis; In the design domain, the ESL is input into the linear static optimization model as an equivalent external force load to drive the design update. The updated design parameters are reimported into the analysis domain for dynamic analysis, thereby forming an iterative feedback mechanism. This closed-loop process is called an outer loop. The outer loop is executed until the convergence criterion is met; The process of the equivalent static load method is as follows: Step 31 : Set initial outer loop count ; design variables ; a small threshold value for the convergence criterion ; Step 31 : using non-linear dynamic analysis; thus, obtaining a non-linear dynamic displacement field ; Step 33: using the formula calculations ; Step 34: linear static response optimization is performed according to the following content, inner loop optimization; In formula (13c), the vector of external forces The ESL is composed of the number of external forces obtained in formula (11) and the number of time steps, which are used as multiple loading conditions in the linear optimization process; denotes the total number of design variables; Step 35: When go to Step 6; when the following conditions are met: then the optimization is finished and the final optimization result is obtained ; if not, go to step 26; Step 36: update the design variables and go to step 32; The above content details the application of the equivalent static load in the nonlinear dynamic response structural optimization process; First, a complete nonlinear transient dynamic analysis needs to be performed to accurately obtain the time history response of the structure under the action of a given dynamic load; At the key time point, the real nonlinear displacement field of the structure at this time is extracted. Then, based on the real displacement field, the equivalent static load that can produce the same displacement field at this time is calculated. Next, the equivalent static load is applied as an external load to the linear model of the same structure, and the moving deformable component method is used for structural optimization under the linear model framework. The design variables are updated, and the whole process is repeated until the preset convergence criterion is met.

6. The method for optimizing a structure against blast effects taking into account material damage according to claim 5, characterized in that: Step 4 is specifically: after obtaining the minimum flexibility design under the static equivalent working condition in step 3, the design is submitted to the nonlinear dynamic response in step 1. Steps 1, 2 and 3 are executed again to finally complete the optimization design of the explosion impact resistant structure.

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