Engineering structure topological optimization method and system for rapid solution under transient stress constraint

Abstract

The invention discloses an engineering structure topological optimization method and system for rapid solution under transient stress constraint, which takes the square of the average dynamic flexibility of the whole structure as a target function, and adopts a modal displacement method for quasi-static response compensation in order to solve the problem of huge calculated amount consumption of transient dynamic analysis. Stress control considering transient analysis is realized, and in order to control the calculation efficiency, transient stress after P-norm aggregation is adopted for constraint; and based on an adjoint method, deriving the sensitivity of a target function and the transient stress after P-norm aggregation, and solving an optimization problem by adopting an optimization algorithm based on a moving asymptote method. An optimization example shows that the method can effectively meet the stress constraint requirement while reducing the transient dynamics analysis calculation amount.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of structural and multidisciplinary optimization design, and relates to a topological optimization and design method and system of an engineering structure. BACKGROUND

[0002] Traditional transient dynamic finite element analysis usually adopts Newmark and other direct integration algorithms in a complete degree of freedom space to solve external loads by time stepping. Although such methods have good universality and numerical stability, in actual engineering, when the number of degrees of freedom of the structure is huge, the configuration is complex or the analysis time history is long, large-scale algebraic equations need to be assembled and solved at each time step, resulting in a number-level increase in overall calculation amount, low calculation efficiency, high resource consumption, and difficulty in meeting the needs of multiple iterative optimization in the engineering design stage.

[0003] On the other hand, the stress constraint in the existing topological optimization method is mostly based on static working conditions, and the stress level of the structure under constant load or equivalent static load is controlled, ignoring the transient dynamic effect widely existing in actual engineering, and unable to accurately describe the real stress evolution process of the structure in the entire time history. For the above reasons, there is an urgent need for an engineering structure topological optimization method that can quickly solve under transient stress constraint. SUMMARY

[0004] The purpose of the present application is to at least solve one of the problems of long calculation time, low calculation efficiency and difficulty in accurately reflecting the engineering transient load working condition when stress constraint is performed in transient dynamic finite element topological optimization, and to provide a topological optimization method that can effectively control transient stress while ensuring calculation accuracy.

[0005] To achieve the above purpose, some embodiments of the present application propose an engineering structure topological optimization method for fast solving under transient stress constraint, which comprises the following steps:

[0006] S0: constructing a topological optimization equation of a transient dynamic finite element model of the engineering structure; comprising:

[0007] establishing a transient dynamic finite element model of the engineering structure comprising a plurality of elements, the transient dynamic finite element model being represented by a transient dynamic finite element equation , wherein K is a global stiffness matrix of the engineering structure, C is a global damping matrix thereof, M is a global mass matrix thereof, and the dimensions are ; is the displacement of the engineering structure at the initial time, is the velocity of the engineering structure at the initial time; F(t) is an external load, which is an N-dimensional vector; is a displacement response matrix of the engineering structure, a velocity response matrix of the engineering structure, an acceleration response matrix of the engineering structure;

[0008] a topology optimization formulation of the transient dynamic finite element model, wherein a square of an average dynamic flexibility of the engineering structure is taken as an objective function:

[0009]

[0010] wherein T is a total time of an external load loading; is a design variable representing an e-th element of the transient dynamic finite element model; is a volume representing the e-th element of the transient dynamic finite element model; is a transient stress aggregated by P-norm; a constraint condition set by the topology optimization formulation is that a sum of total element volumes is smaller than a set volume requirement V and the transient stress aggregated by P-norm is smaller than a set stress requirement under the condition that a square of the average dynamic flexibility is minimized;

[0011] Step S1: input initial values of the design variables ; based on the initial values of the design variables , a RAMP interpolation model is used; initial values of a global stiffness matrix K, a global mass matrix M and a global damping matrix C are derived and initial values of modes are inputted; wherein, is a stiffness matrix of an arbitrary element , is a mass matrix of the element ; and are stiffness matrices and mass matrices of the time t, respectively, and are stiffness matrices and mass matrices of the time t+1, respectively, is a penalty factor; the global stiffness matrix K, the global mass matrix M and the global damping matrix C are composed of the stiffness matrix and the mass matrix of each element e obtained by the RAMP interpolation model; the global damping matrix C is obtained by the global stiffness matrix K and the global mass matrix M;

[0012] ​​​Step S2: Based on the initial values ​​of the global stiffness matrix K, global mass matrix M, and global damping matrix C, solve for the structural characteristic matrix of the engineering structure and perform q+1 order subspace projection;

[0013] Step S3: Solve the displacement response matrix of the structure in the q+1 order subspace using the Newmark method. ; and through the obtained displacement response matrix To solve for the square of the dynamic compliance of the objective function at the mean time step. And the transient stress after P-norm polymerization;

[0014] Step S4: Solve for the sensitivity of the objective function using the adjoint method. And the sensitivity of the transient stress after P-norm polymerization as a constraint function ;

[0015] Step S5: Based on the objective function Sensitivity The sensitivity of the transient stress after P-norm polymerization as a constraint function An iterative algorithm is used for optimization to solve for the design variables in the next iteration. And set an iteration stopping criterion, wherein the iteration stopping criterion can be set as: when the design variables between two adjacent iteration steps... If the maximum difference is less than the preset value or the number of iterations is greater than the preset value, the optimization will terminate.

[0016] In some embodiments, in step S5, if the stopping criterion is not met in a certain iteration step, the design variables are updated, and the process returns to step S2 to continue solving until the stopping criterion is met.

[0017] In some embodiments, step S2 includes step S21, solving for the quasi-static response vector. Step S22: Solve the characteristic equation of the q-order subspace; and step S23: Update the eigenvector of the characteristic equation, and use the obtained quasi-static response vector... The quasi-static response vector is added to the eigenvector as an additional reduced-order basis, that is, the quasi-static response vector is added to the eigenvector of the characteristic equation of the q-order subspace. The global stiffness matrix K, the global mass matrix M, and the global damping matrix C are reduced to the q+1 order subspace.

[0018] In some embodiments, in step S21, according to the formula Solving for the quasi-static response vector Where F is the external load The constant vector and quasi-static response vector in the text. Satisfying quality normalization, that is: The quasi-static response is placed into the desired q-order mode to form a new q+1-order reduced basis. Then, the modal displacement method is used to reduce the order and solve the problem. The Newmark method is used to solve the transient response value of the structure in the q+1 subspace.

[0019] In some embodiments, in step S22, according to Solve the characteristic equation of the q-th order subspace, where , These are the eigenvalues ​​in the subspace. Let be the modal vector in the subspace.

[0020] In some embodiments, the iterative algorithm is the moving asymptote method.

[0021] Some embodiments of this application also provide an engineering structure topology optimization system for rapid solution under transient stress constraints, which includes a processor and a memory, wherein the memory stores computer code, and the processor executes the computer code to implement the method described in any of the above.

[0022] The beneficial effects of this invention include: by introducing a quasi-static response compensation method based on modal displacement, this method reduces the degree of freedom and time step computation of transient dynamic analysis while ensuring the accuracy of transient response, thereby improving the overall computational efficiency of topology optimization; by using P-norm aggregated transient stress to construct transient stress constraints, it achieves unified control of stress levels throughout the entire process and in multiple locations, thus more realistically reflecting the service status of engineering structures under complex transient load conditions. Attached Figure Description

[0023] Figure 1 This is a flowchart of a method for rapidly solving dynamic topology optimization under transient stress constraints according to an embodiment of this application.

[0024] Figure 2 This is a schematic diagram of a two-dimensional cantilever beam according to an embodiment of this application.

[0025] Figure 3 The diagram shows the finite element model and stress cloud diagram of the cantilever beam before and after optimization according to an embodiment of this application. Part A shows the finite element model before optimization, part B shows the stress cloud diagram before optimization, part C shows the finite element model after optimization, and part D shows the stress cloud diagram after optimization. Detailed Implementation

[0026] The method of the present invention will now be described in detail with reference to the accompanying drawings.

[0027] In summary, this application proposes a method and system for rapid topology optimization of engineering structures under transient stress constraints. This belongs to the category of efficient topology optimization methods and systems for structural dynamics analysis. The objective function is the square of the dynamic flexibility of the structure at its mean time, and the transient stress aggregated by P-norm is used as the constraint function. Throughout this paper, the engineering structure is also referred to simply as "structure."

[0028] To overcome the low efficiency of traditional transient dynamic analysis, this application employs a modal superposition method based on quasi-static modal compensation. Furthermore, to reduce the overall stress on the structure, transient stress is used as a constraint. However, due to the large computational cost of traditional element stress constraints for cases with a large degree of freedom, a P-norm aggregation method is used to handle stress conditions, achieving overall structural stress control through the constraint aggregation stress. The Moving Asymptote Method (MMA) gradient algorithm is then used as the optimization algorithm. Considering the large computational cost required to solve for sensitivity using direct methods, some embodiments of this application use the Adjoint Method (AMS) to solve for sensitivity.

[0029] Comparing the proposed scheme with the dynamic flexibility topology optimization of traditional dynamics, it can be found that the topology optimization configuration using transient stress as a constraint produces some smooth transition parts compared with the traditional configuration, thereby achieving stress constraint of the overall structure.

[0030] Example 1:

[0031] The method for rapid solution of engineering structure topology optimization under transient stress constraints according to this application includes the following steps:

[0032] Step S0: Construct the topology optimization formula for the transient dynamic finite element model of the engineering structure.

[0033] Step S0 specifically includes:

[0034] 1. Finite element analysis of transient dynamic systems.

[0035] During normal service, engineering structures are typically subjected to a variety of complex operating conditions. Existing structures are prone to high stress levels in certain areas, resulting in insufficient safety margins and potential long-term issues such as fatigue cracking, local instability, or even overall failure. To address these technical shortcomings, including excessive structural stress and poor overall safety, it is necessary to redesign and optimize the existing structure. This application proposes a rapid solution method for topology optimization of engineering structures under transient stress constraints, used to optimize the topology of the original structural design domain.

[0036] 1.1 Transient dynamic finite element analysis based on the Newmark method.

[0037] For an N-DOF finite element structure, its transient dynamic finite element equations are expressed as:

[0038] (1)

[0039] Where K is the global stiffness matrix of the engineering structure, C is its global damping matrix, and M is its global mass matrix, with dimensions of . F(t) represents the external load, which is an N-dimensional vector. The global damping matrix C can be a classical damping matrix. Let be the displacement of the engineering structure at the initial moment. The velocity of the engineering structure at the initial moment; Let be the displacement response matrix of the engineering structure. Here is the velocity response matrix of the engineering structure. The acceleration response matrix of the engineering structure

[0040] External load It can be broken down into a constant term. and a time-related item The product of, i.e.:

[0041] (2)

[0042] For solving such transient dynamic problems, direct integration methods such as Newmark can be used.

[0043] In the interval In this method, the Newmark integration method makes the following assumptions:

[0044] (3)

[0045] in, and Let them be t-th and t-th respectively. Acceleration at a given moment; The parameter value is determined by the integration accuracy. The parameter value is determined by stability. and When the time condition is met, Newmark converges unconditionally. The coefficients of this method can be determined using these two parameter values, i.e.:

[0046] , , , ,

[0047] , , , , (4)

[0048] Forming an effective stiffness matrix :

[0049] (5)

[0050] For each time step The solution is obtained using the following formula. Payload at time This allows for the calculation of displacement, velocity, and acceleration at various time points.

[0051] (6)

[0052] (7)

[0053] (8)

[0054] in: for The external load at time t. This is achieved through formula (7). Solving for the displacement of the interval The dynamic compliance C at the mean time can be solved using the obtained displacement. Since direct integration methods such as Newmark are computationally intensive and inefficient in structural dynamics analysis with a large number of degrees of freedom and dense segmentation, order reduction algorithms can be used to accelerate the solution.

[0055] 1.2 Modal displacement method based on quasi-static response compensation for order reduction.

[0056] Current research on order reduction algorithms for transient dynamics can be divided into two categories: modal-based algorithms, such as the modal displacement method and modal acceleration method, with the latter, which has better convergence, utilizing quasi-static responses for correction to improve solution accuracy; and Krylov-based algorithms, such as the Ritz method, which often use Krylov expansion based on quasi-static responses to obtain the model's order reduction basis. Therefore, considering the quasi-static response containing high-frequency information in the order reduction model can improve the solution accuracy of the structural transient response. Traditional modal displacement methods reduce the order of the original structure using the solved eigenvectors; however, since its accuracy is usually related to the modal order solved by the modal displacement method, a modal displacement method based on quasi-static response compensation is used as an additional order reduction basis to achieve accuracy compensation. This method includes the following steps:

[0057] First, solve for the quasi-static response vector. :

[0058] (9)

[0059] Where F is the external load The constant vector and quasi-static response vector in the text. Satisfying quality normalization, that is: The quasi-static response is placed into the desired q-order mode to form a new q+1-order reduced basis. Then, the modal displacement method is used to reduce the order and solve the problem. In the q+1 subspace, the Newmark method is used to solve the transient response value of the structure. This improves the computational efficiency while ensuring accuracy. In order to solve the problem of large computational cost of the characteristic equation in the modal displacement method, a continuous iterative method of analysis and design is used to solve the eigenvectors and eigenvalues.

[0060] When using the modal displacement method, it is unavoidable to solve the characteristic equation, i.e., formula (10), but the traditional method has a large computational load. The continuous iterative method of analysis and design uses a set of approximate natural frequencies and mode vectors to replace the exact feature pairs in one topology optimization iteration. As the optimization process progresses, the natural frequencies and modes will gradually approach the exact feature pairs, thereby achieving simultaneous optimization convergence of the objective function and natural frequencies and modes, and realizing fast solution.

[0061] (10)

[0062] in, The eigenvalues ​​of the characteristic equation are the squares of the natural frequencies. is the eigenvector of the characteristic equation, i.e., the mode vector.

[0063] In the solution process, when the optimization iteration reaches k, the mode vector at the k-th iteration is... The solution can be obtained by following these steps:

[0064] (11)

[0065] In the formula , These are the global stiffness matrix and global mass matrix at the k-th iteration. For the pseudo-mode vector generated after k iterations, This is the modal vector obtained in the (k-1)th iteration.

[0066] (12)

[0067] in , These are the eigenvalues ​​in the subspace. Let be the modal vector in the subspace.

[0068] (13)

[0069] Since equation (12) is calculated in a subspace, the difficulty of solving it is greatly reduced compared to the original equation. Compared with the traditional dynamic topology optimization method, this method greatly reduces the solution time and can better improve the computational efficiency.

[0070] 2. Perform transient stress polymerization.

[0071] The transient stress matrix of any element, such as the e-th element, at time t can be expressed as:

[0072] (14)

[0073] Where D represents the elasticity matrix, B represents the displacement-strain matrix, and for a two-dimensional problem, the von Mises stress can be expressed as:

[0074] (15)

[0075] The parameter matrix H is:

[0076] (16)

[0077] As mentioned above, von Mises stress is discrete in both time and space and has a matrix form, allowing stress calculation at each spatiotemporal discretization point. However, processing it using element stress constraints would be computationally intensive; therefore, this application employs a P-norm aggregation method to handle global stress. For the spatiotemporally discrete von Mises stress, its P-norm aggregation function can be expressed as:

[0078] (17)

[0079] in, The transient stress after P-norm polymerization, The number of segments in time T; Let be the von Mises stress of the e-th element at time t; P is the polymerization parameter.

[0080] 3. Construct topology optimization formulas.

[0081] Based on the transient structural dynamics finite element model, the square of the overall average dynamic compliance of the structure at any given time is taken as the objective function, and a topology optimization formula is constructed, which can be expressed as:

[0082] (18)

[0083] Where: C represents the dynamic flexibility at the mean time; T is the total time of external load application; u(t) is the displacement response matrix of the structure; For the design variables of the e-th unit, the design variables are... Controlled within the minimum value of given design variables Between and 1; Let e ​​be the volume of the e-th unit; This represents the total number of units; Transient stress after P-norm polymerization; The set stress value; the constraints set by the optimized formula are: the sum of the total element volumes must be less than or equal to the set volume requirement V, and the stress after P-norm polymerization. Less than or equal to the set stress Under the given conditions, calculate the square of the average dynamic compliance of the entire structure at any given time. The minimum value.

[0084] Since the SIMP (Solid Isotropic Material Penalty Model) method model may encounter problems such as local modes in solving dynamic problems, this application adopts the RAMP (Rational Material and Penalty Model) interpolation model for discretization, as shown in formula (19).

[0085] ; ; (19)

[0086] in, For unit stiffness matrix, For unit The quality matrix. and They are respectively The stiffness matrix and mass matrix at time t. as well as They are respectively The stiffness matrix and mass matrix, It is a punishment factor.

[0087] The global stiffness matrix K and global mass matrix M can be obtained from the RAMP interpolation model for each element e. and The global damping matrix C can be obtained using the Rayleigh damping model, meaning that the global damping matrix C can be derived from the global stiffness matrix K and the global mass matrix M.

[0088] 4. Optimize processes

[0089] Step S1: Input the design variables The initial value, based on the design variables. The initial values ​​are obtained by using the RAMP interpolation model, i.e., formula (19), to derive the global stiffness matrix K, global mass matrix M and global damping matrix C, and input the initial values ​​of the modes.

[0090] Step S2: Using the initial values ​​of the global stiffness matrix K, global mass matrix M, and global damping matrix C, solve for the structural characteristic matrix of the engineering structure and perform q+1 order subspace projection. Specifically, this includes step S21, solving for the quasi-static response vector according to formula (9). Step S22: Solve the characteristic equation of the q-order subspace according to formula (12); Step S23: Update the eigenvector of the characteristic equation and use the obtained quasi-static response vector. The quasi-static response vector is added to the eigenvector as an additional reduced-order basis, that is, the quasi-static response vector is added to the eigenvector of the characteristic equation of the q-order subspace. The global stiffness matrix K, global mass matrix M, and global damping matrix C are reduced to a q+1 order subspace, i.e., projected onto the q+1 order subspace.

[0091] Step S3: Solve the displacement response matrix of the engineering structure in the q+1 order subspace using the Newmark method. That is, the displacement response matrix of the engineering structure is solved using formulas (3) to (8). And through the obtained displacement response matrix To solve for the objective function, which is the square of the dynamic compliance at the mean time step. and the transient stress after P-norm polymerization. ;

[0092] Step S4: Solve the objective function using the adjoint method. Sensitivity And the sensitivity of the transient stress after P-norm polymerization as a constraint function .

[0093] Step S5: Based on the objective function Sensitivity Sensitivity of transient stress after P-norm polymerization as a constraint function Iterative algorithms, such as the Moving Asymptote Method (MMA), are used for optimization to solve for the design variables in the next iteration. And set an iteration stopping criterion, wherein the iteration stopping criterion can be set as: when the design variables between two adjacent iteration steps... If the maximum difference is less than a preset value, or the iteration step is greater than a preset value (e.g., a specific value), the optimization process will terminate. If the stopping criterion is not met, the design variables are updated, and the process returns to step S2 to continue solving until the stopping criterion is met. A detailed flowchart of the optimization process is shown below. Figure 1 .

[0094] Example: Topology optimization of a two-dimensional cantilever beam structure.

[0095] A comparative analysis is conducted on a two-dimensional cantilever beam structure using both unconstrained and constrained conditions. This two-dimensional cantilever beam structure is... A rectangular design domain with a thickness of 0.001mm, such as... Figure 2 As shown, the left side is a fixed constraint, and a half-sine excitation external load F(t) is added to the lower node on the right side. The loading time is T=0.005s, and the frequency of this external load is... Number of segments The Young's modulus, Poisson's ratio, and density are taken as 1.9 GPa, 0.3, and 0.3 GPa, respectively. The aggregation factor P is 12. Since using the instantaneous stress after P-norm polymerization as a constraint is prone to local optima, random values ​​of [0-1] are used for the structural design variables, with the volume requirement V set to 0.3, and the iteration stopping requirement being that the design variable is less than 0.3. Or the number of iterations is greater than 300.

[0096] By comparing the topology optimization results under two working conditions—with and without stress constraints—the corresponding optimal configuration and its stress contour plot can be obtained, such as... Figure 3 As shown. Figure 3 As shown in sections A and B, without applying stress constraints, the optimization results tend to form the shortest force path. Only a few main load-bearing members are retained inside the structure, and only crossbars participate in the force in the area near the load end. The maximum equivalent stress of the structure as a whole is about 950 MPa.

[0097] After introducing the P-norm transient stress constraint described in this application, the optimized configuration differs significantly from the unconstrained case: on the one hand, the original lower crossbars near the load application location disappear; on the other hand, multiple diagonal stiffening members are generated inside the structure, replacing the original single force path with multiple force transmission paths, effectively dispersing high-stress areas. While maintaining overall stiffness, this reduces local stress concentration, lowering the maximum equivalent stress to approximately 900 MPa, and resulting in a more uniform stress distribution. Figure 3 As shown in parts C and D.

[0098] Example 2:

[0099] Embodiment 2 of the present invention provides a fast solution system for dynamic topology optimization under transient stress constraints, comprising:

[0100] The topology optimization formula construction module is configured to construct the topology optimization formula of the transient dynamic finite element model of the engineering structure according to the above step S0;

[0101] The initial value input module is configured to input the initial values ​​of the transient dynamic finite element model and the initial values ​​of the modes according to the above step S1;

[0102] The structural feature solving and order reduction module is configured to solve the structural features and perform q+1 order subspace projection according to the above step S2.

[0103] The objective function and aggregate instantaneous stress constraint function solving module is configured to solve the objective function of the topology optimization formula and the constraint function of the instantaneous stress using P-norm aggregation according to the above step S3;

[0104] The sensitivity calculation module is configured to solve for the objective function sensitivity and the constraint function sensitivity according to step S4 above; and

[0105] The iterative optimization module is configured to perform iterative optimization according to step S5 above to obtain the optimal design variables.

[0106] Example 3:

[0107] Embodiment 3 of the present invention provides a computer-readable storage medium storing a program thereon, which, when executed by a processor, implements the steps of the method for rapidly solving dynamic topology optimization under transient stress constraints as described in Embodiment 1 of the present invention.

[0108] Example 4:

[0109] Embodiment 4 of the present invention provides an electronic device, including a memory, a processor, and a program stored in the memory and executable on the processor. When the processor executes the program, it implements the steps in the method for rapidly solving dynamic topology optimization under transient stress constraints as described in Embodiment 1 of the present invention. Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of hardware embodiments, software embodiments, or embodiments combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage and optical storage) containing computer-usable program code.

[0110] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0111] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0112] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0113] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The program can be stored in a computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. The storage medium can be a magnetic disk, optical disk, read-only memory (ROM), or random access memory (RAM), etc.

[0114] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for rapid solution of engineering structure topology optimization under transient stress constraints, characterized in that, Including the following steps: S0: Topology optimization formulation for constructing the transient dynamic finite element model of the engineering structure; include A transient dynamic finite element model of the engineering structure, comprising multiple elements, is established. This transient dynamic finite element model is derived from the transient dynamic finite element equations. In this representation, K is the global stiffness matrix of the engineering structure, C is its global damping matrix, and M is its global mass matrix, all with dimensions of 1. ; Let be the displacement of the engineering structure at the initial moment. Let be the initial velocity of the engineering structure; F(t) is the external load, which is an N-dimensional vector. Let be the displacement response matrix of the engineering structure. Here is the velocity response matrix of the engineering structure. Here is the acceleration response matrix of the engineering structure; Construct the topology optimization formulation of the transient dynamic finite element model, and express the square of the average dynamic compliance of the engineering structure. Consider it as an objective function: ； Where: T is the total time of external load application; Let represent the design variable of the e-th element in the transient dynamic finite element model; Let represent the volume of the e-th element in the transient dynamic finite element model; The transient stress after P-norm polymerization is defined by the following constraints in the topology optimization formulation: the sum of the total element volumes must be less than the set volume requirement V, and the transient stress after P-norm polymerization is... It should be less than the set stress. Under the given conditions, solve for the square of the average dynamic compliance. The minimum value; Step S1: Input the design variables The initial value, based on the design variables. The initial values ​​are obtained using the RAMP interpolation model. ; Derive the initial values ​​of the global stiffness matrix K, global mass matrix M, and global damping matrix C, and input the initial values ​​of the modes; where, For any unit stiffness matrix, For unit The quality matrix; and They are respectively The stiffness matrix and mass matrix at time t. as well as They are respectively The stiffness matrix and mass matrix, It is a penalty factor; the global stiffness matrix K and the global mass matrix M are obtained by interpolating each element e through the RAMP interpolation model. and Composition; the global damping matrix C is obtained from the global stiffness matrix K and the global mass matrix M; Step S2: Based on the initial values ​​of the global stiffness matrix K, global mass matrix M, and global damping matrix C, solve for the structural characteristic matrix of the engineering structure and perform q+1 order subspace projection; Step S3: Solve the displacement response matrix of the structure in the q+1 order subspace using the Newmark method. ; and through the obtained displacement response matrix To solve for the square of the dynamic compliance of the objective function at the mean time step. And the transient stress after P-norm polymerization; Step S4: Solve for the sensitivity of the objective function using the adjoint method. And the sensitivity of the transient stress after P-norm polymerization as a constraint function ; Step S5: Based on the objective function Sensitivity The sensitivity of the transient stress after P-norm polymerization as a constraint function An iterative algorithm is used for optimization to solve for the design variables in the next iteration. And set an iteration stopping criterion, wherein the iteration stopping criterion can be set as: when the design variables between two adjacent iteration steps... If the maximum difference is less than the preset value or the number of iterations is greater than the preset value, the optimization will terminate.

2. The method for rapid solution of engineering structure topology optimization under transient stress constraints according to claim 1, characterized in that, In step S5, if the stopping criterion is not met in a certain iteration step, the design variables are updated, and the process returns to step S2 to continue solving until the stopping criterion is met.

3. The method for rapid solution of engineering structure topology optimization under transient stress constraints according to claim 1, characterized in that, Step S2 includes step S21, solving for the quasi-static response vector. Step S22: Solve the characteristic equation of the q-order subspace; and step S23: Update the eigenvector of the characteristic equation, and use the obtained quasi-static response vector... The quasi-static response vector is added to the eigenvector as an additional reduced-order basis, that is, the quasi-static response vector is added to the eigenvector of the characteristic equation of the q-order subspace. The global stiffness matrix K, the global mass matrix M, and the global damping matrix C are reduced to the q+1 order subspace.

4. The method for rapid solution of engineering structure topology optimization under transient stress constraints according to claim 3, characterized in that, In step S21, according to the formula Solving for the quasi-static response vector Where F is the external load The constant vector and quasi-static response vector in the text. Satisfying quality normalization, that is: The quasi-static response is placed into the desired q-order mode to form a new q+1-order reduced basis. Then, the modal displacement method is used to reduce the order and solve the problem. The Newmark method is used to solve the transient response value of the structure in the q+1 subspace.

5. The method for rapid solution of engineering structure topology optimization under transient stress constraints according to claim 3, characterized in that, In step S22, according to Solve the characteristic equation of the q-th order subspace, where , These are the eigenvalues ​​in the subspace. Let be the modal vector in the subspace.

6. The method for rapid solution of engineering structure topology optimization under transient stress constraints according to claim 3, characterized in that, The Newmark method is used to solve the displacement function of the structure in the q+1 order subspace. : in, and Let them be t and respectively Acceleration at a given moment; The parameter value is determined by the integration accuracy. These are parameter values ​​determined by stability, among which and Therefore, the coefficient is: , , , , , , , Forming an effective stiffness matrix : For each time step The solution is obtained using the following formula. Payload at time This allows for the calculation of displacement, velocity, and acceleration at various time points. ； ； ； in: for External load at any given time.

7. The method for rapid solution of engineering structure topology optimization under transient stress constraints according to claim 1, characterized in that, The transient stress after P-norm polymerization is passed through Solve for, where, The number of segments in time T; Let be the von Mises stress of the e-th element at time t; P is the polymerization parameter.

8. The method for rapid solution of engineering structure topology optimization under transient stress constraints according to claim 1, characterized in that, The iterative algorithm is the moving asymptote method.

9. A topology optimization system for engineering structures that provides fast solutions under transient stress constraints, characterized in that, The method includes a processor and a memory, the memory storing computer code, and the processor executing the computer code to implement the method of any one of claims 1 to 8.

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