Structure full-scale topological optimization method under dynamic load

Abstract

The invention belongs to the related technical field of structure optimization, and discloses a full-scale topological optimization method of a structure under dynamic load, which comprises the following steps of: (1) constructing local volume constraints to represent the allowable maximum material volume in each grid neighborhood of the structure to be optimized, and aggregating all the local volume constraints in a design domain into a total constraint; (2) dispersing the duration of the dynamic load, performing dynamic finite element analysis in each time step, taking a continuous density field of the structure as a design variable, minimizing the dynamic flexibility of the structure as a target function, taking a dynamic balance equation of the structure as a control equation, and constructing a constraint function based on global volume constraint and local volume constraint obtained by aggregation, so as to obtain a dynamic load; further constructing a full-scale topological optimization model under the dynamic load; and (3) solving the control equation, carrying out dynamic finite element analysis on the to-be-optimized structure, and solving the full-scale topological optimization model to obtain the optimal density distribution of the structure. The method considers the influence of the dynamic load.

Description

Technical Field

[0001] The present invention belongs to the technical field related to structural optimization, and more specifically, relates to a full-scale topology optimization method for structures under dynamic loads. Background Art

[0002] Dynamic loads are ubiquitous in engineering scenarios such as spacecraft takeoff and landing shock, automotive collision energy absorption, and building structure earthquake resistance. Such dynamic load conditions pose requirements for the dynamic performance of structures under the premise of lightweight. The full-scale topology optimization method is an effective method for designing porous filled structures, which can reasonably distribute materials in the principal stress direction and design porous filled structures with the characteristics of bone bionics. Such structures are widely used in fields such as aerospace. However, traditional full-scale topology optimization mostly focuses on static load conditions and is difficult to effectively obtain dynamic response characteristics, while the full-scale topology optimization method for structures under dynamic loads can better simulate the actual working condition loads and design lightweight and porous filled structures with better dynamic performance.

[0003] Regarding the topology optimization of dynamic loads, relevant technical personnel in this field have conducted some research. For example, the paper "Giraldo-Londono O, Paulino G H. PolyDyna: a Matlab implementation for topology optimization of structures subjected to dynamic loads[J]. Structural and Multidisciplinary Optimization, 2021, 64(2): 957-990." proposed a topology optimization method for structures subjected to aperiodic dynamic loads. By solving the dynamic finite element model through the time-domain integration method, topology optimization design with the objectives of minimizing dynamic compliance, minimizing strain energy, and minimizing mean square displacement under various boundary conditions was achieved. However, only single-scale optimization was considered in this method, and the potential of materials was not fully exploited to achieve a design with a higher degree of freedom. Moreover, it was unable to design porous structures with characteristics such as light weight, high strength, buffering, and energy absorption. Another example is the paper "Wu J, Aage N, Westermann R, et al. Infill optimization for additive manufacturing approaching bone-like porous structures[J]. IEEE transactions on visualization and computer graphics, 2017, 24(2): 1127-1140." Inspired by the bone structure, a topology optimization design method for bone-like porous structures was proposed. This full-scale method can avoid the scale separation effect of traditional cross-scale methods and ensure the natural connection of the filling structure without additional constraint conditions. However, this method is only limited to the static load condition and does not consider the influence of dynamic loads.

[0004] Therefore, how to perform full-scale topology optimization design on a structure while considering the influence of dynamic loads on the dynamic effects of the structure to obtain a porous filling structure with excellent dynamic performance is an urgent problem to be solved. Summary of the Invention

[0005] In view of the above defects or improvement requirements of the prior art, the present invention provides a full-scale topology optimization method for structures under dynamic loads, aiming to solve the problem of how to perform full-scale topology optimization on a structure while considering the influence of dynamic loads on the dynamic response of the structure.

[0006] To achieve the above object, according to one aspect of the present invention, a full-scale topology optimization method for structures under dynamic loads is provided. The method includes the following steps:

[0007] (1) Construct local volume constraints to represent the maximum allowable material volume within each grid neighborhood of the structure to be optimized, and use the p-norm function to aggregate all local volume constraints within the design domain into a total constraint;

[0008] (2) Discretize the duration of the dynamic load into t time steps, and perform dynamic finite element analysis within each discrete time step. Using the structural continuous density field as the design variable, minimizing the structural dynamic compliance as the objective function, and using the dynamic equilibrium equation of the structure as the control equation, construct a constraint function based on the global volume constraint and the aggregated local volume constraints, and then construct a full-scale topology optimization model under dynamic load;

[0009] (3) Use the HHT-α method to solve the control equation and perform dynamic finite element analysis of the structure to be optimized, and then solve the full-scale topology optimization model to obtain the optimal structural continuous density field.

[0010] Furthermore, the local volume constraint for each grid neighborhood within the design domain is:

[0011]

[0012] where ρ i is the Boolean value of the density of each grid within the neighborhood, and α local is the maximum allowable material volume within each grid neighborhood; is the set of neighborhood grids whose distance from the centroid of all centroids to the centroid of grid e is less than the given influence radius R1, that is:

[0013]

[0014] Furthermore, use the p-norm function to aggregate all local volume constraints within the design domain into a total constraint, specifically:

[0015]

[0016] where p is the parameter of the p-norm function.

[0017] Furthermore, the mathematical expression of the full-scale topology optimization model is:

[0018] find {x1,x2,…x N} T

[0019]

[0020] 0≤x e ≤1,e=1,…,N

[0021] where x is the design variable, N is the total number of design variables, and x eis the density of the e-th design variable; c is the objective function representing the dynamic compliance of the structure, N t is the t-th time step within the duration of the dynamic load; M, C, and K are the mass matrix, damping matrix, and stiffness matrix respectively, u i , u i are the acceleration vector, velocity vector, and displacement vector respectively within each time step, f i is the force vector within each time step; g1(x) and g2(x) are the constraint functions for the local volume and global volume respectively, ρ e is the boolean value of the mesh density within the discrete design domain, is the local volume fraction of mesh e in the specified neighborhood, p is the p-norm function parameter, v e is the volume of the mesh, α local is the maximum allowable material volume for each mesh within its neighborhood, α total is the upper limit of the maximum material usage within the design domain.

[0022] Furthermore, the calculation formula for the dynamic compliance of the structure is:

[0023]

[0024] The constraint functions include local volume constraint and total volume constraint, which are respectively:

[0025]

[0026] Furthermore, after calculating the value of the objective function based on the results of dynamic finite element analysis, the sensitivities of the objective function and constraint functions are solved by combining the discrete-then-differentiate method and the adjoint method, and the design variables are updated based on the obtained sensitivity results, and the full-scale topology optimization model is iteratively solved continuously until the optimal density distribution of the structure to be optimized under dynamic load is obtained, completing the topology optimization design.

[0027] Furthermore, the mass matrix, stiffness matrix, and damping matrix of the structure are calculated during each iteration, and the corresponding formulas are:

[0028]

[0029] C = α r M + β r K

[0030] where, is the volume interpolation function, m e is the element mass matrix, is the material interpolation function, k e is the element stiffness matrix, α r and β r are the Rayleigh damping parameters.

[0031] Further, the volume interpolation function and the material interpolation function are calculated by using the Threshold threshold projection function. The calculation formulas of the volume interpolation function and the material interpolation function are as follows:

[0032]

[0033] In the formula, the parameter ε << 1, m V (x e ) is the volume interpolation function under the Threshold threshold projection, and are the Threshold threshold projection function parameters, is the filtering density, m E (x e ) is the RAMP material interpolation function, and p0 is the RAMP penalty parameter.

[0034] The present invention also provides a full-scale topology optimization system for structures under dynamic loads. The system includes a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, it executes the full-scale topology optimization method for structures under dynamic loads as described above.

[0035] The present invention also provides a computer-readable storage medium. The computer-readable storage medium stores machine-executable instructions. When the machine-executable instructions are called and executed by a processor, the machine-executable instructions cause the processor to implement the full-scale topology optimization method for structures under dynamic loads as described above.

[0036] Generally speaking, compared with the prior art through the above technical solutions conceived by the present invention, the full-scale topology optimization method and device for structures under dynamic loads provided by the present invention mainly have the following beneficial effects:

[0037] 1. The present invention constructs a full-scale topology optimization model under dynamic loads, analyzes the dynamic response of the structure at each discrete time step of the load duration to consider the influence of dynamic loads, introduces local volume constraints to control the material distribution, realizes the filling design of bone-like porous structures under arbitrary time-domain dynamic loads, effectively expands the applicable range of topology optimization load conditions, and provides a new idea for the design of porous structures under dynamic loads.

[0038] 2. The present invention uses the p-norm function to aggregate all local volume constraints into a total constraint, enabling effective numerical solution, avoiding excessive material aggregation to form large solid regions, making the material distribution more uniform within the design domain, and achieving full-scale topology optimization design. Compared with traditional cross-scale topology optimization design, the full-scale method can not only avoid the scale separation effect, improve the connectability of microstructures, but also significantly reduce the computational cost and improve the design efficiency.

[0039] 3. The present invention uses the HHT-α method as the time integration algorithm to solve the governing equations and perform dynamic finite element analysis. Combining the method of discrete-then-differentiate and the adjoint method for sensitivity analysis on the full-scale topology optimization model discretized in time and space, it avoids the consistency error problem in sensitivity calculation caused by treating time as a continuous variable. Compared with the topology optimization design under traditional static loads, the method provided by the present invention can accurately fit dynamic load conditions and further enhance the application potential in the field of practical engineering. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 is a flowchart of a full-scale topology optimization method for structures under dynamic loads provided by the present invention;

[0041] Figure 2 is a schematic diagram of the initial design domain, constraint boundaries, and dynamic loads of a beam fixed at both ends constructed in an embodiment of the present invention;

[0042] Figure 3 is a schematic diagram of the dynamic load applied in an embodiment of the present invention;

[0043] Figure 4 is a schematic diagram of the final optimization result in an embodiment of the present invention;

[0044] Figure 5 In (a), (b), and (c) of are schematic diagrams of the variation of the maximum displacement, velocity, and acceleration of the structure in an embodiment of the present invention with time;

[0045] Figure 6 is a schematic diagram of the optimization iteration process in an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0046] In order to make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0047] Please refer to Figure 1, the present invention provides a full-scale topology optimization method for structures under dynamic loads. The topology optimization method realizes the filling design of bone-like porous structures under arbitrary time-domain dynamic loads, effectively expanding the applicable range of topology optimization load conditions, providing new ideas for the design of porous structures under dynamic loads, and further enhancing the application potential of topology optimization in the field of practical engineering. On the premise of taking into account the influence of dynamic loads on the dynamic response of structures, the topology optimization method combines the full-scale topology optimization method to fully exert the material potential and design a lightweight porous filling structure with good dynamic performance.

[0048] The topology optimization method mainly includes the following steps:

[0049] Step 1, construct local volume constraints to represent the maximum allowable material volume in each grid domain of the structure to be optimized, and use the p-norm function to aggregate all local volume constraints in the design domain into a total constraint.

[0050] Specifically, define parameters such as the initial design domain, material properties, and boundary conditions of the structure to be optimized, discretize the design domain into N grid cells, and represent the filling state of the grid by the Boolean value of the grid density.

[0051] Use local volume constraints to represent the maximum allowable material volume in each grid neighborhood, and use the p-norm function to aggregate all local volume constraints in the design domain into a total constraint, which specifically includes the following sub-steps:

[0052] (1) Discretize the design domain into N grid cells, and assign a Boolean value to each grid cell to describe its filling state, specifically:

[0053] ρ e ={0,1}

[0054] ρ e is the Boolean value of each grid density, representing the void-phase material (ρ e =0) and the filling material (ρ e =1) respectively.

[0055] (2) Define the set of neighborhood grids whose distance from the centroid of all centroids to the centroid of grid e is less than the given influence radius R1 Specifically:

[0056]

[0057] where r i is the centroid of each grid cell in the neighborhood, and r eis the centroid of grid e. The influence radius R1 can control the porosity and microstructure morphology of the structure, and its value is set artificially. A smaller influence radius makes the local constraints strict and generates a porous structure with a high porosity. A larger influence radius reduces the porosity of the structure while improving the computational efficiency and convergence.

[0058] (3) The local volume constraint of each grid neighborhood in the design domain is expressed as:

[0059]

[0060] where ρi is the Boolean value of the density of each grid in the neighborhood, and its value takes ρ i ={0, 1}, representing the void-phase material (ρ i =0) and the filling material (ρ i =1) respectively; α local is the maximum allowable material volume in each grid neighborhood; is the set of neighborhood grids whose distance from the centroid of all centroids to the centroid of grid e is less than the given influence radius R1, that is:

[0061]

[0062] Among them, the local volume constraint is used to control the generation of the microstructure, avoid the scale separation problem generated by the traditional cross-scale method, and significantly improve the computational efficiency.

[0063] (4) The p-norm function is used to aggregate all local volume constraints in the design domain into a total constraint, specifically:

[0064]

[0065] where p is the parameter of the p-norm function. The p-norm function is used to approximate the maximum value function, aggregate a large number of local volume constraints into a single constraint for numerical optimization. The value of p is given artificially. The larger the p value, the more accurate the approximation of the p-norm function to the maximum value function, and the stricter the execution of the local volume constraint for each grid. However, an overly large p value will increase the nonlinearity of the optimization problem and reduce the solution efficiency.

[0066] Step 2: Discretize the duration of the dynamic load into t time steps. Conduct dynamic finite element analysis within each discrete time step. Take the structural continuous density field as the design variable, minimize the structural dynamic compliance as the objective function, take the dynamic equilibrium equation of the structure as the control equation, construct a constraint function based on the global volume constraint and the aggregated local volume constraint, and then construct a full-scale topology optimization model under dynamic load.

[0067] Step 2 includes the following sub-steps:

[0068] (1) Define a time-varying dynamic load f(t) and discretize the load duration T into t time steps. f Discretize it into t time steps.

[0069] (2) Construct a full-scale topology optimization model under dynamic loads. The mathematical expression of the full-scale topology optimization model is:

[0070] find{x1,x2,…x N} T

[0071]

[0072] 0≤x e ≤1,e = 1,…,N

[0073] In the formula, x is the design variable, N is the total number of design variables, and x e is the density of the e-th design variable; c is the objective function, representing the dynamic compliance of the structure, and N t is the t-th time step discretized within the dynamic load duration; M, C, and K are the mass matrix, damping matrix, and stiffness matrix respectively, u i are the acceleration vector, velocity vector, and displacement vector within each time step respectively, and f i is the force vector within each time step; g1(x) and g2(x) are the constraint functions for local volume and global volume respectively, and ρ e is the Boolean value of the mesh density within the discrete design domain, is the local volume fraction of mesh e in the specified neighborhood, p is the p-norm function parameter, v e is the volume of the mesh, and α local is the maximum allowable volume of materials for each mesh within its neighborhood, and α total is the upper limit of the maximum material usage within the design domain.

[0074] The dynamic compliance of the structure is used to measure the dynamic stiffness of the structure under dynamic loads and is one of the manifestations of the dynamic performance of the structure. In the full-scale topology optimization model, the objective function is to minimize the dynamic compliance of the structure. The calculation formula for the dynamic compliance of the structure is:

[0075]

[0076] The constraint functions include local volume constraints and overall volume constraints, specifically:

[0077]

[0078] Step 3: Use the HHT-α method to solve the governing equations and perform a dynamic finite element analysis of the structure to be optimized, and then solve the full-scale topology optimization model to obtain the optimal density distribution of the structure.

[0079] During the solution process of the full-scale topology optimization model, after calculating the objective function value based on the results of dynamic finite element analysis, the sensitivity of the objective function and the constraint function is solved by combining the discrete-then-differentiate method and the adjoint method, and the design variables are updated based on the obtained sensitivity results. The full-scale topology optimization model is continuously iteratively solved, and finally the optimal density distribution of the structure to be optimized under dynamic loads is obtained, completing the topology optimization design.

[0080] During the solution process of the full-scale topology optimization model, the mass matrix, stiffness matrix, and damping matrix of the structure are calculated at each iteration. The corresponding formulas are:

[0081]

[0082] C = α r M + β r K

[0083] Where is the volume interpolation function, m e is the element mass matrix, is the material interpolation function, k e is the element stiffness matrix, α r and β r are the Rayleigh damping parameters.

[0084] The element mass matrix and the element stiffness matrix are expressed as:

[0085]

[0086] Where ρ0 is the material mass density, N e is the shape function matrix of element e, B e is the strain-displacement matrix of element e, and D0 is the constitutive matrix of linear isotropic material.

[0087] The Threshold threshold projection function is used to calculate the volume interpolation function and the material interpolation function. The calculation formulas of the volume interpolation function and the material interpolation function are respectively:

[0088]

[0089] In the formula, the parameter ε << 1 to avoid numerical instability when x e → 0. m V (x e ) is the volume interpolation function under Threshold threshold projection, and are the Threshold threshold projection function parameters, is the filtered density, m E (xe ) is the interpolation function of the RAMP material, and p0 is the RAMP penalty parameter.

[0090] At each iteration, after calculating the mass, stiffness, and damping matrices of the structure, the governing equations are solved based on the HHT-α method and dynamic finite element analysis is performed to calculate the acceleration, velocity, and displacement vectors within each time step.

[0091] As a generalized Newmark-β method, HHT-α regulates the integration format of the governing equations through the numerical damping parameter α, making the iterative process unconditionally stable. The basic form of the HHT-α method is:

[0092]

[0093] where u i 、 u i are the acceleration, velocity, and displacement vectors at time i respectively. α is the basic parameter of the HHT-α method. Reasonable selection of α ensures that the algorithm has at least second-order accuracy and unconditional stability.

[0094] Based on the acceleration, velocity, and displacement vectors at each moment, after calculating the objective function value for each iteration, the sensitivity of the objective function and the sensitivity of the constraint function are solved by combining the discrete-then-differentiate method and the adjoint method; furthermore, based on the sensitivity of the objective function and the sensitivity of the constraint function, the MMA optimization algorithm is used to update the design variables, and the density filtering and Threshold threshold projection function are used to process the design variables.

[0095] Through the Newmark-β finite difference relationship, the update forms of the displacement and velocity fields are:

[0096]

[0097] where β and γ are the Newmark-β finite difference relationship parameters, satisfying:

[0098]

[0099] Substituting the updated displacement and velocity fields into the basic form of the HHT-α method, the residual of the discrete form of the governing equations is obtained, specifically:

[0100]

[0101] Solving the above residual equation, the acceleration vector at time i is obtained The velocity vector at time i is further obtained and the displacement vector u i .

[0102] Calculate the objective function value based on the acceleration, velocity, and displacement vectors at the i-th moment, and solve the sensitivities of the objective function and the constraint function by combining the discrete-then-differentiate method and the adjoint method. At each iteration, update the design variables using the MMA algorithm, and process the design variables using density filtering and the Threshold threshold projection function to obtain the physical density. The distribution of the physical density is the topology optimization result.

[0103] Specifically, update the design variables using the MMA algorithm, use density filtering to avoid numerical instability phenomena such as checkerboarding and mesh dependence, and use the Threshold threshold projection to reduce the gray-scale elements in the optimization process and obtain a clear topology configuration.

[0104] After each iteration, determine whether the objective function meets the set threshold, that is, the convergence condition. If the convergence condition is met, output the current topology structure; otherwise, continue the iteration.

[0105] The following uses specific embodiments to further elaborate on the present invention in detail.

[0106] As Figure 2 shown, taking the design domain of a two-dimensional fixed beam as an example, the design domain size is length L = 400 mm, width H = 80 mm, and thickness t = 10 mm. The two ends of the design domain are fixed, and the load application point is at the bottom midpoint. The load adopts a half-cycle sine load form, and its expression is f(t) = 4000sin(π / t f ), where t f = 0.1 s is the load duration. Discretize it using 400×80 = 32000 four-node finite element meshes. The material elastic modulus E = 20 MPa, and the Poisson's ratio μ = 0.3. The maximum local volume is taken as α local = 0.6, and the maximum overall material volume is taken as α total = 0.5.

[0107] As Figure 3 shown is the half-cycle sine load applied to the structure, with a load peak of 4000 N and a duration of 0.1 s. Figure 4 is the final optimization result. Figure 5 In (a)-(c) are the maximum displacement, velocity, and acceleration curves of the optimized structure respectively. Figure 6 is the optimization iteration process. From Figure 4 it can be seen that under dynamic loads, the full-scale optimization method can generate a structure with pores and good microstructural connectivity, and this structure has certain bone-like characteristics. From Figure 5 it can be seen that under dynamic loads, the maximum displacement, velocity, and acceleration of the structure change with time, having certain dynamic characteristics, further demonstrating the necessity of considering dynamic loads.

[0108] The present invention constructs a local volume constraint based on the p-norm function, realizes effective numerical solution, avoids the excessive aggregation of materials to form large solid regions, and makes the materials more evenly distributed within the design domain; constructs a full-scale topology optimization model under dynamic loads, and realizes the full-scale topology optimization design of arbitrary time-domain dynamic loads; uses the HHT-α method to solve the control equations, and solves the time-domain integral solution problem; uses the method of discrete-then-differentiate and the adjoint method to solve the sensitivities of the objective function and the constraint function, and avoids the consistency error problem in sensitivity calculation caused by taking time as a continuous variable; uses the MMA algorithm to update the design variables and obtains the final topology optimization result.

[0109] The present invention realizes the filling design of bone-like porous structures under the action of arbitrary time-domain dynamic loads, effectively expands the applicable range of topology optimization load conditions, provides new ideas for the design of porous structures under dynamic loads, and further enhances the application potential of topology optimization in the field of practical engineering.

[0110] The present invention also provides a full-scale topology optimization system for structures under dynamic loads. The system includes a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, it executes the full-scale topology optimization method for structures under dynamic loads as described above.

[0111] The present invention also provides a computer-readable storage medium. The computer-readable storage medium stores machine-executable instructions. When the machine-executable instructions are called and executed by a processor, the machine-executable instructions cause the processor to implement the full-scale topology optimization method for structures under dynamic loads as described above.

[0112] Those skilled in the art can easily understand that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A method for full-scale topology optimization of a structure under dynamic load, characterized in that: The method comprises the following steps: (1) Construct a local volume constraint to represent the maximum material volume allowed in each grid area of ​​the structure to be optimized, and use the p-norm function to aggregate all local volume constraints in the design domain into a total constraint; (2) The duration of the dynamic load is discretized into t time steps, and a dynamic finite element analysis is performed in each discrete time step. The continuous density field of the structure is used as the design variable, the minimization of the dynamic flexibility of the structure is used as the objective function, and the dynamic equilibrium equation of the structure is used as the control equation. A constraint function is constructed based on the global volume constraint and the local volume constraint obtained by aggregation, and then a full-scale topology optimization model under dynamic load is constructed. (3) The HHT-α method is used to solve the control equations and perform dynamic finite element analysis of the structure to be optimized, and then the full-scale topology optimization model is solved to obtain the optimal density distribution of the structure.

2. The method for full-scale topology optimization of a structure under dynamic load according to claim 1, characterized in that: The local volume constraint for each mesh neighborhood within the design domain is: In the formula, ρ i is the Boolean value of each grid density in the neighborhood, α local is the maximum volume of material allowed within each grid neighborhood; is the set of all neighboring grids whose centroids are less than the given influence radius R1 from the centroid of grid e, that is:

3. The method for full-scale topology optimization of a structure under dynamic load according to claim 2, characterized in that: The p-norm function is used to aggregate all local volume constraints in the design domain into a total constraint, specifically: Where p is the p-norm function parameter.

4. The method for full-scale topology optimization of a structure under dynamic load according to claim 1, characterized in that: The mathematical expression of the full-scale topology optimization model is: find{x1,x2,…x N } T 0≤x e ≤1,e=1,…,N In the formula, x is the design variable, N is the total number of design variables, and x e is the density of the e-th design variable; c is the objective function, which represents the dynamic flexibility of the structure, N t is the tth discrete time step within the duration of the dynamic load; M, C, K are the mass matrix, damping matrix, and stiffness matrix, respectively, and u i , u i are the acceleration vector, velocity vector, and displacement vector in each time step, respectively, and f i is the force vector within each time step; g1(x) and g2(x) are the constraint functions of the local volume and the global volume, respectively, and ρ e is a Boolean value for the mesh density in the discretized design domain, is the local volume fraction of the grid e in the specified neighborhood, p is the p-norm function parameter, v e is the volume of the grid, α local is the maximum volume of material allowed for each grid in its neighborhood, α total It is the maximum usage limit of the material in the design domain.

5. The method for full-scale topology optimization of a structure under dynamic load according to claim 4, characterized in that: The calculation formula of structural dynamic flexibility is: The constraint function includes local volume constraint and total volume constraint, which are:

6. The method for full-scale topology optimization of a structure under dynamic load according to claim 1, characterized in that: After calculating the objective function value based on the results of dynamic finite element analysis, the sensitivity of the objective function and constraint function is solved by combining the discretization-then-differentiation method and the adjoint method. The design variables are updated based on the obtained sensitivity results, and the full-scale topology optimization model is continuously iterated and solved. Finally, the optimal density distribution of the structure to be optimized under dynamic load is obtained, and the topology optimization design is completed.

7. The method for full-scale topology optimization of a structure under dynamic load according to claim 6, characterized in that: The mass matrix, stiffness matrix and damping matrix of the structure are calculated at each iteration, and the corresponding formulas are: C=a r M+β r K in, is the volume interpolation function, m e is the unit mass matrix, is the material interpolation function, k e is the element stiffness matrix, α r With β r is the Rayleigh damping parameter.

8. The method for full-scale topology optimization of a structure under dynamic load according to claim 7, characterized in that: The volume interpolation function and material interpolation function are calculated using the Threshold projection function. The calculation formulas of the volume interpolation function and the material interpolation function are: In the formula, the parameter ε<<1, m V (x e ) is the volume interpolation function under Threshold projection, and is the Threshold projection function parameter, is the filtration density, m E (x e ) is the RAMP material interpolation function, and p0 is the RAMP penalty parameter.

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