Explicit topology optimization framework-based ultra-high-speed impact-resistant structure design optimization method

By combining an explicit topology optimization framework and a moving deformable component method with a non-gradient genetic algorithm, the problems of large computational load and difficult simulation in the design of ultra-high speed impact protection structures by traditional methods are solved, and efficient and accurate structural optimization and simulation are achieved.

CN121389323AActive Publication Date: 2026-01-23DALIAN UNIV OF TECH
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Patent Information

Application Number
CN202511563353.7
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2025-10-30
Publication Date
2026-01-23
Estimated Expiration
2045-10-30

AI Technical Summary

Technical Problem

In the design of ultra-high-speed impact protection structures, existing technologies, such as traditional topology optimization methods, cannot effectively describe the severe plastic deformation, melting, and vaporization processes of materials. They also involve large computational loads and are difficult to simulate with high fidelity, making it difficult to achieve the optimization objectives.

Method used

The Moving Deformable Component (MMC) method based on an explicit topology optimization framework is adopted, combined with non-gradient genetic algorithm (GA) and smooth particle hydrodynamics (SPH), to optimize the structure with a small number of design variables. Commercial software is used for nonlinear dynamic analysis and genetic algorithm to update the design variables.

Benefits of technology

The system achieves efficient optimization design of ultra-high-speed impact-resistant structures, reduces computational costs and time, generates clear geometric boundaries and high-precision SPH models, and can more accurately simulate ultra-high-speed impact processes.

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Abstract

The invention belongs to the technical field of computational mechanics relating to nonlinear topological optimization, and particularly relates to an ultra-high-speed impact-resistant structure design optimization method based on an explicit topological optimization framework, in a framework based on a mobile deformable component method, an upper limit and a lower limit need to be set for a design variable of the mobile deformable component method; then, the genetic algorithm randomly generates multiple groups of candidate design variables, and an initial structure configuration is obtained; the configuration is then converted into a smoothed particle fluid dynamic model, and corresponding boundary conditions are applied; then obtaining structural response of mass and displacement, and constructing an objective function and related constraint conditions thereof; and finally, according to a design variable updating criterion of a genetic algorithm, applying crossover and mutation genetic operation so as to generate a next-generation candidate design variable, and after iteration is finished, selecting an optimal individual as a final configuration according to a target function and a constraint condition. According to the method, the number of design variables is extremely small, so that optimization design of the ultra-high-speed impact-resistant structure becomes possible.
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Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of computational mechanics related to nonlinear topology optimization, and particularly relates to a super-high-speed impact-resistant structure design optimization method based on an explicit topology optimization framework. BACKGROUND

[0002] Hyper Velocity Impact (HVI) protection is one of the core technologies to ensure the survivability of aerospace vehicles. Its threat sources mainly come from two aspects: one is space debris and micro-meteoroids in the space environment; the other is kinetic energy interceptor, fragments and directional energy weapon projectiles in military applications. With the rapid development of hypersonic attack and defense systems, the importance of HVI protection has risen from the safety of spacecraft to the height of strategic security and military technology advantage.

[0003] At present, the mainstream protection structure design is still based on the Whipple protection structure and its numerous improved types. The basic idea is "sacrifice for protection", which is to consume the energy of the impacting debris by the graded interception, fragmentation, melting, vaporization and diffusion of the multi-layer structure, so as to protect the main cabin wall. The Whipple basic configuration is composed of an outer "sacrifice screen" (Bumper Shield) and an inner "main cabin wall" (Backwall). The sacrifice screen can make the impacting object break, melt and diffuse into a debris cloud, thereby increasing the contact area with the main cabin wall and reducing the pressure. The enhanced Whipple protection structure is optimized on the basis of the Whipple basic configuration, including: Stuffed Whipple protection structure - adding one or more layers of high-performance fiber fabric (such as Kevlar, Nextel) or metal mesh between the sacrifice screen and the main cabin wall. These interlayers can further fragment and capture the debris cloud and absorb its kinetic energy, significantly improving the protection performance; Multi-Shock Shield protection structure - composed of multiple spaced thin screens, which can gradually consume the energy of the debris cloud through repeated impact-fragmentation processes; Metal matrix composite protection structure - using new lightweight high-strength materials such as aluminum-based and magnesium-based composites, which can significantly reduce the weight of the structure under the same protection level.

[0004] Strong protective structures are the "shields" of spacecrafts to deal with threats and ensure mission success. But the significance of this shield is to protect, not to burden. The real engineering wisdom is not to endlessly stack protection, but to forge a shield that is indestructible but as light as nothing. For statics or some weak nonlinear problems, the technical route of using traditional topology optimization methods is quite mature. However, for materials that undergo severe plastic deformation, melting, vaporization, or even ionization, the traditional topology optimization theory framework based on linear or weak nonlinear mechanics is completely unable to describe this extreme process. During sensitivity analysis, due to the high discontinuity and high nonlinearity of the problem, it is extremely difficult to obtain the analytical sensitivity, and the differential sensitivity requires a complete nonlinear dynamic analysis of all design variables at each iteration, which makes it difficult to implement gradient-based topology optimization strategies. High-fidelity simulation of high-speed impact requires meshless methods such as Smoothed Particle Hydrodynamics (SPH), which is extremely expensive for a single calculation. Topology optimization is a process that requires thousands of iterations of calculations, and the traditional SIMP method has a large number of design variables, which is proportional to the number of meshes, resulting in an explosive increase in computational load, especially in three-dimensional problems, making it almost impossible to implement in practical engineering. The optimization goal of low-speed impact is usually to maximize stiffness or energy absorption. The core of hypervelocity impact protection is the "breakage-diffusion" debris cloud, and its optimization goals (such as debris cloud shape, maximum backside collapse size, etc.) are difficult to express using traditional mechanical response functions.

[0005] Based on traditional implicit description topology optimization methods such as SIMP, the inherent defects of large number of variables, large amount of calculation, and unclear boundaries are amplified infinitely in this extreme problem. Therefore, an explicit topology optimization framework with fewer variables and more direct geometric representation is particularly important. The Moving Morphable Components (MMC) method is proposed in the prior art, which represents the structure topology through a set of explicit description such as geometric components like beams and plates and their motion variables. The components are connected and integrated with each other to form different topological structures. This method has clear geometric description, which makes it easy to add manufacturing constraints during optimization and the optimization results can be directly imported into CAD for modeling, reducing the burden of post-processing. At the same time, this method gets clear and smooth geometric boundaries, which can be well combined with meshless methods such as SPH to generate SPH particle models with high precision, and then more accurately simulate the hypervelocity impact process. At the same time, its fewer design variables make it possible to get the topology structure in a smaller design space than the pixel-based optimization method, which makes the Moving Morphable Components method perfectly combined with non-gradient algorithms.

[0006] To this end, the application provides a super-high-speed impact-resistant structure design optimization method based on an explicit topology optimization framework. SUMMARY

[0007] The application aims to provide a super-high-speed impact-resistant structure design optimization method based on an explicit topology optimization framework, which is based on a framework of a moving deformable component method, uses existing industrial software to accurately analyze the complex nonlinear dynamics process, and uses a non-gradient genetic algorithm (GA) to update the design variables. The moving deformable component method has a small number of design variables, usually only a few hundred or even tens, compared with the pixel-based method which has thousands of design variables, making it possible to optimize the design of super-high-speed impact-resistant structures.

[0008] The technical scheme adopted by the application is as follows: A super-high-speed impact-resistant structure design optimization method based on an explicit topology optimization framework, first, in the framework based on the moving deformable component method (MMC), the upper and lower limits of the design variables of the moving deformable component method need to be set to ensure that they only change within the predetermined range; Then, the genetic algorithm randomly generates a set of candidate design variables, and an initial structure configuration is obtained from the candidate design variables; the configuration is then converted into a smoothed particle hydrodynamics (SPH) model, and the corresponding boundary conditions are applied; Then, an explicit dynamics method is used for analysis to obtain the mass and displacement response of the structure, and a target function and its related constraints are constructed according to the output structure response; Finally, according to the design variable update criterion of the genetic algorithm, cross and mutation genetic operations are applied to generate the next generation of candidate design variables; after the iteration is completed, the optimal individual is selected as the final configuration according to the target function and the constraint condition.

[0009] The application includes the following detailed steps: Step 1: parameterize modeling according to the design variables of the moving deformable component method MMC and output a grid file; Step 2: convert the grid model file into an SPH particle model in a commercial software; Step 3: perform explicit dynamics analysis and extract the results; Step 4: update the design variables of the next generation according to the information of the target function, the constraint function, and the design variables using the criterion of the genetic algorithm.

[0010] The application achieves the following technical effects: The present application is based on a moving morphable component method framework, uses existing industrial software to accurately analyze its complex nonlinear dynamic process, and uses a non-gradient genetic algorithm (Genetic Algorithm, GA) to update the design variables. Compared with the pixel-based topology optimization idea, the number of design variables of this method is very small, usually only a few hundred or even tens of thousands, compared with the traditional pixel-based method with thousands of design variables, making the optimization design of super-speed impact-resistant structure possible. BRIEF DESCRIPTION OF DRAWINGS

[0011] Figure 1 are different parameters of the present application corresponding component shape diagram; Figure 2 are different parameters in the present application the first embodiment described root two-dimensional component shape diagram; in the figure (a): uniform width; (b): linear variable width; (c): quadratic variable width; Figure 3 is a two-dimensional topology optimization evolution diagram of the present application based on the moving morphable component method; Figure 4 is a super-speed impact-resistant structure optimization design flowchart of the present application based on the moving morphable component method; Figure 5 is a unit cell configuration in the design space of the optimization method of the present application. DETAILED DESCRIPTION

[0012] In order to make the purpose and advantages of the present application more clear and obvious, the present application will be specifically described below in combination with embodiments. It should be understood that the following text is only used to describe one or several specific embodiments of the present application, and does not strictly limit the specific protection scope requested by the present application.

[0013] As shown in Figure 1 , a super-speed impact-resistant structure design optimization method based on an explicit topology optimization framework, first in the framework based on the moving morphable component method (Moving Morphable Components, MMC), the design variables of the moving morphable component method need to be set upper and lower limits to ensure that they only change within the predetermined range; Subsequently, a genetic algorithm randomly generates a set of candidate design variables, and an initial structure configuration is obtained therefrom; the configuration is then converted into a smoothed particle hydrodynamics (Smoothed Particle Hydrodynamics, SPH) model, and the corresponding boundary conditions are applied; Subsequently, an explicit dynamic method was used for analysis to obtain the structural response in terms of mass and displacement. Based on these output structural responses, the objective function and its related constraints were constructed. Finally, based on the design variable update criteria of the genetic algorithm, crossover and mutation genetic operations are applied to generate the next generation of candidate design variables; after the iteration is completed, the optimal individual is selected as the final configuration according to the objective function and constraints.

[0014] This invention includes the following detailed steps: Step 1: Parametrically model and output mesh files based on the design variables of the Moving Deformable Component (MMC) method; Step 2: Convert the mesh model file into an SPH particle model using commercial software; Step 3: Perform explicit kinetic analysis and extract the results; Step 4: Based on the objective function, constraint function, and design variable information, update the design variables of the next generation using the criteria of the genetic algorithm.

[0015] In step 1, structural components with hyperelliptical shapes are used as basic elements in the optimization process, and the topology of the structure is represented by a Topology Description Function (TDF). The mathematical form of the topology description function is as follows: in, Represents the given structural design domain. Indicated in the structural design domain The area containing all components; Indicates the interior of the structure. Indicates the boundary of the structure. Then it represents the exterior of the structure; for a structure composed of The topology description function of the structure composed of root components Depend on The calculation yielded, where Indicates the first The TDF value of the root component.

[0016] In two dimensions The TDF mathematical expression for the root component is written as: in Here, It is a relatively large even number used to adjust the contour features of the hyperellipse shape of a 2D component (typically set). ),and Indicates the half-length of a two-dimensional component. Represents the coordinates of the center point of the two-dimensional component. local coordinate system global coordinate system inclination angle, denotes the half-width of the two-dimensional component.

[0017] parameters controls the sharpness of the super-elliptical component profile, when takes infinite value, the shape of the component approaches a rectangle; in three dimensions, when takes infinite value, the component is a cuboid, and its topological description function can be found in the relevant papers, which will not be repeated here.

[0018] According to the different mathematical expressions of , the shape of the two-dimensional component is different, and the shape is: 1) uniform width, the mathematical expression of is: wherein, denotes the uniform half-width of the two-dimensional component, and the design variable vector of the first dimensional component is written as: 2) linear variable width, the mathematical expression of is: wherein, denote the half-widths of the two ends of the two-dimensional component, respectively, and the design variable vector of the first dimensional component is written as: 3) quadratic variable width, the mathematical expression of is: wherein, denote the half-widths of the two ends and the middle of the two-dimensional component, respectively, and the design variable vector of the first dimensional component is written as: Figure 2 are different described in the first dimensional component shape diagram.

[0019] In the two-dimensional topological optimization process based on the mobile variable component method, the components in the design domain are deformed, moved, overlapped and covered to form the topology of the overall optimized structure, with reference to Figure 3 .

[0020] Under the mobile variable component method MMC topological optimization framework, the optimization expression of the general problem can be written as: wherein, denotes the objective function, represents the constraint condition that needs to be satisfied in the optimization problem, represents the design variable allowed set. Unlike the traditional topology optimization method based on grid elements, each component has few design parameters, which can greatly reduce the number of design variables in the optimization process. In large-scale computing problems, the MMC method can effectively reduce the computing time required for optimization solution and improve the efficiency of optimization design.

[0021] Based on the above form of geometric component description, in the structural topology optimization problem, The design variable vector of the component can be written as: The MMC design variable in the above has a clear geometric meaning, which is converted into a geometric parameter. Then these geometric parameters are converted into geometric descriptions that can be recognized in geometric software (such as SpaceClaim, SolidWorks, CATIA); Then by establishing a parameterized modeling script in the geometric modeling environment, the corresponding geometric model is automatically updated or reconstructed according to the MMC variable, so as to realize the seamless connection from the numerical optimization result to the three-dimensional geometric entity. This step does not need to be repeated manually, and only the MMC parameters need to be updated to quickly generate the corresponding geometric configuration.

[0022] After obtaining the complete three-dimensional geometric model based on the MMC variable, it needs to enter the grid division stage; At this time, the grid parameters need to be given in advance, such as the expected unit type (for example, tetrahedron, hexahedron or mixed unit), the average unit size and the constraint of the maximum and minimum unit size. Then, call the automatic meshing algorithm in the geometric software or the accompanying finite element pre-processing module to automatically subdivide the model. It needs to be particularly emphasized that this process does not rely on manual step-by-step intervention, but is automatically completed by the software through setting reasonable meshing criteria. In order to improve the calculation accuracy based on the SPH method, the regularity and unit quality of the grid should be ensured as much as possible, such as controlling the aspect ratio, twist degree of the unit and the size transition of the adjacent unit, to avoid numerical instability in the subsequent particleization.

[0023] In step 2, after completing the MMC-based structural topology optimization and obtaining the final grid model, the grid model needs to be further converted into an SPH particle model for subsequent explicit dynamics analysis. The specific process can be realized in mature commercial finite element / explicit dynamics software (such as LS-DYNA, ABAQUS / Explicit, etc.), and can be automatically processed by calling or customizing scripts.

[0024] ​Firstly, a proper particleization strategy should be chosen according to the geometric characteristics of the obtained MMC lattice. For structures with complex topology or containing irregular details, the "element centroid method" can be adopted, i.e. generating one SPH particle at the geometric centroid of each finite element, so as to better maintain the overall mass distribution and geometric characteristics of the original configuration. For regular geometric bodies (such as regular cuboids, cylinders or symmetric structures), the "point seeding" function provided by commercial software can be used to automatically arrange particles in the geometric domain according to the given particle spacing, thereby effectively reducing the modeling complexity and computational cost while ensuring the calculation accuracy. If necessary, local densification strategies can also be applied in key areas, with higher density of particle division in areas sensitive to stress concentration or impact response, to improve the local simulation accuracy.

[0025] After the particle generation is completed, the corresponding boundary conditions should be determined according to the actual position and boundary environment of the structure in space. For example, fixed or displacement boundaries should be applied in the constrained areas, and corresponding external forces, velocities or impact conditions should be applied in the loading areas to truly reflect the experimental or engineering scenarios. At the same time, appropriate material parameters should be defined for the model to ensure the stability and physical accuracy of the explicit dynamics solution.

[0026] Subsequently, key solution parameters for explicit dynamics analysis need to be configured, including analysis step size, time integration control, interaction criteria between SPH particles (such as kernel function type, smoothing length, particle spacing control), and contact algorithms suitable for specific problems. On this basis, convergence and stability criteria should be defined, such as total energy balance, time step stability condition or variation amplitude of key response quantities, to ensure the reliability of numerical results. Finally, the physical quantities to be output (such as particle point displacement, stress, strain, etc.) and their output frequency should be selected, and the file format and storage strategy should be reasonably set to facilitate later data analysis and visualization.

[0027] The above procedures can be realized automatically through the secondary development interface or script language (such as Python, key file macros, etc.) provided by commercial software.

[0028] After the pre-processing based on SPH particle model is completed, the calculation can be started in commercial explicit dynamics software (such as LS-DYNA, ABAQUS / Explicit, etc.). After obtaining the complete numerical response, a reasonable mathematical description needs to be constructed according to the research target or optimization requirements, that is, the objective function and constraint function are formulated. For example, the damage degree or energy absorption amount of a certain key plate can be taken as the optimization objective function to represent the protection performance of the structure under extreme working conditions; at the same time, the material usage, total mass, maximum stress or displacement limit are taken as constraint conditions to ensure that the structure meets the strength and stiffness requirements and meets the material and manufacturing cost restrictions. If multiple objective optimization is involved, weighted coefficients or hierarchical strategies can be introduced to integrate multiple objectives into a single evaluation index.

[0029] In the genetic algorithm, multi-objective optimization or weighted single-objective optimization is used for the objective function and constraint function.

[0030] After the construction of the objective function and the constraint condition and the extraction of the design variables and response data obtained in the last round of calculation, the core stage of the genetic algorithm is entered, that is, the update and evolution of the next generation of design variables; this process follows the standard evolution criteria of genetic algorithm, including selection, crossover and mutation basic operations.

[0031] First, the selection is performed according to the comprehensive fitness of the individuals in the last generation under the objective function and the constraint condition. Common strategies include roulette wheel selection, tournament selection or rank-based selection method to ensure that individuals with higher fitness have a greater probability of entering the next generation, while maintaining a certain diversity.

[0032] Then in the crossover link, the design variable information of the selected parent individuals is recombined through single-point, two-point or uniform crossover, etc. to generate offspring with new characteristics, so as to realize a larger range of exploration in the solution space. Mutation operation randomly changes some design variables with a small probability to avoid the algorithm falling into local optimum and maintain the diversity of the population. For MMC design variables, mutation can be manifested as perturbation of geometric parameters such as component position, size or angle.

[0033] Generally, the trade-off between structural performance and material usage, i.e. the trade-off between the objective function and the constraint function, is involved in optimization, which is embodied as a multi-objective optimization in genetic algorithm. In the multi-objective optimization scenario, the genetic algorithm adopts a Pareto front strategy, and a set of mutually trade-off solutions are screened out by comparing the non-dominant relationship of each individual on multiple objectives, so as to provide diversified optimization schemes for designers. If more preference is given to a single comprehensive objective, the multi-objective performance indicators can also be combined into a single objective function by weighting summation or hierarchical optimization strategy according to the importance coefficient, so as to realize a more simplified optimization process.

[0034] The following strategies can be adopted in the iteration process to reduce the calculation amount and improve the stability of the analysis: algorithm flow Figure 4 a. For the case of non-convergence, it is identified that it is automatically stopped after exceeding the expected calculation time, and the objective function is set to a very large value.

[0035] b. For the design variable that does not meet the volume constraint, the objective function is set to a very large value.

[0036] c. A database of design variables is established, and for the same design variable, the previous objective function and constraint function are directly used to avoid repeated analysis.

[0037] d. For some small-sized units (small-mass SPH particles) that do not affect the main path of the structure, selective adjustment is performed to increase the analysis step size and reduce the total analysis time.

[0038] In the classic algorithm based on pixel description of topological structure in the past, the number of design variables using non-gradient algorithm is large, and the calculation complexity cannot be realized at present. However, only a small number of design variables are needed to accurately describe the topology of the structure by using the method, and in the nonlinear analysis, since the configuration is explicit, the SPH particles more accurately describe the structure boundary when converted into the SPH particle model. Based on the method in the present application, a complex structure as shown in Figure 5 If designed according to the traditional method, several tens of times or even hundreds of times of design variables are needed, which requires several tens of times or even hundreds of times of time for nonlinear dynamics with high calculation cost, which is almost unacceptable.

[0039] ​The present application is based on the framework of the moving deformable components method, uses existing industrial software to accurately analyze its complex nonlinear dynamic process, and uses a non-gradient genetic algorithm (Genetic Algorithm, GA) to update the design variables. The number of design variables of the moving deformable components method is very small, usually only a few hundred or even tens, compared with the traditional pixel-based method with thousands of design variables, making it possible to optimize the design of super-high-speed impact-resistant structures.

[0040] The above only describes the preferred embodiments of the present application, and it should be pointed out that for ordinary skilled in the art, without departing from the principles of the present application, a number of improvements and refinements can be made, which should be considered as the protection scope of the present application. The structures, devices and operation methods not specifically described and explained in the present application are implemented according to the conventional means in the art, unless otherwise specified and limited.

Claims

1. A method for designing and optimizing a super-high-speed impact-resistant structure based on an explicit topology optimization framework, characterized in that: Firstly, upper and lower bounds of the design variables of the mobile variable component method need to be set in the framework of the mobile variable component method; Then, a set of candidate design variables is randomly generated by the genetic algorithm, and an initial structural configuration is obtained from the candidate design variables; the configuration is then converted into a smoothed particle hydrodynamics model, and corresponding boundary conditions are applied; Then, an explicit dynamic method is used for analysis to obtain the structural response of mass and displacement, and a target function and related constraint conditions are constructed based on the output structural response; Finally, the next generation of candidate design variables is generated by applying cross and mutation genetic operations according to the design variable update criteria of the genetic algorithm; after the iteration ends, the optimal individual is selected as the final configuration according to the target function and constraint conditions.

2. The method of claim 1, wherein: The following detailed steps are included: Step 1: parameterize modeling according to the design variables of the mobile variable component method MMC and output a grid file; Step 2: convert the grid model file into an SPH particle model in the software; Step 3: perform a display dynamic analysis and extract the results; Step 4: update the design variables of the next generation using the criteria of the genetic algorithm according to the information of the target function, constraint function, and design variables.

3. The method of claim 2, wherein: In step 1, a structural component with a hyper-elliptical shape feature is used as a basic element in the optimization process, and the topological configuration of the structure is represented using a topological description function. The mathematical form of the topological description function of the structure is as follows: where, denotes a given structural design domain, denotes the region of all components in the structural design domain ; denotes the interior of the structure, denotes the boundary of the structure, then denotes the exterior of the structure; for a structure consisting of root components, the topological description function is computed from where denotes the TDF value of the th root component; In two dimensions, the The TDF mathematical expression for the root set is written as: wherein here, is a relatively large even number for adjusting the contour feature of the two-dimensional component hyper-elliptical shape (typically set ), while denotes the half-length of the two-dimensional component, denotes the coordinates of the center point of the two-dimensional component, denotes the tilt angle of the local coordinate system with respect to the global coordinate system , and denotes the half-width of the two-dimensional component; Parameters Controlling the degree of circularity of the hyper-elliptical assembly profile, when Taking infinite value, the shape of the assembly is infinitely close to a rectangle; in three dimensions, when Taking infinite value, the assembly is a cuboid; According to Different mathematical expressions result in different shapes for the two-dimensional components. These shapes include: 1) uniform width, which is The mathematical expression for this is: where, denotes the uniform half-width of the two-dimensional component, then the first The design variable vector of the two-dimensional component is written as: 2) linear variable width, which The mathematical expression for this is: where, denote the half-widths of the two-dimensional component at its two ends, respectively, then the first The design variable vector of the two-dimensional component is written as: 3) a secondary width variation, which is mathematically expressed as: wherein, respectively denote the half-widths at the ends and the half-width of the middle of the two-dimensional component, respectively, then the design variable vector of the two-dimensional component is written as: wherein, In the two-dimensional topology optimization process based on the mobile deformable component method, the components in the design domain form the topology of the overall optimized structure through deformation, movement, overlap and covering. Under the framework of the mobile variable component method topology optimization, the optimization equation of the general problem is written as: wherein, represents an objective function, represents a set of constraints that need to be satisfied in the optimization problem, represents a set of constraints that need to be satisfied in the optimization problem, represents a set of constraints that need to be satisfied in the optimization problem, represents a set of constraints that need to be satisfied in the optimization problem, the design variable vector of the root component is written as: The mobile variable component method MMC design variables have clear geometric implications, which are converted into geometric parameters; then these geometric parameters are converted into geometric descriptions that can be recognized in geometric software; then by establishing a parameterized modeling script in the geometric modeling environment, the corresponding geometric model is automatically updated or reconstructed according to the mobile variable component method MMC variables, thereby realizing seamless connection from numerical optimization results to three-dimensional geometric entities; this step does not need to be repeated manually, and only the mobile variable component method MMC parameters need to be updated to quickly generate the corresponding geometric configuration; After obtaining the complete three-dimensional geometric model based on the mobile variable component method MMC variables, the grid partitioning stage needs to be entered; at this time, the grid parameters need to be given in advance; then, the automatic meshing algorithm in the geometric software or the built-in automatic meshing algorithm in the finite element pre-processing module is called to automatically partition the model.

4. The method of claim 2, wherein: In step 2, after completing the structure topology optimization based on the mobile variable component method MMC and obtaining the final grid model, the grid model needs to be further converted into an SPH particle model; the specific process is realized in mature commercial finite element / explicit dynamic software, and can be automatically processed by calling or customizing scripts; The above processes can be realized automatically through the secondary development interface or script language provided by the software.

5. The method of claim 2, wherein: In step 3, after completing the pre-processing based on the SPH particle model, the calculation can be started in the commercial explicit dynamic software; after obtaining the complete numerical response, a reasonable mathematical description needs to be constructed according to the research target or optimization requirement, i.e., the target function and constraint function are formulated.

6. The method of claim 2, wherein: In step 4, in the genetic algorithm, the multi-objective optimization or weighted single-objective optimization is used to reflect the target function and constraint function; After completing the construction of the target function and constraint conditions and extracting the design variables and response data obtained in the last round of calculation, the core stage of the genetic algorithm, i.e., the update and evolution of the design variables of the next generation, is entered; this process follows the standard evolution criteria of the genetic algorithm, including the basic operations of selection, cross, and mutation; Firstly, selection is performed according to the fitness of the individuals in the previous generation under the objective function and constraints; commonly used strategies include roulette wheel selection, tournament selection or ranking-based selection methods to ensure that individuals with higher fitness have a greater probability of entering the next generation, while maintaining a certain diversity; Then in the crossover stage, the design variable information of the selected parent individuals is recombined through single-point, two-point or uniform crossover to generate offspring with new characteristics; mutation operation randomly changes some design variables with a small probability to avoid the algorithm falling into local optimum and maintain the diversity of the population; for the design variables of the mobile variable assembly method MMC, mutation is manifested as the perturbation of the geometric parameters of the assembly position, size or angle.

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