Topology and size joint optimization design method and system for hierarchical composite structure

Abstract

The invention relates to the technical field of structural design, and discloses a topology and size joint optimization design method and system for a hierarchical composite structure, and the method comprises the following steps: dividing a structural domain into a plurality of hierarchical sub-domains, defining the size constraint range of each sub-domain, and distributing a multi-phase material for each sub-domain; grid discretization processing is carried out on the structural domain, a topological design variable is given to each discrete unit, acoustic unit modeling is carried out on the sound field domain, sound pressure boundary conditions are defined, and coupling boundary conditions are applied to the interface of the sound field domain and the structural domain; solving an acoustic-structure coupling equation based on a finite element method, calculating an objective function and constraint conditions, analyzing the sensitivity of the objective function to topological variables by adopting an adjoint method, and iteratively updating the topological design variables through an optimization algorithm until a convergence criterion is met; and on the basis of a topological optimization result, constructing a neural network agent model of an input layer, a hidden layer and an output layer, and carrying out global optimization on sub-domain size parameters by adopting a genetic algorithm so as to minimize a target function.

Description

Technical Field

[0001] The present invention relates to the technical field of structural design, and in particular to a method and system for joint optimization design of topology and size of a hierarchical composite structure. Background Art

[0002] Noise pollution remains a significant threat to people's health and well-being in everyday life. Noise issues encompass both structural vibration and acoustic propagation. Traditional optimization design typically involves separate efforts to optimize a system's acoustic and structural performance. Consequently, after achieving optimal performance in each area, extensive iteration and practice are required to achieve the optimal match. This traditional approach presents significant drawbacks. It consumes significant time and effort and fails to fully exploit the optimal performance of both. To scientifically and efficiently analyze acoustic propagation characteristics, the interaction between the two must be considered, effectively analyzing the acoustic-structure coupling problem as a whole. Furthermore, topology optimization, as an advanced design method with high degrees of freedom, can identify the optimal material topology for structural performance during the conceptual design phase, minimizing structural weight and reducing material consumption. It has been widely used in many industries, including aerospace. Therefore, to meet lightweight design requirements, expand application scenarios, and enhance structural performance, employing an acoustic-structure coupling topology optimization framework to achieve coupled acoustic-structural design has the potential to break through traditional design limitations, improve structural design efficiency, and yield high-quality, innovative structural configurations.

[0003] However, existing acoustic-structure coupling topology optimization design frameworks typically only consider the topological distribution of a single material within their design domain. With the rapid development of industries such as new energy vehicles, aviation, aerospace, high-end manufacturing, and military applications, the manufacturing industry is increasingly prioritizing lightweight, highly malleable, and multiphase composite materials. Current topology optimization design frameworks based on a single material design domain are no longer able to meet the demands of comprehensive structural multifunctionality. The design of multiphase composite materials has become a focus of attention. Furthermore, traditional topology optimization design only considers a single interval within its design domain. The emergence of layered composite materials, however, overcomes the shortcomings of single materials while retaining their advantages, resulting in overall mechanical properties superior to those of the original material. Therefore, optimizing the overall performance of a structure by filling it with materials of varying properties within a multilayered structure has become a key area of research in optimization design. Furthermore, in previous topology optimization research, topology optimization and dimensional optimization were typically considered separate modules, without considering the inherent advantages of each optimization technique for collaborative design. Summary of the Invention

[0004] The present invention provides a method and system for joint optimization design of topology and size of a hierarchical composite structure, so as to solve the problems existing in the existing structural design methods.

[0005] In order to achieve the above object, the present invention is implemented through the following technical solutions: In a first aspect, the present invention provides a method for joint optimization design of topology and size of a hierarchical composite structure, comprising the following steps: S1. Divide the structural domain into multiple hierarchical subdomains, define the size constraint range of each hierarchical subdomain, including length and height, and assign a multiphase material to each hierarchical subdomain, wherein the multiphase material includes at least two materials with different properties; S2. Discretize the structural domain into a grid and assign topological design variables to each discrete unit. Model the acoustic unit of the acoustic field, define the sound pressure boundary conditions, and apply coupling boundary conditions at the interface between the acoustic field and the structural domain. S3. Construct an acoustic-solid coupling equation based on the acoustic field domain and the structural domain, solve the acoustic-solid coupling equation to calculate the objective function and constraints in the acoustic-solid coupling equation, use the adjoint method to analyze the sensitivity of the objective function to the topology design variables, iteratively update the topology design variables through the optimization algorithm until the convergence criterion is met, and take the objective function, constraints, sensitivity, and topology design variables that meet the convergence criterion as the topology optimization result; S4. Based on the topology optimization results, a topology optimization model is obtained, and a neural network proxy model of the input layer, hidden layer, and output layer is constructed. A genetic algorithm is used to globally optimize the hierarchical subdomain size parameters to minimize the objective function and obtain the optimal structural acoustic performance as the size optimization result.

[0006] Optionally, in S1, the number of the hierarchical subdomains is four, and the size constraint of each hierarchical subdomain satisfies: , ; in, are the length of the bottom side of each level subdomain, H is the height of the level subdomain, L min and L max H is the minimum and maximum allowed length of the hierarchical subdomain space. min and H max The minimum and maximum values allowed for the height of a hierarchy subdomain.

[0007] Optionally, in S2, the multiphase material includes at least two of a metal matrix, a lightweight composite material, and a high damping phase.

[0008] Optionally, the optimization algorithm in S3 is a moving asymptote algorithm, and the convergence criterion is that the rate of change of the design variable is less than 1% or the fluctuation of the objective function is less than 0.5%; The acoustic-solid coupling equation in S3 satisfies the following mathematical model: ; Where Z is the system matrix, U is the displacement vector, F is the load vector, y is the topology design variable, subscript i Represents the number of the subdomain space at the level, subscript j Represents the number of the unit in the hierarchical subdomain space, are the length of the bottom side of each level subdomain, H is the height of the level subdomain, L min and L max H is the minimum and maximum allowed length of the hierarchical subdomain space. min and H max The minimum and maximum values allowed for the height of the hierarchical subdomain. is the constraint condition, is the constraint condition for the volume of each phase material under the specified volume, To minimize the objective function.

[0009] Optionally, the neural network proxy model in S4 is a BP neural network, whose input layer includes hierarchical subdomain size parameters and height, the hidden layer is two layers and each layer contains 10 nodes, and the output layer is a single-objective sound pressure level objective function or a multi-objective function of the comprehensive performance of acoustic-solid coupling.

[0010] Optionally, the parameters of the genetic algorithm in S4 are set as follows: population size is 50, evolutionary generations is 100, crossover probability is 0.8, and mutation probability is 0.05.

[0011] Optionally, the method further includes: S5. Feed the size optimization results back to the topology optimization model, recalculate the objective function and material distribution, and verify the global optimality.

[0012] Optionally, if the objective function does not converge in S5, the number of hidden layer nodes of the neural network is adjusted or the algorithm parameters are optimized and then S3 to S4 are repeated.

[0013] Optionally, the objective function is minimization of sound pressure level and / or minimization of structural flexibility, and the constraint condition is that the volume fraction of each material phase meets a preset value.

[0014] In a second aspect, an embodiment of the present application provides a system for joint optimization design of topology and size of a hierarchical composite structure, including a processor and a memory; Memory for storing computer programs; The processor is configured to implement any one of the method steps described in the first aspect when executing a program stored in the memory.

[0015] Beneficial effects: The method for joint optimization of the topology and size of hierarchical composite structures provided by this invention integrates the structural size optimization and topology optimization into the same optimization framework, achieving the goal of collaborative optimization design, reducing the number of iterations in the optimization process, and improving the efficiency of optimization calculations. Furthermore, by introducing the design concept of hierarchical composite materials into the topology optimization framework, the characteristic of hierarchical composite materials can be utilized to simultaneously select multiple materials within multiple design subdomains to meet multifunctional design requirements. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 Flowchart of the topology and size joint optimization design method of the hierarchical composite structure according to the preferred embodiment of the present invention; Figure 2 Schematic diagram of an improved topology optimization design model according to a preferred embodiment of the present invention; Figure 3 A flowchart of a method for joint optimization design of topology and size of a hierarchical composite structure provided in a preferred embodiment of the present invention. DETAILED DESCRIPTION

[0017] The following is a clear and complete description of the technical solutions of the present invention. It should be understood that the embodiments described are only a portion of the embodiments of the present invention, not all of them. All other embodiments derived by persons of ordinary skill in the art based on the embodiments of the present invention without inventive effort are intended to fall within the scope of protection of the present invention.

[0018] Unless otherwise defined, the technical or scientific terms used in the present invention shall have the usual meanings understood by persons of ordinary skill in the field to which the present invention belongs. The words "first", "second" and similar terms used in the present invention do not indicate any order, quantity or importance, but are only used to distinguish different components. Similarly, words such as "one" or "a" do not indicate a quantity limitation, but rather indicate the existence of at least one. Words such as "connected" or "connected" are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. "Up", "down", "left", "right" and the like are only used to indicate relative positional relationships. When the absolute position of the object being described changes, the relative positional relationship also changes accordingly.

[0019] See Figure 1 , an embodiment of the present application provides a method for joint optimization design of topology and size of a hierarchical composite structure, comprising the following steps: S1. Divide the structural domain into multiple hierarchical subdomains, define the size constraint range of each hierarchical subdomain, including length and height, and assign a multiphase material to each hierarchical subdomain, wherein the multiphase material includes at least two materials with different properties; S2. Discretize the structural domain into a grid and assign topological design variables to each discrete unit. Model the acoustic unit of the acoustic field, define the sound pressure boundary conditions, and apply coupling boundary conditions at the interface between the acoustic field and the structural domain. S3. Construct an acoustic-solid coupling equation based on the acoustic field domain and the structural domain, solve the acoustic-solid coupling equation to calculate the objective function and constraints in the acoustic-solid coupling equation, use the adjoint method to analyze the sensitivity of the objective function to the topology design variables, iteratively update the topology design variables through the optimization algorithm until the convergence criterion is met, and take the objective function, constraints, sensitivity, and topology design variables that meet the convergence criterion as the topology optimization result; S4. Based on the topology optimization results, a topology optimization model is obtained, and a neural network proxy model of the input layer, hidden layer, and output layer is constructed. A genetic algorithm is used to globally optimize the hierarchical subdomain size parameters to minimize the objective function and obtain the optimal structural acoustic performance as the size optimization result.

[0020] In the above-mentioned embodiment, by integrating the structural sizing and topology optimization into the same optimization framework, the goal of collaborative design optimization can be achieved, reducing the number of iterations in the optimization process and improving the efficiency of the optimization calculation. Furthermore, by introducing the design concept of hierarchical composite materials into the topology optimization framework, the characteristic of hierarchical composite materials can be utilized to simultaneously select multiple materials within multiple design subdomains to meet multifunctional design requirements.

[0021] Optionally, in S1, the number of the hierarchical subdomains is four, and the size constraint of each hierarchical subdomain satisfies: , ; in, are the length of the bottom side of each level subdomain, H is the height of the level subdomain, L min and L max H is the minimum and maximum allowed length of the hierarchical subdomain space. min and H max The minimum and maximum values allowed for the height of a hierarchy subdomain.

[0022] In the above embodiment, the multi-level structure design is realized by dividing the original structure domain design space into multiple sub-domain spaces. This example uses four-layer sub-domain space as an explanation, and the sub-domain space can be expanded accordingly, where L1, L2, L3 and L4 are the bottom lengths of each sub-domain space, and L min and L max The minimum and maximum values allowed for the length of the subdomain space. H is the height of the subdomain space, H min and H max The minimum and maximum values allowed for the subdomain height.

[0023] Optionally, in S2, the multiphase material includes at least two of a metal matrix, a lightweight composite material, and a high damping phase.

[0024] Optionally, the optimization algorithm in S3 is a moving asymptote algorithm, and the convergence criterion is that the rate of change of the design variable is less than 1% or the fluctuation of the objective function is less than 0.5%; The acoustic-solid coupling equation in S3 satisfies the following mathematical model: ; Where Z is the system matrix, U is the displacement vector, F is the load vector, y is the topology design variable, subscript i Represents the number of the subdomain space at the level, subscript j Represents the number of the unit in the hierarchical subdomain space, are the length of the bottom side of each level subdomain, H is the height of the level subdomain, L min and L max H is the minimum and maximum allowed length of the hierarchical subdomain space. min and H max The minimum and maximum values allowed for the height of the hierarchical subdomain. is the constraint condition, is the constraint condition for the volume of each phase material under the specified volume, To minimize the objective function.

[0025] In the above embodiment, in S3, the acoustic-solid coupling analysis domain is divided into the acoustic field domain and the structural domain, wherein the structural domain is used as the design area and the acoustic field domain is used as the non-design area. The acoustic-solid coupling equation is constructed using the structural domain and the acoustic field domain, and the objective function P of the structure under the acoustic-solid coupling is defined. r In this example, the sound pressure level is minimized, and the constraints are .

[0026] In the embodiment, the initial design space of the structural subdomain size parameters is first established by the central composite design method and the Box-Behnken experimental design method, and the input sample point data of the structural subdomain is obtained. Then, each subdomain space is discretized into a grid and each discrete unit is assigned a corresponding topological design variable value ( y 111 ，y 121 ，...，y ijk ),in y is the topology design variable, subscript i Represents the number of the subdomain space, subscript j Represents the unit number in the subdomain space, subscript kRepresents the number of the specified unit material phase. Appropriate boundary conditions are applied to the acoustic field domain and the structural domain, and the influence of the acoustic-solid coupling boundary is considered. The finite element method is used to solve the acoustic-solid coupling problem and obtain the variable distribution of the acoustic field domain and different subdomains. The adjoint method is used to analyze and solve the sensitivity of the objective function and the constraints, and then the moving asymptote optimization algorithm is used to obtain the topological distribution of the multiphase material in each subdomain space. If the change of the multiphase material design variables does not meet the convergence criterion, the topological optimization design variables of the unit are updated to continue a new round of optimization design iteration process until the convergence criterion is met; if the change of the multiphase material design variables meets the convergence criterion, the optimal topological optimization distribution, objective function, design variables and other parameters are output, and an output function library is constructed.

[0027] Optionally, the neural network proxy model in S4 is a BP neural network, whose input layer includes hierarchical subdomain size parameters and height, the hidden layer is two layers and each layer contains 10 nodes, and the output layer is a single-objective sound pressure level objective function or a multi-objective function of the comprehensive performance of acoustic-solid coupling.

[0028] Optionally, the parameters of the genetic algorithm in S4 are set as follows: population size is 50, evolutionary generations is 100, crossover probability is 0.8, and mutation probability is 0.05.

[0029] In the above embodiment, the input and output data are first normalized. In this example, the input data is designed based on the structural dimension parameters L1, L2, L3, L4, and H, while the output data is designed based on the objective function Pr. Appropriate hidden layer parameters and neural network control parameters are then selected to construct neural network models for the input, hidden, and output layers. The BP neural network model is trained using the input and output data obtained using the topology optimization model framework, and data prediction is then performed using the BP neural network model. When the prediction accuracy of the constructed neural network model meets the required accuracy, the input data is initialized, and the trained BP neural network prediction results are used as the individual fitness function in the genetic algorithm model. Parameters such as the number of evolutions, population size, crossover probability, and mutation probability in the genetic algorithm are then set. Finally, the optimal individual for the current iteration of the function is found through selection, crossover, and mutation operations in the genetic algorithm's extreme value optimization process. Selection, crossover, and mutation operations are then repeated until a termination condition is met, thereby outputting the fitness value of the optimal individual and the corresponding input data. After determining the optimal size input data, the topology optimization design of the hierarchical multiphase material can be carried out to obtain the multiphase material distribution under the optimal size subdomain structure.

[0030] Optionally, the method further includes: S5. Feed the size optimization results back to the topology optimization model, recalculate the objective function and material distribution, and verify the global optimality.

[0031] Optionally, if the objective function does not converge in S5, the number of hidden layer nodes of the neural network is adjusted or the algorithm parameters are optimized and then S3 to S4 are repeated.

[0032] Optionally, the objective function is minimization of sound pressure level and / or minimization of structural flexibility, and the constraint condition is that the volume fraction of each material phase meets a preset value.

[0033] like Figure 3 As shown, the specific steps of the above embodiment are as follows, including: Design preparation and parameter definition Hierarchical subdomain partitioning: Divide the structural domain into multiple subdomains (e.g., four layers: L1-L4), defining dimensional constraints for each subdomain. Material phase definition: Based on functional requirements (e.g., lightweight, damping, stiffness), assign multiple material phases to each subdomain (e.g., three phases: metal matrix, lightweight composite, high-damping phase).

[0034] Acoustic-Structure Interaction Modeling and Boundary Conditions Finite element model construction: Structural domain: Use quadrilateral / hexahedral elements to discretize the subdomains, and assign topological design variables to each element (i: subdomain number, j: element number, k: material phase number).

[0035] Acoustic field: Use acoustic units for modeling and define sound pressure boundary conditions (such as the frequency and amplitude of the incident sound wave).

[0036] Coupling interface: Apply coupling boundary conditions at the acoustic field-structure interface to transfer the acoustic pressure load and the structural displacement response, such as Figure 2 shown.

[0037] Topology and size joint optimization process Step 1: Initial design space generation; The central composite design (CCD) or Box-Behnken experimental design method is used to generate initial sample points of subdomain size parameters.

[0038] Step 2: Topology optimization stage; Objective function: Minimize the sound pressure level Pr or minimize the sound pressure level + minimize the structural flexibility, constraining the volume ratio of each material phase.

[0039] Sensitivity analysis: The adjoint method is used to calculate the sensitivity of the objective function to the topological variables, and its corresponding sensitivity is obtained by solving the adjoint formula.

[0040] Optimization iteration: Use the moving asymptote algorithm (MMA) to update the topology variables until the convergence criteria are met (such as the design variable change rate <1% or the objective function fluctuation <0.5%).

[0041] Step 3: Size optimization stage; Agent model construction: Based on the topology optimization results, the BP neural network is trained to establish the mapping relationship between input and output.

[0042] Input layer: 5 nodes (4 size parameters + height).

[0043] Hidden layer: 2 layers, 10 nodes per layer.

[0044] Output layer: 1 node (objective function sound pressure level Pr).

[0045] Global optimization: Genetic algorithm (GA) is used to search for the optimal size parameters: Population size: 50, evolutionary generations: 100.

[0046] Crossover probability: 0.8, mutation probability: 0.05.

[0047] Fitness function: the minimum value of Pr predicted by the neural network.

[0048] Step 4: Collaborative optimization verification; The sizing optimization results are fed back into the topology optimization model to recalculate the sound pressure level and material distribution to verify global optimality.

[0049] If the objective function does not converge, adjust the number of nodes in the hidden layer of the neural network or optimize the algorithm parameters and repeat steps 2-3.

[0050] The embodiment of the present application also provides a topology and size joint optimization design system for a hierarchical composite structure, including a processor and a memory; The memory is used to store computer programs; the processor is used to implement any method step in the method for joint optimization design of topology and size of hierarchical composite structures when executing the program stored in the memory.

[0051] The above describes in detail the preferred embodiments of the present invention. It should be understood that those skilled in the art can make numerous modifications and variations based on the concepts of the present invention without inventive effort. Therefore, any technical solutions that can be derived by those skilled in the art through logical analysis, reasoning, or limited experimentation based on the concepts of the present invention and the prior art should be within the scope of protection defined by the claims.

Claims

1. A method for joint optimization design of topology and size of hierarchical composite structures, characterized in that: The following steps are involved: S1. Divide the structural domain into multiple hierarchical subdomains, define the size constraint range of each hierarchical subdomain, including length and height, and assign a multiphase material to each hierarchical subdomain, wherein the multiphase material includes at least two materials with different properties; S2. Discretize the structural domain into a grid and assign topological design variables to each discrete unit. Model the acoustic unit of the acoustic field, define the sound pressure boundary conditions, and apply coupling boundary conditions at the interface between the acoustic field and the structural domain. S3. Construct an acoustic-solid coupling equation based on the acoustic field domain and the structural domain, solve the acoustic-solid coupling equation to calculate the objective function and constraints in the acoustic-solid coupling equation, use the adjoint method to analyze the sensitivity of the objective function to the topology design variables, iteratively update the topology design variables through the optimization algorithm until the convergence criterion is met, and take the objective function, constraints, sensitivity, and topology design variables that meet the convergence criterion as the topology optimization result; S4. Based on the topology optimization results, a topology optimization model is obtained, and a neural network proxy model of the input layer, hidden layer, and output layer is constructed. A genetic algorithm is used to globally optimize the hierarchical subdomain size parameters to minimize the objective function and obtain the optimal structural acoustic performance as the size optimization result.

2. The method for joint optimization design of topology and size of a hierarchical composite structure according to claim 1, characterized in that: In S1, the number of the hierarchical subdomains is four, and the size constraint of each hierarchical subdomain satisfies: ， ； in, are the length of the bottom side of each level subdomain, H is the height of the level subdomain, L min and L max H is the minimum and maximum allowed length of the hierarchical subdomain space. min and H max The minimum and maximum values allowed for the height of a hierarchy subdomain.

3. The method for joint optimization design of topology and size of a hierarchical composite structure according to claim 1, characterized in that: In S2, the multiphase material includes at least two of a metal matrix, a lightweight composite material, and a high damping phase.

4. The method for joint optimization design of topology and size of a hierarchical composite structure according to claim 1, characterized in that: The optimization algorithm described in S3 is a moving asymptote algorithm, and the convergence criterion is that the rate of change of the design variable is less than 1% or the fluctuation of the objective function is less than 0.5%; The acoustic-solid coupling equation in S3 satisfies the following mathematical model: ； Where Z is the system matrix, U is the displacement vector, and F is the load vector. y is the topology design variable, subscript i Represents the number of the subdomain space at the level, subscript j Represents the number of the unit in the hierarchical subdomain space, are the length of the bottom side of each level subdomain, H is the height of the level subdomain, L min and L max H is the minimum and maximum allowed length of the hierarchical subdomain space. min and H max The minimum and maximum values allowed for the height of the hierarchical subdomain. is the constraint condition, is the constraint condition for the volume of each phase material under the specified volume, To minimize the objective function.

5. The method for joint optimization design of topology and size of a hierarchical composite structure according to claim 1, characterized in that: The neural network agent model described in S4 is a BP neural network, whose input layer contains the hierarchical subdomain size parameters and height, the hidden layer is two layers and each layer contains 10 nodes, and the output layer is a single-objective sound pressure level objective function or a multi-objective function of the comprehensive performance of acoustic-solid coupling.

6. The method for joint optimization design of topology and size of a hierarchical composite structure according to claim 1, characterized in that: The parameters of the genetic algorithm described in S4 are set as follows: population size is 50, evolutionary generations is 100, crossover probability is 0.8, and mutation probability is 0.

05.

7. The method for joint optimization design of topology and size of a hierarchical composite structure according to claim 1, characterized in that: The method further comprises: S5. Feed the size optimization results back to the topology optimization model, recalculate the objective function and material distribution, and verify the global optimality.

8. The method for joint optimization design of topology and size of a hierarchical composite structure according to claim 7, characterized in that: If the objective function does not converge in S5, the number of hidden layer nodes of the neural network or the optimization algorithm parameters are adjusted and S3 to S4 are repeated.

9. The method for joint optimization design of topology and size of a hierarchical composite structure according to claim 1, characterized in that: The objective function is minimization of the sound pressure level and / or minimization of the structural flexibility, and the constraint condition is that the volume fraction of each material phase meets a preset value.

10. A topology and size joint optimization design system for hierarchical composite structures, characterized in that: Including processor and memory; Memory for storing computer programs; A processor, configured to implement the method steps described in any one of claims 1 to 9 when executing a program stored in a memory.

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