Performance multi-objective optimization-based parameterized periodic thin-wall structure and design method thereof

Abstract

The invention discloses a parameterized periodic thin-wall structure design method based on performance multi-objective optimization. The method comprises the following steps: selecting a plurality of structure geometric parameters as design variables; selecting a plurality of specific parameter combinations in the value range; defining an optimization target and refining the optimization target into a plurality of optimization sub-targets; obtaining performance data of each optimization sub-target under each specific parameter combination, and further obtaining a comprehensive score of each optimization target; analyzing the mapping relation between the structural geometric parameter design variable and the optimization target, and constructing a corresponding response surface model; evaluating the prediction capability of the response surface model; establishing a mathematical model for multi-objective optimization of the periodic thin-walled structure; solving the mathematical model to output a solution set on a Pareto leading edge; and selecting an optimal solution set on the Pareto leading edge to obtain a corresponding specific parameter combination and a thin-wall structure. The thin-wall structure designed by the invention has parameter controllability, structural periodicity and industrial manufacturability while keeping the key mechanical advantages of a biological structure.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of structural design and advanced manufacturing, and particularly relates to a parameterizable periodic thin-walled structure based on performance multi-objective optimization and a design method thereof. BACKGROUND

[0002] Thin-walled structures have become a core design paradigm widely used in modern engineering due to their lightweight, high specific strength, high specific stiffness, and excellent energy absorption performance, and have shown significant advantages in the fields of automobile body lightweight, spacecraft cabin structure, building curtain wall, electronic device shell, and impact buffering device. Through topological optimization and advanced material collaborative design, thin-walled structures can achieve equivalent or even superior mechanical properties to traditional structures while reducing weight, greatly improving energy absorption efficiency. With the development of material function integration and the demand for extreme service environment, thin-walled structures not only bear the load and protection functions, but also gradually develop multi-functional integrated capabilities such as thermal insulation, heat dissipation, vibration reduction, acoustic regulation, and electromagnetic shielding, becoming an important development direction of advanced structural design.

[0003] In recent years, through the combination of multi-scale topological optimization and bionic structure design methods, thin-walled structures can achieve equivalent or even superior mechanical properties to traditional solid structures while reducing weight, and have multi-field collaborative response capabilities, providing a new idea for high-performance and multi-functional integrated engineering structure design. For example, the unique three-dimensional interconnected porous network of natural sponge skeleton realizes the collaborative optimization of material distribution-structure stability-energy dissipation in long-term evolution, and has excellent impact buffering performance; the hollow skeleton structure of birds greatly reduces weight while maintaining structural stability and torsional performance through the hollow wall plus transverse support truss configuration, which has been widely used in lightweight design of aviation; bamboo joint structure exhibits good bending and compression resistance and crack blocking ability through the change of joint thickness and internal cavity stiffening mechanism. In addition, biological structures in nature, such as plant stems, insect wings, and marine biological skeletons, exhibit multi-scale collaborative mechanical optimization characteristics of porosity-layering-multi-scale, which also provide rich prototypes for lightweight high-strength design of engineering structures.

[0004] However, the three-dimensional design of natural structures based on biological evolution faces a dilemma: on the one hand, structures that excessively replicate the topological complexity of biological prototypes (such as porous honeycombs and fiber cross-linking) can improve local performance, but their highly irregular structures are difficult to parameterize, severely limiting their controllable manufacturing and large-scale application in engineering practice; on the other hand, excessive simplification of structural geometry (such as idealized honeycombs, porous foams, and regular pore arrays) improves manufacturing feasibility, but their mechanical properties are far from achieving the synergistic enhancement level of natural structures. Therefore, there is an urgent need to develop a biomimetic thin-walled structure design method that can retain the key mechanical advantages of biological structures while possessing controllable parameters, structural periodicity, and industrial manufacturability. Summary of the Invention

[0005] To overcome the shortcomings of existing thin-walled structure design methods in achieving both parameterized controllability and maintaining key mechanical properties of biological structures, this invention provides a parameterized periodic thin-walled structure and its design method based on multi-objective performance optimization. Through a multi-objective topology optimization strategy, it aims to achieve parameter controllability, structural periodicity, and industrial manufacturability while retaining the key mechanical advantages of biological structures.

[0006] According to one aspect of the present invention, a parameterizable periodic thin-walled structure design method based on multi-objective performance optimization is provided, comprising:

[0007] Step S1: Select several structural geometric parameters from the parameter design library as design variables;

[0008] Step S2: Set the value range of each design variable, and select several specific parameter combinations within the value range;

[0009] Step S3: Define the optimization objective and refine it into multiple quantifiable sub-objectives;

[0010] Step S4: Construct the corresponding thin-walled structure geometric model based on the selected specific parameter combinations, and obtain the performance data of each optimization sub-objective under each specific parameter combination through a combination of simulation and experiment.

[0011] Step S5: Score each optimization sub-objective based on the performance data of each optimization sub-objective, and obtain a comprehensive score for each optimization objective based on the scores;

[0012] Step S6: Determine whether the total number of optimization objectives does not exceed 3; if it does not exceed 3, proceed to step S7; otherwise, use the weighted average method to merge some optimization objectives until the total number of optimization objectives does not exceed 3.

[0013] Step S7: The least squares method is used to analyze the mapping relationship between the structural geometric parameters design variables and the optimization objective, and a response surface model based on a second-order polynomial fitting function is constructed.

[0014] Step S8: Evaluate the predictive ability of the response surface model; if it is qualified, proceed to step S9; if it is not qualified, return to step S2 to reselect parameters.

[0015] Step S9: Establish a mathematical model for multi-objective optimization of periodic thin-walled structures;

[0016] Step S10: Solve the mathematical model using a non-dominated sorting genetic algorithm and output the solution set on the Pareto front;

[0017] Step S11: Select an optimal solution set on the Pareto front to obtain a specific parameter combination and the corresponding thin-walled structure.

[0018] Further, in step S1, the parameter design library includes the following parameters: DC coefficient, cosine coefficient, sine coefficient, function period length, total length of function prototype, thin wall height, thin wall thickness, amplitude control parameter, partition thickness, included angle between adjacent thin wall structures, transverse gap between adjacent cells, longitudinal gap between adjacent cells, single-layer chamber length, single-layer chamber width, number of cells in a single-layer chamber, total number of periods, and total number of layers.

[0019] Further, in step S3, one or more optimization objectives are selected; the optimization objectives include structural mechanical properties, structural thermal properties, structural electrical properties, structural acoustic properties, and structural magnetic properties; the structural mechanical properties include the following sub-objectives that can be optimized: structural strength, structural stiffness, fatigue strength, specific energy absorption, and peak impact force; the structural thermal properties include the following sub-objectives that can be optimized: heat transfer rate, coefficient of thermal expansion, thermal conductivity, thermal diffusivity, thermal shock resistance, and effective heat dissipation area; the structural electrical properties include the following sub-objectives that can be optimized: thermoelectricity and resistivity; the structural acoustic properties include the following sub-objectives that can be optimized: sound absorption coefficient, sound insulation, acoustic impedance, and noise attenuation coefficient; the structural magnetic properties include the following sub-objectives that can be optimized: magnetic susceptibility, magnetic permeability, coercivity, hysteresis loss, and eddy current loss.

[0020] Further, step S5 includes: multiplying the performance score of each sub-objective of the optimization objective by the corresponding weight coefficient;

[0021] The weighted sum is obtained by summing the products of all sub-objectives; the weighted sum is then divided by the sum of all weight coefficients to obtain the weighted average of the optimization objective.

[0022] Furthermore, in step S7, the least squares method is used to analyze the mapping relationship between the structural geometric parameter design variables and the optimization objective, and a response surface model based on a second-order polynomial fitting function is constructed. The corresponding mathematical expression is as follows: In the formula, To optimize the predicted response value of the target; , , and These represent the offset term, linear offset coefficient, second-order offset coefficient, and interaction term coefficient, respectively. and Design variables representing different structural geometric parameters; The number of variables to design for structural geometric parameters.

[0023] Furthermore, in step S8, the predictive ability of the response surface model is evaluated using the multiple correlation coefficient, as shown in the formula: In the formula, Represents the multiple correlation coefficient. It is the total number of specific parameter combinations. Indicates the first A specific combination of parameters, It is the first Finite element simulation results corresponding to a specific combination of parameters The average value of the finite element simulation results representing all specific parameter combinations. It is the first The calculated values ​​of the response surface model corresponding to a specific combination of parameters.

[0024] Further, step S10 includes:

[0025] S101: Generate the initial candidate solution set;

[0026] S102: Perform fast non-dominated sorting on all individuals in the initial candidate solution set to divide the individuals into different non-dominated layers;

[0027] S103: Based on the non-dominated hierarchy, select individuals from the candidate solution set to participate in crossover and mutation operations to generate the offspring candidate solution set;

[0028] S104: Update the current generation number;

[0029] S105: Merge the current generation's candidate solution set with the child generation's candidate solution set to form a new candidate solution set;

[0030] S106: If it is necessary to continue generating new candidate solution sets, proceed to step S107; if no further evolution is needed, proceed to step S1011.

[0031] S107: Perform fast non-dominated sorting on the new candidate solution set to obtain a new non-dominated hierarchical structure;

[0032] S108: Calculate the crowding degree for each individual in each non-dominated layer to obtain the individual crowding degree;

[0033] S109: Select individuals from the merged population to form a new candidate solution set based on the non-dominated hierarchy and individual crowding;

[0034] S1010: Repeated crossover and mutation operations generate the next generation of candidate solutions based on the new candidate solution set;

[0035] S1011: Determine whether the current algebra has reached the set maximum number of iterations; if the maximum number of iterations has been reached, output the non-dominated individuals in the current candidate solution set, which is the Pareto front solution set; if not, return to step S104 and continue the evolution.

[0036] According to one aspect of the present invention, a parameterizable periodic thin-walled structure based on multi-objective performance optimization is provided, constructed using the aforementioned parameterizable periodic thin-walled structure design method based on multi-objective performance optimization. The periodic thin-walled structure is composed of multiple stacked sandwich structures; each sandwich structure includes upper and lower partitions and a parameterizable periodic corrugated thin-walled core material sandwiched in between, with adjacent layers connected by shared partitions; wherein the cross-sectional patterns of different layer heights of the thin-walled structure are constituted by a family of functions generated from the same set of mathematical function prototypes, the function family being: In the formula, For a family of functions, For amplitude control parameters, h is the distance from the bottom of the thin-walled structure to the cross-section corresponding to the amplitude. The overall height of the thin-walled structure; Amplitude control parameters and standardization The functional relationship between them; This is the function prototype. , where x is variables, Where is the DC coefficient, L is the function period length, m is the total number of harmonics, and n is the harmonic order. , These are the cosine and sine coefficients of the nth harmonic, respectively. function prototype The total length.

[0037] According to one aspect of the present invention, an electronic device is provided, including a memory and a processor, the memory storing program instructions executable by the processor, the processor invoking the program instructions to execute the parameterizable periodic thin-walled structure design method based on multi-objective performance optimization.

[0038] According to one aspect of the present invention, a non-transitory computer-readable storage medium is provided, the non-transitory computer-readable storage medium storing computer instructions that cause the computer to execute the parameterizable periodic thin-walled structure design method based on multi-objective performance optimization.

[0039] The above technical solution establishes a periodic thin-walled structure that can be mathematically described and parameterized by a parameterized periodic thin-walled structure design method based on multi-objective performance optimization. The parameterized periodic thin-walled structure is composed of multiple layers of sandwich structures stacked together. Each sandwich structure includes two rigid partitions on the top and bottom and a parameterized periodic corrugated thin-walled core material sandwiched in the middle.

[0040] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0041] (1) This invention effectively balances energy absorption, structural stability, vibration control, multi-functional performance integration capability and manufacturing feasibility through a multi-objective topology optimization strategy, providing a new path for constructing high-performance, multi-functional integrated engineering structures.

[0042] (2) This invention combines biomimetic features with engineering practicality and has broad application prospects in fields such as automotive energy-absorbing components, aviation buffer components, biological scaffolds, and lightweight packaging shells. Attached Figure Description

[0043] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the accompanying drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0044] Figure 1 This is a flowchart illustrating a multi-objective optimization method for periodic thin-walled structure parameters provided in an embodiment of the present invention.

[0045] Figure 2 A schematic diagram of the NSGA-II genetic algorithm provided in the embodiments of this application;

[0046] Figure 3 A schematic diagram of the optimization parameters of the NSGA-II algorithm provided in the embodiments of the present invention;

[0047] Figure 4 A schematic diagram of the Pareto optimization front solution set provided in an embodiment of the present invention;

[0048] Figure 5 A schematic diagram of a parameterizable periodic thin-walled structure provided in an embodiment of this application;

[0049] Figure 6 A projection view of the top end face of a single-layer chamber structure provided in an embodiment of the present invention;

[0050] Figure 7 Function prototypes provided for embodiments of the present invention A schematic diagram.

[0051] In the figure, 1 is the top end face of the single-layer chamber structure; 2 is the reference plane with a height of h. Detailed Implementation

[0052] It should be noted that:

[0053] The terms “comprising” and “having”, and any variations thereof, in the specification, claims, and accompanying drawings of this invention are intended to cover a non-exclusive inclusion, such as a process, method, system, product, or apparatus that includes a series of steps or units, not necessarily limited to those explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0054] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. In addition, the technical features of the various embodiments or individual embodiments provided by the present invention can be arbitrarily combined to form new technical solutions. Such combinations are not bound by the order of steps and / or structural composition patterns, but must be based on the ability of those skilled in the art to implement them. When the combination of technical solutions is contradictory or cannot be implemented, it should be considered that such a combination of technical solutions does not exist and is not within the scope of protection claimed by the present invention.

[0055] This invention proposes an industrially manufactureable periodic parameterized thin-walled structure and its parameter optimization method by establishing a mathematically describable and parameter-tunable periodic three-dimensional model. Furthermore, through a multi-objective topology optimization strategy, it effectively balances energy absorption, structural stability, vibration control, multifunctional performance integration capabilities, and manufacturing feasibility, providing a new path for constructing high-performance, multifunctional integrated engineering structures. This structural design method combines biomimetic features with engineering practicality, and has broad application prospects in fields such as automotive energy-absorbing components, aerospace buffer assemblies, biological scaffolds, and lightweight packaging shells.

[0056] Please refer to Figure 1 This invention provides a parameterizable periodic thin-walled structure design method based on multi-objective performance optimization, comprising the following steps:

[0057] Step S1: Select several structural geometric parameters from the parameter design library as design variables.

[0058] In step S1, the parameter design library contains the following structural geometric parameters: DC coefficient Cosine coefficient sine coefficient , function period length Function prototype Total length Thin-wall height thin-walled and thick-walled Amplitude control parameters partition thickness Angle between adjacent thin-walled structures Horizontal gaps between adjacent cell bodies Longitudinal gaps between adjacent cell bodies Single-layer chamber length Single-layer chamber width Number of cells in a single-layered chamber Total number of cycles and total number of floors .

[0059] In this embodiment, the following structural geometric parameter design variables are selected from the parameter design library for parameter optimization: cosine coefficient. sine coefficient (The harmonic order is set to 3 to meet the accuracy requirements), function period length It should be noted that the structural geometric parameter design variables can be dynamically selected from a preset parameter design library, and their combination mode varies according to the actual engineering design requirements, which will not be limited here.

[0060] Step S2: Set the value range of each design variable, and select several specific parameter combinations within the value range.

[0061] In step S2, the value range of the structural geometric parameter design variables selected in step S1 needs to be set. Determining the value range of the structural geometric parameter design variables requires comprehensive consideration of the actual engineering situation and the geometric characteristics of the structure itself. After determining the value range of the structural geometric parameter design variables, a suitable experimental design method is selected, and appropriate data processing software (such as Isight, Optimus, Noesis Solutions, etc.) is used to obtain the values ​​within the value range. The specific parameter combinations should be designed with parameter values ​​distributed as evenly as possible within their range. Evenly distributed sample points can more accurately fit the mapping relationship between the design variables and the optimization objective, reducing bias. Understandably, the experimental design methods, data processing software, and the number of specific parameter combinations also need to be set according to the actual situation, and are not limited here.

[0062] It is important to note the cosine coefficient. sine coefficient Determines the function prototype (function prototype) (Please refer to the following text for the geometric shape. If the wall thickness is too large, the outer contour of the cross-section of the thin-walled structure will be...) Where the radius of curvature is smaller than the wall thickness, the wall becomes pointed, which distorts the shape of the thin-walled structure and affects its performance. Therefore, in this case, the cosine coefficient... and sine coefficient The values ​​should be limited to a reasonable range. In this embodiment, the range of values ​​for the structural geometric parameter design variables is as follows:

[0063]

[0064] It should be noted that the structural geometric parameter design variables in the residual parameter design library are constant values, specifically as follows: DC coefficient. =0, thin-wall height =5mm, thin wall thickness =0.1mm, partition thickness =0.2mm, angle between adjacent thin-walled structures = Horizontal gaps between adjacent cell bodies =5mm, longitudinal gap between adjacent cells =6mm, single-layer chamber length =30mm, single-layer chamber width =30mm, number of cells in a single-layer chamber =9. Function Prototype Total length L0=2mm, total number of layers N=3, amplitude control parameters In h= Take 1mm at h There exists a functional relationship at this point, specifically: Understandably, the values ​​of the structural geometric parameter design variables in the aforementioned remaining parameter design library can be set according to actual needs, and are not limited here.

[0065] In this embodiment, the optimal Latin hypercube design method in the Isight software is used to generate 100 (i.e., ...) within a set value range. =100) A sample of specific parameter combinations for the design variables of structural geometric parameters.

[0066] Step S3: Define the optimization objective and refine it into multiple quantifiable sub-objectives.

[0067] In step S3, one or more optimization objectives can be selected for optimization. Optimization objectives include, but are not limited to, structural mechanical properties, structural thermal properties, structural electrical properties, structural acoustic properties, and structural magnetic properties. Structural mechanical properties include, but are not limited to, the following sub-objectives that can be optimized: structural strength, structural stiffness, fatigue strength, and specific energy absorption. ( M represents the total energy absorbed when the structure is compressed to density, and M represents the total mass of the thin-walled structure, as well as the peak impact force. The structural thermal properties, including but not limited to the following sub-objectives, can be optimized: heat transfer rate. The structural electrical properties include, but are not limited to, the following sub-objectives that can be optimized: thermal expansion coefficient, thermal conductivity, thermal diffusivity, thermal shock resistance, and effective heat dissipation area. The structural acoustic properties include, but are not limited to, the following sub-objectives that can be optimized: sound absorption coefficient, sound insulation, acoustic impedance, and noise attenuation coefficient. The structural magnetic properties include, but are not limited to, the following sub-objectives that can be optimized: magnetic susceptibility, permeability, coercivity, hysteresis loss, and eddy current loss.

[0068] In this embodiment, two optimization objectives were selected: structural mechanical properties and structural thermal properties. The structural mechanical properties include the following sub-objectives: specific energy absorption. Peak collision force and quality The structural thermal performance includes the following sub-optimization objectives: heat transfer rate .

[0069] Step S4: Construct the corresponding thin-walled structure geometric model based on the selected specific parameter combinations, and obtain the performance data of each optimization sub-objective under each specific parameter combination through a combination of simulation and experiment.

[0070] In step S4, the structural mechanical properties, structural thermal properties, structural electrical properties, structural acoustic properties, and structural magnetic properties can be modeled and simulated through experiments or simulation software.

[0071] In step S4, the structural mechanical properties are modeled and simulated through experiments or using existing commercially available software tools (such as Ansys / ABAQUS / COMSOL Multiphysics / Altair HyperWorks / SolidWorks Simulation software); the structural thermal properties are modeled and simulated through experiments or using existing commercially available software tools (such as Ansys / COMSOL Heat Transfer / ABAQUS / FloTHERM / SolidWorks Thermal Simulation software); the structural electrical properties are modeled and simulated through experiments or using existing commercially available software tools (such as COMSOL AC / DC Module / Ansys / CST Studio Suite / QuickField / JMAG software); the structural acoustic properties are modeled and simulated through experiments or using existing commercially available software tools (such as Ansys / COMSOL Acoustics Module / LMSVirtual.Lab / Actran / Abaqus Acoustics software); and the structural magnetic properties are modeled and simulated through experiments or using existing commercially available software tools (such as Ansys / COMSOL Magnetic Fields / JMAG / CST EMStudio / Opera Simulation software).

[0072] In this embodiment, Solidworks software is used to establish a corresponding three-dimensional model (i.e., thin-walled structure geometric model) based on the specific parameter combination of the design variables for each structural geometric parameter. Then, Ansys software is used to perform mechanical simulation and transient thermal simulation on each three-dimensional model and record the effective calculation results to obtain the finite element simulation results corresponding to each specific parameter combination. Then, based on the finite element simulation results, the performance data of each optimization sub-objective under each specific parameter combination are obtained.

[0073] Step S5: Score each optimization sub-objective based on the performance data of each optimization sub-objective, and obtain a comprehensive score for each optimization objective based on the scores.

[0074] In step S5, based on the performance data of each optimization sub-objective under each specific parameter combination, the optimization objectives under each parameter group are scored according to the scoring criteria. For optimization objectives containing multiple sub-objectives, weighting coefficients are introduced, and their performance values ​​are normalized and then weighted averaged to obtain the comprehensive score of the optimization objective. The core steps for calculating the weighted average are: weighting: multiply the performance score of each sub-objective of the optimization objective by its corresponding weight coefficient; summation: sum the products to obtain the weighted sum; normalization: divide the weighted sum by the sum of all weight coefficients to obtain the weighted average of the optimization objective. In essence, the weighted average of the optimization objective is the comprehensive score of that optimization objective.

[0075] In this embodiment, based on the performance data of each optimization sub-objective, the specific energy absorption under each specific parameter combination is evaluated according to the scoring criteria. Peak collision force Mass M and heat transfer rate Rate it. and Combined into the first dimension optimization objective F (each assigned a weight) and M is set as the second dimension optimization objective. This is set as the third dimension of the optimization objective. Then, a weighted average is calculated on the performance scores of the sub-objectives in the first dimension to obtain the final weighted average of the first dimension's optimization objective F. The details are as follows: ;in, The score is based on the specific energy absorption. The rating is for peak impact force. The weighting coefficient for specific energy absorption. is the weighting coefficient for the peak collision force, and F is the comprehensive score of the first dimension optimization objective. The weighted average score obtained through the above operations effectively and objectively reflects the comprehensive performance of this set of specific parameters on the optimization objective.

[0076] It should be noted that the specific value of the weight coefficient should be determined based on the degree of influence of each optimization sub-objective on the overall optimization objective, and in combination with actual engineering requirements (such as performance bottlenecks and priorities). No limit is set here.

[0077] Step S6: Determine whether the total number of optimization objectives does not exceed 3; if it does not exceed 3, proceed to step S7; otherwise, use the weighted average method to merge some optimization objectives until the total number of optimization objectives does not exceed 3.

[0078] In this embodiment, the total number of optimization objectives is 3, namely, the first-dimensional optimization objective F, the second-dimensional optimization objective M, and the third-dimensional optimization objective. If there are no more than 3, proceed to step S7.

[0079] Step S7: The least squares method is used to analyze and process the mapping relationship between the structural geometric parameters design variables and the optimization objective, and a response surface model based on the second-order polynomial fitting function is constructed.

[0080] In step S7, the mathematical expression of the constructed response surface model based on the second-order polynomial fitting function is as follows: In the formula, To optimize the predicted response value of the target; , , and These represent the offset term, linear offset coefficient, second-order offset coefficient, and interaction term coefficient, respectively. and Design variables representing different structural geometric parameters; The number of design variables for structural geometric parameters. Among them, the total number of response surface coefficients is... The number of experimental design schemes must be guaranteed. (i.e., the total number of specific parameter combinations taken in step S2) is greater than Only then can the second-order polynomial response surface model be initialized.

[0081] It should be noted that, for the comprehensive score of each specific parameter combination and its corresponding optimization objective, the improved response surface methodology can be used to determine the unknown parameters of the response surface model. , , Specifically, the various combinations of parameters are substituted into the response surface model. and The comprehensive score of the corresponding optimization objective is substituted into the response surface model. The unknown parameters of the response surface model can then be obtained. , , Then, the unknown parameters and structural geometry parameters (design variables) are substituted into the mathematical expression of the response surface model to obtain the response function for each optimization objective. Approximate relationship (i.e., mapping relationship) between structural geometric parameters and design variables.

[0082] In this embodiment, the first-dimensional optimization objective F, the second-dimensional optimization objective M, and the third-dimensional optimization objective are obtained. A second-order polynomial response surface model is used to establish the functional relationship between the optimization objective and the structural geometric parameters design variables, specifically:

[0083] ;

[0084] ;

[0085] ;

[0086] in, , , , These represent the offset term, linear offset coefficient, second-order offset coefficient, and interaction term coefficient of the first-dimensional optimization objective F, respectively. , , , These represent the offset term, linear offset coefficient, second-order offset coefficient, and interaction term coefficient of the second-dimensional optimization objective M, respectively. , , , These represent the optimization objectives in the third dimension. The offset term, linear offset coefficient, second-order offset coefficient, and interaction term coefficient; and These represent different structural geometric parameter design variables; the number of structural geometric parameter design variables. In this embodiment, the number of structural geometric parameter design variables is 7, namely... , , , , , , It should be noted that, , , , , , , , , , , , All are unknown coefficients. The first-dimensional optimization objective F, the second-dimensional optimization objective M, and the third-dimensional optimization objective obtained in step S5 are... The comprehensive scores are respectively substituted into the first dimension optimization objective F, the second dimension optimization objective M, and the third dimension optimization objective mentioned above. The corresponding unknown coefficients can be obtained by using a second-order polynomial response surface model.

[0087] Step S8: Evaluate the predictive ability of the response surface model; if it is qualified, proceed to step S9; if it is not qualified, return to step S2 to reselect several specific parameter combinations.

[0088] In step S8, after the response surface model is established, the predictive ability of the response surface model needs to be evaluated. If the response surface model is within the allowable error range, the predictive ability of the response surface model is considered qualified, and the process proceeds directly to the next step (i.e., step S9). If the response surface model is not within the allowable error range, the predictive ability of the response surface model is considered unqualified, and the process returns to step S2 to reselect several specific parameter combinations.

[0089] In this embodiment, the multiple correlation coefficient is used to evaluate the predictive ability of the response surface model, which can be specifically described as follows: In the formula, It is the multiple correlation coefficient. It is an indicator for evaluating the accuracy of the response surface model in fitting the experimental samples. The closer a value is to 1, the smaller the error value. It is the total number of specific parameter combinations. Indicates the first A specific combination of parameters, It is the first Finite element simulation results corresponding to a specific combination of parameters The average value of the finite element simulation results representing all specific parameter combinations. It is the first The calculated values ​​of the response surface model for a specific combination of parameters. It should be noted that, depending on the actual situation, other evaluation indicators (e.g., average value) can also be selected in this invention. Maximum value Root mean square error (etc.) to evaluate the predictive power of response surface models.

[0090] It should be noted that the error analysis results of the response surface model obtained by this invention are based on calculations. As can be seen, the response surface model constructed in this invention has high fitting accuracy and good reliability. Therefore, the established response surface model can be used for subsequent optimization design.

[0091] Step S9: Establish a mathematical model for multi-objective optimization of periodic thin-walled structures.

[0092] In this embodiment, a mathematical model for multi-objective optimization of periodic thin-walled structures is established, specifically as follows:

[0093]

[0094] Step S10: Solve the mathematical model using a non-dominated sorting genetic algorithm, and output the solution set on the Pareto front. Specifically, as follows... Figure 2 As shown, step S10 includes steps S101-S1011.

[0095] S101: Generate the initial candidate solution set.

[0096] In this invention, a specific set of values ​​(i.e., a specific combination of parameters) of the structural geometric parameter design variables represents a candidate solution to the problem. First, this candidate solution needs to be encoded into a symbol string with a specific structure, called a chromosome. A chromosome consists of several symbols, each symbol being called a gene, and the length of the entire symbol string is the length of the chromosome. Each chromosome corresponds to a solution to the problem, also called an individual. N unique individuals are randomly and uniformly generated within the feasible region to form an initial candidate solution set, also called the initial population. Based on the optimization objective function defined in step S7 (the mapping relationship between the geometric structural design variables and the weighted average of various optimization objectives, which can be understood as a functional relationship), the objective function value corresponding to each individual is calculated (i.e., the objective function value corresponding to the individual corresponds to the geometric structural design variable, which corresponds to the weighted average of various optimization objectives), serving as its fitness value, used to quantify the overall performance and quality of the solution in terms of the optimization objectives.

[0097] S102: Perform fast non-dominated sorting on all individuals in the initial candidate solution set to divide the individuals into different non-dominated layers.

[0098] S103: Based on the non-dominated hierarchy, select individuals from the candidate solution set to participate in crossover and mutation operations to generate the offspring candidate solution set.

[0099] Crossover operation: This involves pairing up portions of chromosomes and randomly exchanging gene segments within each pair to generate new chromosomes. The probability of crossover is controlled by a predefined crossover probability, and the degree of crossover or the range of variation can be determined by the crossover distribution index.

[0100] Mutation operation: Randomly select a small number of chromosomes from the candidate solution set, and invert one of the genes (i.e., reverse its sign) to form a new solution. The probability of mutation is determined by the set mutation probability or mutation distribution index.

[0101] S104: Update the current generation. That is, update the current generation to Gen = Gen + 1.

[0102] S105: Merge the current generation's candidate solution set with the child generation's candidate solution set to form a new candidate solution set;

[0103] S106: If it is necessary to continue generating new candidate solution sets, proceed to step S107; if no further evolution is needed, proceed to step S1011.

[0104] S107: Perform fast non-dominated sorting on the new candidate solution set to obtain a new non-dominated hierarchical structure;

[0105] S108: Calculate the crowding degree for each individual in each non-dominated layer to obtain the individual crowding degree;

[0106] S109: Select individuals from the merged population to form a new candidate solution set based on the non-dominated hierarchy and individual crowding;

[0107] S1010: Repeated crossover and mutation operations generate the next generation of candidate solutions based on the new candidate solution set;

[0108] S1011: Determine whether the current algebra has reached the set maximum number of iterations; if the maximum number of iterations has been reached, output the non-dominated individuals in the current candidate solution set, which is the Pareto front solution set; if not, return to step S104 and continue the evolution.

[0109] It should be noted that non-dominated individuals belong to the Pareto front of the current population, meaning they cannot further optimize a certain objective without sacrificing other objectives. For example, for individual A to dominate individual B, it must satisfy the following conditions: A is no worse than B on all objective functions (i.e., ≤ or ≥, depending on the direction of optimization); and A is strictly better than B on at least one objective.

[0110] In this embodiment, the second-generation non-dominated sorting genetic algorithm NSGA-II, combined with crowding distance and elitist strategy, is selected in the Isight software to optimize the objective. The optimization parameters of the NSGA-II algorithm are selected as follows: Figure 3 As shown. By executing the optimization procedure, the Pareto optimization front solution set for the multi-objective optimization of the periodic thin-walled structure parameters is obtained as follows. Figure 4 As shown.

[0111] Step S11: Select an optimal solution set on the Pareto front to obtain a specific parameter combination and the corresponding thin-walled structure.

[0112] In step S11, since the optimization objectives cannot be simultaneously optimal, an optimization solution set can be selected on the Pareto front according to the actual engineering design requirements or the preference for the optimization objectives, so as to obtain a specific parameter combination and a thin-walled structure constructed from the specific parameter combination.

[0113] like Figure 5As shown, based on the same technical concept as the aforementioned embodiments, this invention also provides a parameterizable periodic thin-walled structure based on multi-objective performance optimization. This structure is constructed using the aforementioned parameterizable periodic thin-walled structure design method based on multi-objective performance optimization. The periodic thin-walled structure is composed of multiple stacked sandwich structures. Each sandwich structure includes upper and lower rigid partitions (partition thickness denoted by tg) and a parameterizable periodic corrugated thin-walled core material sandwiched in between. Adjacent layers are connected by shared partitions; that is, the bottom partition of the upper sandwich structure also serves as the top partition of the lower sandwich structure. In this embodiment, the partitions are made of high-stiffness materials to withstand in-plane compressive loads, while the corrugated thin-walled core material is periodically bent along the vertical direction, providing excellent shear resistance and energy absorption performance. The porous structure in the structure provides good heat dissipation and convection characteristics.

[0114] like Figure 6 As shown, the cross-sectional patterns of different story heights of the thin-walled structure are composed of a family of functions generated by the same mathematical function prototype. The general form of the family of functions is: ,in, For amplitude control parameters, function prototype Total length. Amplitude control parameters. and standardization There is a functional relationship Where h is the distance between the bottom of the thin-walled section and the cross-section corresponding to the amplitude. This represents the overall height of the thin-walled structure. Functional relationship. It can be linear, for example: It can also be non-linear, for example... No restrictions are imposed here.

[0115] Please refer to the appendix for details. Figure 7 , Figure 7 The function prototype is A schematic diagram. Function prototype. ,in, Where is the DC coefficient, L is the function period length, m is the total number of harmonics to meet the accuracy requirements, and n is the harmonic order. , These are the cosine and sine coefficients of the nth harmonic, respectively. Function amplitude. ;in, for function prototype The maximum value achieved. The thin-walled structure exhibits a tapered geometric feature, with the thin-wall thickness denoted by t. Adjacent thin-walled structures are separated by an angle. They are arranged in an alternating pattern to form a single cell, and the lateral spacing between adjacent cell bodies is... The longitudinal spacing between adjacent cell bodies is Multiple cell bodies are arranged in a staggered manner with the same spacing S to form a single-layer chamber structure. The length of the chamber structure is... The width of the chamber structure is The porosity (porosity refers to the percentage of pore volume in a material to the total volume, reflecting the density or porous nature of the material) of the single-layer chamber structure is controlled at 70%. Approximately 90% of the structure consists of multiple chambers stacked on top of each other to form an overall structure (i.e., a complete periodic thin-walled structure). In this embodiment, the entire chamber contains 9 individual cells, which are arranged alternately at equal intervals. Three identical thin-walled structures are arranged together at 120° angles to form a single cell.

[0116] Based on the same technical concept as the foregoing embodiments, the present invention also provides an electronic device, including a memory and a processor, wherein the memory stores program instructions that are executed by the processor, and the processor invokes the program instructions to execute the parameterizable periodic thin-walled structure design method based on multi-objective performance optimization.

[0117] Based on the same technical concept as the foregoing embodiments, the present invention also provides a non-transitory computer-readable storage medium storing computer instructions that cause the computer to execute the parameterizable periodic thin-walled structure design method based on multi-objective performance optimization.

[0118] In summary, this invention establishes a mathematically describable and parameter-tunable periodic three-dimensional model, proposes an industrially manufactureable periodic parameterized thin-walled structure and its parameter optimization method, and further utilizes a multi-objective topology optimization strategy to effectively balance energy absorption, structural stability, vibration control, multifunctional performance integration capabilities, and manufacturing feasibility, providing a new path for constructing high-performance, multifunctional integrated engineering structures. This structural design method combines biomimetic features with engineering practicality, and has broad application prospects in fields such as automotive energy-absorbing components, aerospace buffer assemblies, biological scaffolds, and lightweight packaging shells.

[0119] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the technical solutions of the embodiments of the present invention.

Claims

1. A parameterizable periodic thin-walled structure design method based on multi-objective performance optimization, characterized in that, include: Step S1: Select several structural geometric parameters from the parameter design library as design variables; Step S2: Set the value range of each design variable, and select several specific parameter combinations within the value range; Step S3: Define the optimization objective and refine it into multiple quantifiable sub-objectives; Step S4: Construct the corresponding thin-walled structure geometric model based on the selected specific parameter combinations, and obtain the performance data of each optimization sub-objective under each specific parameter combination through a combination of simulation and experiment. Step S5: Score each optimization sub-objective based on the performance data of each optimization sub-objective, and obtain a comprehensive score for each optimization objective based on the scores; Step S6: Determine if the total number of optimization targets does not exceed 3; if it does not exceed 3, proceed to step S7. Otherwise, a weighted average method is used to merge some optimization objectives until the total number of optimization objectives does not exceed three. Step S7: The least squares method is used to analyze the mapping relationship between the structural geometric parameters design variables and the optimization objective, and a response surface model based on a second-order polynomial fitting function is constructed. Step S8: Evaluate the predictive ability of the response surface model; if it is qualified, proceed to step S9; if it is not qualified, return to step S2 to reselect parameters. Step S9: Establish a mathematical model for multi-objective optimization of periodic thin-walled structures; Step S10: Solve the mathematical model using a non-dominated sorting genetic algorithm and output the solution set on the Pareto front; Step S11: Select an optimal solution set on the Pareto front to obtain a specific parameter combination and the corresponding thin-walled structure.

2. The parameterizable periodic thin-walled structure design method based on multi-objective performance optimization as described in claim 1, characterized in that, In step S1, the parameter design library includes the following parameters: DC coefficient, cosine coefficient, sine coefficient, function period length, total length of function prototype, thin wall height, thin wall thickness, amplitude control parameter, partition thickness, included angle between adjacent thin wall structures, transverse gap between adjacent cells, longitudinal gap between adjacent cells, single-layer chamber length, single-layer chamber width, number of cells in a single-layer chamber, total number of periods, and total number of layers.

3. The parameterizable periodic thin-walled structure design method based on multi-objective performance optimization as described in claim 1, characterized in that, In step S3, one or more optimization objectives are selected; the optimization objectives include structural mechanical properties, structural thermal properties, structural electrical properties, structural acoustic properties, and structural magnetic properties; the structural mechanical properties include the following sub-objectives that can be optimized: structural strength, structural stiffness, fatigue strength, specific energy absorption, and peak impact force; the structural thermal properties include the following sub-objectives that can be optimized: heat transfer rate, coefficient of thermal expansion, thermal conductivity, thermal diffusivity, thermal shock resistance, and effective heat dissipation area; the structural electrical properties include the following sub-objectives that can be optimized: thermoelectric properties and resistivity; the structural acoustic properties include the following sub-objectives that can be optimized: sound absorption coefficient, sound insulation, acoustic impedance, and noise attenuation coefficient; The structural magnetic properties include the following sub-objectives that can be optimized: magnetic susceptibility, magnetic permeability, coercivity, hysteresis loss, and eddy current loss.

4. The parameterizable periodic thin-walled structure design method based on multi-objective performance optimization as described in claim 1, characterized in that, Step S5 includes: Multiply the performance score of each sub-objective of the optimization objective by its corresponding weight coefficient; The weighted sum is obtained by summing the products of all sub-objectives; Dividing the weighted sum by the sum of all weight coefficients yields the weighted average of the optimization objective.

5. The parameterizable periodic thin-walled structure design method based on multi-objective performance optimization as described in claim 1, characterized in that, In step S7, the least squares method is used to analyze the mapping relationship between the structural geometric parameters, design variables, and optimization objectives, and a response surface model based on a second-order polynomial fitting function is constructed. The corresponding mathematical expression is as follows: In the formula, To optimize the predicted response value of the target; , , and These represent the offset term, linear offset coefficient, second-order offset coefficient, and interaction term coefficient, respectively. and Design variables representing different structural geometric parameters; The number of variables to design for structural geometric parameters.

6. The parameterizable periodic thin-walled structure design method based on multi-objective performance optimization as described in claim 1, characterized in that, In step S8, the predictive ability of the response surface model is evaluated using the multiple correlation coefficient, as shown in the formula: In the formula, Represents the multiple correlation coefficient. It is the total number of specific parameter combinations. Indicates the first A specific combination of parameters, It is the first Finite element simulation results corresponding to a specific combination of parameters The average value of the finite element simulation results representing all specific parameter combinations. It is the first The calculated values ​​of the response surface model corresponding to a specific combination of parameters.

7. The parameterizable periodic thin-walled structure design method based on multi-objective performance optimization as described in claim 1, characterized in that, Step S10 includes: S101: Generate the initial candidate solution set; S102: Perform fast non-dominated sorting on all individuals in the initial candidate solution set to divide the individuals into different non-dominated layers; S103: Based on the non-dominated hierarchy, select individuals from the candidate solution set to participate in crossover and mutation operations to generate the offspring candidate solution set; S104: Update the current generation number; S105: Merge the current generation's candidate solution set with the child generation's candidate solution set to form a new candidate solution set; S106: If it is necessary to continue generating new candidate solution sets, proceed to step S107; if no further evolution is needed, proceed to step S1011. S107: Perform fast non-dominated sorting on the new candidate solution set to obtain a new non-dominated hierarchical structure; S108: Calculate the crowding degree for each individual in each non-dominated layer to obtain the individual crowding degree; S109: Select individuals from the merged population to form a new candidate solution set based on the non-dominated hierarchy and individual crowding; S1010: Repeated crossover and mutation operations generate the next generation of candidate solutions based on the new candidate solution set; S1011: Determine whether the current algebra has reached the set maximum number of iterations; if the maximum number of iterations has been reached, output the non-dominated individuals in the current candidate solution set, which is the Pareto front solution set; if not, return to step S104 and continue the evolution.

8. A parameterizable periodic thin-walled structure based on multi-objective performance optimization, characterized in that, The structure is constructed using a parameterizable periodic thin-walled structure design method based on multi-objective performance optimization as described in any one of claims 1 to 7. The periodic thin-walled structure is composed of multiple stacked sandwich structures. Each sandwich structure includes upper and lower partitions and a parameterizable periodic corrugated thin-walled core material sandwiched in between. Adjacent layers are connected by shared partitions. The cross-sectional patterns of different layer heights of the thin-walled structure are constituted by a family of functions generated from the same mathematical function prototype, and the function family is as follows: In the formula, For a family of functions, For amplitude control parameters, h is the distance from the bottom of the thin-walled structure to the cross-section corresponding to the amplitude. The overall height of the thin-walled structure; Amplitude control parameters and standardization The functional relationship between them; This is the function prototype. , where x is variables, The DC coefficient is... Let m be the length of the function period, m be the total number of harmonics, and n be the harmonic order. , These are the cosine and sine coefficients of the nth harmonic, respectively. function prototype The total length.

9. An electronic device, characterized in that, The system includes a memory and a processor, wherein the memory stores program instructions that are executed by the processor, and the processor invokes the program instructions to execute a parameterizable periodic thin-walled structure design method based on performance multi-objective optimization as described in any one of claims 1 to 7.

10. A non-transitory computer-readable storage medium, characterized in that, The non-transitory computer-readable storage medium stores computer instructions that cause the computer to execute the parameterizable periodic thin-walled structure design method based on multi-objective performance optimization as described in any one of claims 1 to 7.

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