Structural customization rigidity optimization method based on genetic algorithm

Abstract

The invention discloses a structure customization rigidity optimization method based on a genetic algorithm, and belongs to the field of structure optimization. According to the method, a complex structure is optimized based on a genetic algorithm, including layering of a macrostructure and optimization of geometric parameters of a microstructure. The implementation method comprises the following steps: under the constraint of the configuration of the macrostructure and the geometric parameters of the microcosmic cells, optimizing to obtain the geometric parameters for filling the microcosmic cells among different parts of the macrostructure, and realizing the rigidity matching among different cells, so that the rigidity of the optimized macrostructure reaches a preset value. In the optimization process, an interface of simulation software and a genetic algorithm is established, mechanical property analysis is carried out on the complex model in the simulation software, simulation data are extracted and transmitted to the genetic algorithm, and optimization of microscopic cell geometric parameters is carried out. Simulation software and a genetic algorithm are coupled, collaborative optimization of macro and microstructure is achieved, the problem that rigidity customization of a complex three-dimensional model is difficult is solved, and the efficiency and precision of rigidity optimization of structure customization are improved.

Description

Technical Field

[0001] The present invention belongs to the field of structural optimization and relates to an optimization method for customized stiffness of structures based on a genetic algorithm. Background Art

[0002] In practical engineering applications, the selection of structures and materials is an important factor determining the mechanical properties of structures. Due to its own lightweight and multi-functional characteristics, the lattice structure has been widely used in key components in the aerospace field and also shows broad application prospects in other engineering fields with high requirements for lightweight. At present, by designing the overall or local structure in the form of a lattice, the lightweight of the structure can be effectively achieved. By optimizing the stiffness distribution of the structure, the amount of material used in the structure can be reduced without affecting the structural performance, realizing lightweight design. In addition, by customizing the stiffness, the stability and stiffness uniformity of the structure can be enhanced, and the control of the vibration characteristics of the structure can be realized. However, there are problems in the existing three-dimensional structure optimization design that the model is complex and it is difficult to realize the parametric modeling of the structure through Python, which limits the optimization design of fixed-configuration structures. In addition, three-dimensional structures also have the problems of more design variables and a large amount of calculation, making it difficult to obtain the optimal result, which greatly limits the mechanical properties of the structure. Summary of the Invention

[0003] The main purpose of the present invention is to provide an optimization method for customized stiffness of structures based on a genetic algorithm, which optimizes complex structures based on the genetic algorithm, including the layering of the macroscopic structure and the optimization of the geometric parameters of the microscopic structure. Under the constraints of the macroscopic structure configuration and the geometric parameters of the microscopic unit cells, the geometric parameters of the microscopic unit cells filled between different parts of the macroscopic structure are optimized to achieve the stiffness matching between different unit cells, so that the stiffness of the optimized macroscopic structure reaches a preset value. During the optimization process, an interface between the simulation software and the genetic algorithm is established. The simulation software analyzes the mechanical properties of the complex model, extracts the simulation data and transfers it to the genetic algorithm for the optimization of the geometric parameters of the microscopic unit cells. By coupling the simulation software and the genetic algorithm, the collaborative optimization of the macro-micro structures is realized, the problem of difficult customization of the stiffness of complex three-dimensional models is solved, and the efficiency and accuracy of the optimization of the customized stiffness of the structure are improved.

[0004] The object of the present invention is achieved by the following technical solutions:

[0005] A method for customizing and optimizing the stiffness of a structure based on a genetic algorithm discloses that a complex three-dimensional model is imported into a simulation software. Different modules are divided according to the forces on the macroscopic structure in the simulation software. Through the elastic theory, a mapping relationship between the geometric parameters of the microscopic unit cell and the Young's modulus is established. Based on the optimization objective of customizing the stiffness of the macroscopic structure and the constraints of the geometric parameters of the microscopic unit cell in the genetic algorithm, an optimization objective function and a fitness function are established. Through the fitness function, the relationship between the optimized geometric parameters of the unit cell and the stiffness of the macroscopic structure is established. An interface between the simulation software and the optimization algorithm is built to automatically import the simulation software for mechanical property analysis, and the results of the finite element analysis are extracted and transmitted to the genetic algorithm. Microscopic structures with different geometric parameters are filled between different macroscopic modules, so as to realize the stiffness matching between different modules and reach the preset stiffness value. In the genetic algorithm, an initial population of geometric parameters of the microscopic unit cell is generated. Through the mapping relationship between the geometric parameters and the Young's modulus, a corresponding finite element model of the macroscopic structure is established. The stiffness of the whole macroscopic structure is calculated in the simulation software, and this stiffness value is transmitted to the genetic algorithm to calculate the fitness value under the initial population. According to the fitness value, the regenerated individuals are selected, and through the crossover and mutation operations of the genetic algorithm, a new population is generated, which is used as the new optimized parameters and the corresponding finite element model is obtained. Through the evolutionary iteration of the finite element and the genetic algorithm, the optimal structural parameters are obtained, and the stiffness of the structure gradually converges to the set solution, that is, the customization and optimization of the structure stiffness are realized based on the genetic algorithm.

[0006] A method for customizing and optimizing the stiffness of a structure based on a genetic algorithm disclosed by the present invention includes the following steps:

[0007] Step 1: The equivalent mechanical properties of a structure are jointly determined by the material and configuration of the structure. The equivalent mechanical properties of the structure include strength and stiffness. Based on the unit cell type and the periodic arrangement characteristics in space, homogenization calculation is carried out to establish the analytical relationship between the geometric parameters of the microscopic unit cell and the equivalent mechanical properties of the macroscopic structure, and the mechanical properties of the material of the equivalent entity are obtained. Taking the equivalent parameters of the lattice structure as the material input, the external shape structure is calculated and analyzed at the macroscopic scale, so as to obtain the mechanical properties of the macroscopic structure. By adjusting the geometric parameters of the unit cell, stiffness matching is realized.

[0008] Preferably, the microscopic unit cell described in Step 1 selects the BCC structure. The BCC structure does not contain transverse rods and is suitable for 3D printing. In addition, the BCC structure is mainly dominated by bending deformation, has lightweight and high strength and good energy absorption capacity, and is suitable for impact-resistant structures.

[0009] The specific implementation method of Step 1 is:

[0010] Considering the coincidence effect between the rods, the effective length l of the unit cell rods is obtained E

[0011]

[0012] Where: l is the length of the cell member, R is the cell radius, and ψ is the angle between the member radius and the connection surface; the coefficient is a semi-empirical coefficient;

[0013] Under the action of the external force F, the angular displacement of point A along the M1 direction is Δ 1F , under the bending moment M1 = 1, the angular displacement of point A along the M1 direction is δ 11 , so under the combined action of the external force F and M1, the angular displacement of point A along the M1 direction, Δ1, is:

[0014] Δ1 = δ 11 M1 + Δ 1F

[0015] According to the structural symmetry, the structural angular displacement is 0, and the deformation compatibility equation is obtained:

[0016] δ 11 M1 + Δ 1F = 0

[0017] Under the action of the statically determinate system and the external force F acting on point A, the bending moment M, axial force F N , and shear force Fs on the rod AB are respectively:

[0018] M(x) = Fxcosθ,

[0019] F N (x) = -Fsinθ,

[0020] F S (x) = Fcosθ

[0021] θ is the angle between the cell member and the horizontal direction;

[0022] Under the action of the statically determinate system and the unit virtual bending moment M = 1 acting on point A, the bending moment axial force and shear force on the rod AB are respectively:

[0023]

[0024] According to the deformation compatibility equation, the bending moment is obtained as:

[0025]

[0026] The actual force condition of rod AB is:

[0027]

[0028] FN = -Fsinθ,

[0029] F S = Fcosθ

[0030] Apply a unit force F = 1 along the Y direction at point A, and the force condition of the rod is as follows:

[0031]

[0032] Then the displacement ΔY of point A in the vertical direction is:

[0033]

[0034] Obtain:

[0035]

[0036] For the moment of inertia of a circular cross-section E S is the Young's modulus of the material, E S = 71000 MPa, μ = 0.3, circular cross-section shear shape factor The Young's modulus E of the structure in the Y direction Y is:

[0037]

[0038] where L is the cell length size.

[0039] Step 2: Import the 3D model to be optimized into the finite element analysis software to calculate the structural response. Divide the structure in the simulation software, assign different equivalent solid materials to different regions, add structural boundary conditions, apply displacement loads, set the force extraction reference point, divide the mesh, set the history output and field output, and then solve for the stiffness of the macroscopic external structure according to the magnitude of the reaction force extracted under the applied displacement load.

[0040] As an optimization, the finite element analysis software selected in Step 2 is Abaqus.

[0041] Step 2.1: Import the model to be optimized into Abaqus, divide the model to be optimized to obtain multiple modules; divide different regions according to the force condition of the macroscopic structure, and assign the Young's modulus E of different equivalent solid materials obtained in Step 1 to different regions Y , that is, the geometric parameters between the microscopic cells corresponding to each module are different; by arranging microscopic cells with different geometric parameters inside the macroscopic structure, change the stiffness of different regions of the macroscopic structure to achieve the customized stiffness requirements of the overall macroscopic structure;

[0042] Step 2.2: Set boundary conditions for the macroscopic structure in Abaqus; couple the upper surface of the structure to node "M_SET-1" and apply a downward displacement load to this node; fix the lower surface of the structure; perform mesh division on the macroscopic structure and set history output and field output to obtain a finite element analysis model.

[0043] Step 3: Combine Abaqus with the genetic algorithm, and control the finite element analysis of Abaqus and optimize the design parameters through Python scripts. Establish a fitness function f(x) based on the mechanical response and optimization objectives of the macroscopic structure obtained from the finite element analysis, and obtain the relationship between the geometric parameters of the microstructure in different regions and the target stiffness through the fitness function f(x).

[0044] Step 3.1: Combine Abaqus with the genetic algorithm, and perform finite element analysis and extract the reaction force magnitude on the finite element model in Step 2 through Python scripts.

[0045] Step 3.2: Establish a fitness function f(x) based on the reaction force magnitude pred_F obtained in 3.1 and the optimization objective target_F:

[0046] f(x) = 1 / |pred_F - target_RF|

[0047] Obtain the relationship between the geometric parameters of the microscopic cells in different regions and the target reaction force through the fitness function f(x).

[0048] Step 4: Encode the radius R of the microscopic cells in real number coding and randomly generate an initial population N. Establish a finite element analysis model for the cell radius combinations in different regions in the population to extract the mechanical response of the macroscopic structure and perform fitness calculation. Determine the probability of each individual being retained based on the fitness calculation results, and then randomly vary the cell radius R of each individual in the population according to crossover and mutation to obtain a new generation of population, that is, the new microscopic cell radius. After several generations of evolutionary iteration, obtain the optimal individual, which is the combination of microscopic cell radii closest to the optimization objective, that is, complete the customized stiffness optimization of the structure based on the genetic algorithm.

[0049] Step 4.1: Encode the radius of the micro-cell in an integer encoding manner to establish the initial population S; set a DNA length DNA_SIZE encoded in real numbers, a crossover rate CROSSOVER_RATE, a mutation rate MUTATION_RATE, the number of iterations N_GENERATIONS, and the geometric parameter constraint RX_BOUND of the micro-cell, the optimization objective target_F, the cell radius design variable X = [R1, R2, R3, R4, R5, R6], and the Young's modulus of the equivalent solid material E = [E1, E2, E3, E4, E5, E6];

[0050] Step 4.2: The genetic algorithm randomly generates N individuals s1, s2, …, sN in RX_BOUND, that is, the radii of the micro-cells in different regions, and obtains the Young's moduli {E1, E2, …, EN} of the equivalent solid materials through the analytical relationship in 2.1 to form the initial population S = {s1, s2, …, sN}; calculate the fitness function f(x) through Steps 3.1 and 3.2;

[0051] Step 4.3: Calculate the fitness function f(x) according to 3.2 to ensure that individuals with higher fitness have a greater selection probability, and make parameter changes to some chromosomes of the individuals with larger fitness; determine the number of chromosomes c participating in crossover according to the crossover rate CROSSOVER_RATE, randomly determine c chromosomes from S1, pair them for crossover operations, and generate new chromosomes to replace the original chromosomes to obtain the population S2; determine the number of mutation times m determined by the mutation rate MUTATION_RATE, randomly determine m chromosomes from S2, perform mutation operations on them respectively, and generate new chromosomes to replace the original chromosomes to obtain the population S3; complete the random variation of the cell radius R of individual individuals in the population through crossover and mutation;

[0052] Step 4.4: Take the population S3 as the new generation population, that is, the new geometric parameters of the micro-cell, replace S with S3, add 1 to the optimization iteration number N_GENERATIONS, and continue Steps 4.2 and 4.3 to calculate the fitness until the convergence condition is met, that is, after several generations of evolutionary iteration, if the fitness meets the expected value or the number of iterations reaches the maximum value, then take the individual with the largest fitness in S, that is, the most efficient individual, as the optimal population, complete the screening of the micro-cell radius combination, and the optimization ends, that is, complete the optimization of the structural stiffness customization based on the genetic algorithm.

[0053] Beneficial effects:

[0054] 1. A method for customizing and optimizing the structural stiffness based on the genetic algorithm disclosed in the present invention optimizes complex structures based on the genetic algorithm, including the layering of the macroscopic structure and the optimization of the geometric parameters of the microscopic structure. Under the constraints of the macroscopic structure configuration and the geometric parameters of the microscopic unit cells, the geometric parameters of the microscopic unit cells filled between different parts of the macroscopic structure are optimized to achieve the stiffness matching between different unit cells, so that the stiffness of the optimized macroscopic structure reaches a preset value, realizing highly customized structural optimization and meeting the requirements of different preset optimization goals.

[0055] 2. A method for customizing and optimizing the structural stiffness based on the genetic algorithm disclosed in the present invention, during the optimization process, an interface between the finite element software and the genetic algorithm is established. The mechanical properties of the complex model are analyzed by the finite element software, and the simulation data is extracted and transmitted to the genetic algorithm for the optimization of the geometric parameters of the microscopic unit cells. By coupling the simulation software and the genetic algorithm, the collaborative design of the macro-micro structure is realized, the problem of difficult customization of the stiffness of complex three-dimensional models is solved, and the optimization efficiency is improved.

[0056] 3. A method for customizing and optimizing the structural stiffness based on the genetic algorithm disclosed in the present invention. In the genetic algorithm, an initial population of geometric parameters of the microscopic unit cells is generated. Through the mapping relationship between the geometric parameters and the Young's modulus, a corresponding finite element model of the macroscopic structure is established. In the genetic algorithm, the processes of crossover, mutation, and selection are all carried out according to specific probability functions, so as to randomly search the target space, making the optimization process better face the global situation. After multiple generations of continuous evolution, the population gradually evolves towards the direction of the optimal solution, thus significantly improving the accuracy and efficiency of the optimization of the structural parameters.

[0057] 4. A method for customizing and optimizing the structural stiffness based on the genetic algorithm disclosed in the present invention, with the help of Python as a programming tool, can make full use of the functions of Python's multi-threading and multi-processing, and is more suitable for dealing with large-scale discrete problems. Python has strong expansion ability, which can further enhance the parallel optimization ability and performance of the genetic algorithm, improve the efficiency of customizing and optimizing the structural stiffness, quickly find the optimal population, and complete the screening of the combination of the radii of the microscopic unit cells. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0059] Figure 1 It is a schematic diagram of the BCC structure disclosed in the present invention;

[0060] Figure 2 It is a flowchart of a method for customizing and optimizing the structural stiffness based on the genetic algorithm of the present invention;

[0061] Figure 3 It is a three-dimensional structure of the area to be optimized;

[0062] Figure 4 It is an iterative curve of the genetic algorithm;

[0063] Figure 5 It is a reconstructed geometric structure diagram obtained by optimization. Specific implementation manner

[0064] Next, in combination with the drawings of the present invention and specific embodiments, the technical solutions of the present invention will be clearly and completely described. The specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0065] As Figure 2 shown, a method for customizing and optimizing the structural stiffness based on the genetic algorithm disclosed in this embodiment is specifically implemented as follows:

[0066] Step 1: In this example, the BCC structure is used as the filling cell, and the geometric parameters of the cell are as Figure 1 shown. The length of the cell is L = 5 mm, and the value range of the radius R is 0.5 - 2.1 mm. The selected material is aluminum alloy, with Young's modulus Es = 71000 MPa and Poisson's ratio μ = 0.3. An analytical formula for the equivalent mechanical properties of the BCC structure is derived based on the energy method.

[0067] According to the homogenization theory, the equivalent elastic modulus of the BCC structure is derived when a force is applied in the Y direction. The following assumptions are made for the theoretical analysis model. The representative volume element does not need to consider the boundary effect; the deformation of the structure is small deformation, and the geometric shape of the structure does not change; the nodes at the intersections of the structure are all rigid.

[0068] In the actual application process, the length of the structure model is the distance between the two ends of the structure boundary, and due to the influence of the coincidence of the two rods at the node, the effective deformation length of the rod is less than the design value. When the rod is a slender rod, the coincidence effect at the rod is very small and does not need to be considered. However, when the rod is a short and thick rod, the coincidence effect becomes obvious and must be considered in the theoretical model analysis.

[0069] Considering the coincidence effect between the rods, the effective length l of the cell rods is obtained E

[0070]

[0071] where: l is the length of the cell rod, R is the cell radius, ψ is the angle between the rod radius and the connection surface; coefficient is a semi - empirical coefficient;

[0072] Under the action of external force F, the angular displacement of point A along the M1 direction is Δ 1F , under the bending moment M1 = 1, the angular displacement of point A along the M1 direction is δ 11 , so under the combined action of external force F and M1, the angular displacement Δ1 of point A along the M1 direction is:

[0073] Δ1 = δ 11 M1+Δ 1F

[0074] According to the structural symmetry, the structural angular displacement is 0, and the deformation compatibility equation is obtained:

[0075] δ 11 M1+Δ 1F = 0

[0076] Under the action of the statically determinate system, under the condition of external force F acting on point A, the bending moment M, axial force F N , and shear force Fs on the rod AB are respectively:

[0077] M(x)=Fxcosθ,

[0078] F N (x)= - Fsinθ,

[0079] F S (x)=Fcosθ

[0080] θ is the angle between the unit cell rod and the horizontal direction;

[0081] Under the action of the statically determinate system, under the action of the unit virtual bending moment M = 1 acting on point A, the bending moment axial force and shear force on the rod AB are respectively:

[0082]

[0083] According to the deformation compatibility equation, the obtained bending moment is:

[0084]

[0085] The actual force condition of rod AB is:

[0086]

[0087] F N = - Fsinθ,

[0088] F S = Fcosθ

[0089] Apply a unit force F = 1 along the Y direction at point A, and the force-bearing condition of the rod is as follows:

[0090]

[0091] Then the displacement ΔY of point A in the vertical direction is:

[0092]

[0093] Obtain:

[0094]

[0095] For the moment of inertia of a circular cross-section E S is the Young's modulus of the material, E S = 71000 MPa, μ = 0.3, the shear shape factor of the circular cross-section

[0096] The Young's modulus E of the structure in the Y direction Y is:

[0097]

[0098] where L is the cell length size.

[0099] Step 2: Import the three-dimensional model to be optimized into the finite element analysis software to calculate the structural response. In the simulation software, divide the structure into blocks, assign different equivalent solid materials to different regions, add structural boundary conditions, apply displacement loads, set the force extraction reference point, divide the mesh, set the history output and field output, and then solve for the stiffness of the macroscopic external structure according to the magnitude of the reaction force extracted under the applied displacement load.

[0100] As an optimization, the finite element analysis software selected in Step 2 is Abaqus.

[0101] Step 2.1: Import the model to be optimized into Abaqus. The division of the model to be optimized into blocks is a customized design for the macroscopic structural stiffness. The region to be optimized in this example is a three-dimensional cubic structure, and the geometric parameters are as Figure 3 shown, L 实例 = 100 mm, H 实例 = 60 mm, W 实例 = 10 mm. Divide the model to be optimized into blocks to obtain multiple modules; divide different regions according to the force-bearing conditions of the macroscopic structure, and assign the Young's modulus E of different equivalent solid materials obtained in Step 1 to different regions Y, that is, the geometric parameters between the micro-cells corresponding to each module are different; by arranging micro-cells with different geometric parameters inside the macro-structure, the stiffness of different regions of the macro-structure is changed to achieve the customized stiffness requirements of the overall macro-structure;

[0102] Step 2.2: Set boundary conditions for the macro-structure in Abaqus; couple the upper surface of the structure to the node "M_SET-1" and apply a downward displacement load to this node; fix the lower surface of the structure; mesh the macro-structure and set history output and field output to obtain a finite element analysis model.

[0103] Step 3: Combine Abaqus with the genetic algorithm to control the finite element analysis of Abaqus and optimize the design parameters through Python scripts. Establish a fitness function f(x) based on the mechanical response and optimization objective of the macro-structure obtained from the finite element analysis, and obtain the relationship between the geometric parameters of the micro-structures in different regions and the target stiffness through the fitness function f(x).

[0104] Step 3.1: Combine Abaqus with the genetic algorithm to perform finite element analysis and extract the reaction force magnitude of the finite element model in Step 2 through Python scripts;

[0105] Step 3.2: Establish a fitness function f(x) based on the reaction force magnitude pred_F obtained in 3.1 and the optimization objective target_F:

[0106] f(x) = 1 / |pred_F - target_RF|

[0107] Obtain the relationship between the geometric parameters of the micro-cells in different regions and the target reaction force through the fitness function f(x). Among them, target_F is the expected reaction force value, pred_F is the magnitude of the structural reaction force under this design variable extracted from Abaqus when a given design chromosome value is given. In the global optimization search of the genetic algorithm, it is only related to the magnitude of the fitness function, and the relationship between the geometric parameters of the micro-structures in different regions and the target stiffness is obtained through the fitness function f(x).

[0108] Step 4: Encode the radius R of the microscopic cell using real number encoding and randomly generate the initial population N. Establish a finite element analysis model for the cell radius combinations in different regions of the population to extract the mechanical response of the macroscopic structure and calculate the fitness. Determine the probability of each individual being retained based on the fitness calculation results, and then randomly vary the cell radius R of each individual in the population according to crossover and mutation to obtain a new generation of population, that is, the new microscopic cell radius. After several generations of evolutionary iteration, the optimal individual is obtained. The optimal individual is the combination of microscopic cell radii that is closest to the optimization goal, thus completing the structural customized stiffness optimization based on the genetic algorithm.

[0109] Step 4.1: Encode the radius of the microscopic cell in integer encoding to establish the initial population S; in this example, set a real number encoding DNA length DNA_SIZE = 24, crossover rate CROSSOVER_RATE = 0.8, mutation rate MUTATION_RATE = 0.005, number of iterations N_GENERATIONS = 40, and the geometric parameter constraint condition of the microscopic cell RX_BOUND = [0.5, 2.1], the target reaction force is target_F = 5x10 4 N, the cell radius design variable is X = [R1, R2, R3, R4, R5, R6], and the Young's modulus of the equivalent solid material is E = [E1, E2, E3, E4, E5, E6].

[0110] Step 4.2: The genetic algorithm randomly generates N = 100 individuals s1, s2, …, s100 in RX_BOUND, that is, the microscopic cell radii in different regions, and obtains the Young's modulus {E1, E2, …, E6} of the equivalent solid material through the analytical relationship in 2.1 to form the initial population S = {s1, s2, …, sN}; calculate the fitness function f(x) through Steps 3.1 and 3.2;

[0111] Step 4.3: Calculate the fitness function f(x) according to 3.2 to ensure that individuals with higher fitness have a greater selection probability, and change the parameters of some chromosomes of individuals with higher fitness; determine the number of chromosomes c participating in crossover according to the crossover rate CROSSOVER_RATE = 0.8, randomly determine c chromosomes from S1, pair them for crossover operation, and generate new chromosomes to replace the original chromosomes to obtain the population S2; determine the number of mutation times m determined by the mutation rate MUTATION_RATE, randomly determine m chromosomes from S2, perform mutation operations on them respectively, and generate new chromosomes to replace the original chromosomes to obtain the population S3; complete the random variation of the cell radius R of each individual in the population through crossover and mutation;

[0112] Step 4.4: Take the population S3 as the new generation of population, that is, the new microscopic cell geometric parameters, replace S with S3, increment the optimization iteration count N_GENERATIONS by 1, and continue with Steps 4.2 and 4.3 for fitness calculation until the convergence condition is met. That is, after several generations of evolutionary iteration, if the fitness meets the expected value or the iteration count reaches the maximum value, then select the individual with the highest fitness in S, that is, the most efficient individual, as the optimal population, and complete the screening of the microscopic cell radius combination. The iterative convergence graph of the optimization algorithm in this instance is as shown in Figure 4 shown. The obtained microscopic cell geometric parameters are: X = [R1, R2, R3, R4, R5, R6] = [1.9934, 1.6623, 0.5596, 0.6859, 1.5005, 0.64205], and the material properties corresponding to these geometric parameters are E = [E1, E2, E3, E4, E5, E6] = [576698.189, 204927.825, 898.614, 2286.203, 116266.718, 1683.252]. The optimal population, that is, the optimal microscopic cell radius combination, is obtained through Step 4 and is used for reconstructing the model to be optimized in Hypermesh as shown in Figure 5 shown, to establish beam structures with different radii obtained from the optimization. Then import the reconstructed structural model into Abaqus, apply a displacement load of 1 mm on the upper surface in Abaqus. Through analysis, the structural reaction force of the reconstructed model can be obtained as 5066.4 N. After verifying the geometric model and the optimized model reconstructed with the optimized geometric parameters, under the same load conditions, the reaction force error between the two is 1.29%. The optimization result and the expected optimization value target_F = 5000 N meet the preset consistency, which demonstrates the effectiveness of the structural customization stiffness optimization method based on the genetic algorithm and improves the optimization efficiency for achieving the optimization goal of meeting a specific structural stiffness value.

Claims

1. A structure customization stiffness optimization method based on genetic algorithm, characterized in that: It includes the following steps: Step 1: Based on the cell type and the periodic arrangement characteristics in space, perform homogenization calculations on the microscopic cells, establish an analytical relationship between the geometric parameters of the microscopic cells and the Young's modulus of the equivalent solid material. Through this analytical relationship, the geometric parameters of the microscopic cells can be equivalent to the Young's modulus of the solid material; Step 2: Import the three-dimensional model to be optimized into the finite element analysis software to calculate the structural response. Divide the structure in the finite element analysis software, and assign different Young's moduli of the equivalent solid materials obtained in Step 1 to different regions; Add structural boundary conditions, set the force extraction reference points, divide the mesh, set the history output and field output to obtain the finite element analysis model; Step 3: Combine Abaqus with the genetic algorithm, and use Python scripts to perform finite element analysis on the finite element model in Step 2 and extract the magnitude of the reaction force; Combine the magnitude of the reaction force with the optimization objective to establish the fitness function f(x); Through the fitness function f(x), obtain the relationship between the geometric parameters of the microscopic cells in different regions and the optimization objective; Step 4: Encode the radius R of the microscopic cells in different regions in real number coding and randomly generate the initial population S. For the combination of cell radii in different regions in the population, input the combination of cell radii into the finite element analysis model in Step 2, obtain the magnitude of the reaction force through Step 3, and calculate the fitness function f(x); Then randomly change the cell radius R of each individual in the population according to crossover and mutation to obtain a new generation of population, that is, the new microscopic cell radius; After several generations of evolutionary iteration, obtain the optimal individual, and the optimal individual is the combination of microscopic cell radii that is closest to the optimization objective, that is, complete the structural customized stiffness optimization based on the genetic algorithm.

2. The structure customization stiffness optimization method based on genetic algorithm according to claim 1, wherein: It also includes Step 5: Use the combination of microscopic cell radii that is closest to the optimization objective obtained in Step 4 to reconstruct the three-dimensional model to be optimized in Hypermesh, establish beam structures with different radii obtained by optimization, and import the reconstructed beam structure model into Abaqus for verification.

3. A structure customization stiffness optimization method based on genetic algorithm according to claim 1 or 2, characterized in that: The microscopic cell described in Step 1 is a BCC structure without transverse bars.

4. The structure customization stiffness optimization method based on genetic algorithm according to claim 3, characterized in that: The specific implementation method of Step 1 is: Considering the coincidence effect between the bars, the effective length l of the cell bars is obtained E Where: l is the length of the cell member, R is the cell radius, ψ is the angle between the member radius and the connection surface; the coefficient is a semi-empirical coefficient; Under the action of the external force F, the angular displacement of point A along the M1 direction is Δ 1F , under the bending moment of M1 = 1, the angular displacement of point A along the M1 direction is δ 11 , therefore, under the combined action of the external force F and M1, the angular displacement Δ1 of point A along the M1 direction is: Δ1 = δ 11 M1 + Δ 1F According to the structural symmetry, the angular displacement of the structure at the corner is 0, and the deformation compatibility equation is obtained: δ 11 M1 + Δ 1F = 0 Under the action of a statically determinate system, under the external force F acting on point A, the bending moment M, axial force F N , and shear force Fs on rod AB are respectively:[[]] M(x) = Fxcosθ, F N F(x) = -Fsinθ, F S F(x) = F cos θ where θ is the angle between the cell bar and the horizontal direction; Under the action of a statically determinate system, under the action of a unit virtual moment M = 1 acting at point A, the bending moment on rod AB axial force and shear force are respectively According to the deformation compatibility equation, the bending moment is obtained as: The actual force condition of bar AB is: F N = -Fsinθ, F S = F cos θ Apply a unit force F = 1 along the Y direction at point A, and the force condition of the bar is: Then the displacement ΔY of point A in the vertical direction is: It is obtained that: For the moment of inertia of a circular cross-section E S is the Young's modulus of the material, E S = 71000 MPa, μ = 0.3, circular cross-section shear shape factor The Young's modulus E of the structure in the Y direction Y is as follows: where L is the cell length size.

5. A structure customization stiffness optimization method based on genetic algorithm according to claim 1, characterized in that: The specific implementation method of Step 2 is: Step 2.1: Import the model to be optimized into Abaqus, divide the model to be optimized into multiple modules; divide different regions according to the force-bearing conditions of the macrostructure, and assign the Young's modulus E of different equivalent solid materials obtained in Step 1 to different regions, that is, the geometric parameters between the microscopic cells corresponding to each module are different; by arranging microscopic cells with different geometric parameters inside the macrostructure, change the stiffness of different regions of the macrostructure to achieve the customized stiffness requirements of the overall macrostructure; Y , that is, the geometric parameters between the microscopic cells corresponding to each module are different; by arranging microscopic cells with different geometric parameters inside the macrostructure, change the stiffness of different regions of the macrostructure to achieve the customized stiffness requirements of the overall macrostructure; Step 2.2: Set boundary conditions for the macrostructure in Abaqus; Couple the upper surface of the structure to the node "M_SET-1", and apply a downward displacement load to this node; Fix the lower surface of the structure; Divide the mesh of the macrostructure and set the history output and field output to obtain the finite element analysis model.

6. The structure customization stiffness optimization method based on genetic algorithm according to claim 1, characterized in that: The specific implementation method of Step 3 is, Step 3.1: Combine Abaqus with the genetic algorithm, and perform finite element analysis on the finite element model in Step 2 and extract the reaction force magnitude through Python scripts; Step 3.2: Establish a fitness function f(x) based on the reaction force magnitude pred_F obtained in 3.1 and the optimization target target_F: f(x) = 1 / |pred_F - target_RF| Obtain the relationship between the geometric parameters of the microscopic unit cells in different regions and the target reaction force through the fitness function f(x).

7. A structure customization stiffness optimization method based on genetic algorithm according to claim 1, characterized in that: The specific implementation method of Step Four is as follows: Step 4.1: Encode the radius of the microscopic unit cells in the form of integer encoding to establish an initial population S; set a real-number encoded DNA length DNA_SIZE, crossover rate CROSSOVER_RATE, mutation rate MUTATION_RATE, number of iterations N_GENERATIONS, and geometric parameter constraints RX_BOUND of the microscopic unit cells, optimization target target_F, the design variable of the unit cell radius is X = [R1, R2, R3, R4, R5, R6], and the Young's modulus of the equivalent solid material is E = [E1, E2, E3, E4, E5, E6]; Step 4.2: The genetic algorithm randomly generates N individuals s1, s2,..., sN in RX_BOUND, that is, the radii of the microscopic unit cells in different regions, and obtains the Young's modulus {E1, E2,..., EN} of the equivalent solid material through the analytical relationship in 2.1 to form the initial population S = {s1, s2,..., sN}; calculate the fitness function f(x) through Steps 3.1 and 3.2; Step 4.3: Calculate the fitness function f(x) according to 3.2 to ensure that individuals with higher fitness have a greater probability of being selected, and make parameter changes to some chromosomes of individuals with higher fitness; determine the number of chromosomes c participating in crossover according to the crossover rate CROSSOVER_RATE, randomly determine c chromosomes from S1, pair them for crossover operations, and generate new chromosomes to replace the original chromosomes to obtain the population S2; determine the number of mutation times m according to the mutation rate MUTATION_RATE, randomly determine m chromosomes from S2, perform mutation operations on them respectively, and generate new chromosomes to replace the original chromosomes to obtain the population S3; complete the random variation of the unit cell radius R of individual individuals in the population through crossover and mutation; Step 4.4: Take the population S3 as the new generation population, that is, the new geometric parameters of the microscopic unit cells, replace S with S3, add 1 to the optimization iteration number N_GENERATIONS, and continue Steps 4.2 and 4.3 to calculate the fitness until the convergence condition is met, that is, after several generations of evolutionary iterations, if the fitness meets the expected value or the number of iterations reaches the maximum value, then take the individual with the highest fitness in S, that is, the most efficient individual, as the optimal population, complete the screening of the combination of microscopic unit cell radii, and the optimization ends, that is, complete the optimization of the structural stiffness customization based on the genetic algorithm.

8. A structure customization stiffness optimization method based on genetic algorithm according to claim 4, characterized in that: ＝0.6。

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