A Multi-objective Optimization Method for the Low-velocity Impact Performance of Hybrid Composites

Abstract

The present invention discloses a multi-objective optimization method for the low-velocity impact performance of hybrid composite materials, including: establishing a damage model of hybrid fiber composite materials; constructing a laminate structure sample with the ply materials and ply angles of each layer in the laminate as design variables to obtain a hybrid fiber laminate structure sample library; determining the maximum impact force, maximum displacement and energy absorption of each sample in the sample library according to the damage model; extracting multiple samples from the sample library, and constructing a relationship model between ply materials, ply angles and maximum impact force, maximum displacement, energy absorption according to the extracted samples; determining the optimization objectives and optimization constraint conditions of the laminate structure; solving the laminate structure optimization problem according to the relationship model, the optimization objectives and the optimization constraint conditions to obtain an optimal hybrid fiber laminate structure.

Description

Technical Field

[0001] The present invention belongs to the technical field of hybrid composite materials, and particularly relates to a multi-objective optimization method for the low-velocity impact performance of hybrid composite materials. Background Art

[0002] Hybrid fiber composite materials combine the characteristics of multiple fibers, can achieve a balance among various mechanical properties. In addition, the cost of hybrid fiber composite materials is often lower, so they have been widely used in various fields including the automotive industry. There are many classification methods for hybrid fiber composite materials, among which the manufacturing method is considered the most important classification criterion. According to the arrangement of the constituent materials, hybrid composite materials can be divided into the following three categories: (a) interlayer mixing, (b) woven hybridization, (c) fiber bundle hybridization.

[0003] Automobile lightweighting can reduce emissions and energy consumption, and becomes increasingly important today when environmental pollution and energy shortage are gradually intensifying. Using fiber composite materials is an effective lightweighting method. As a typical lightweight material, carbon fiber has a high cost, strong brittleness and is easy to break, which is likely to cause catastrophic failure when used in automobiles. Basalt fiber has stronger toughness and lower price compared with carbon fiber. Combining the two fibers with the same matrix can obtain basalt-carbon fiber interlayer hybrid composite materials. Hybrid composite materials can combine the mechanical properties of the two fibers and reduce costs. When composite materials are used, they usually adopt the form of laminates. Therefore, it is necessary to explore the optimal structure of basalt-carbon fiber hybrid laminates under low-velocity impact conditions. Summary of the Invention

[0004] The present invention designs and develops a multi-objective optimization method for the low-velocity impact performance of hybrid composite materials. The purpose of the present invention is to use the peak force and maximum displacement under low-velocity impact loads as optimization objectives, and weight and energy absorption as constraints, so as to obtain the optimal structure of the interlayer hybrid laminate.

[0005] Another purpose of the present invention is to use the improved NSGA2 algorithm to perform multi-objective optimization on the ply materials and ply angles of the laminate, which can enhance the global search ability and convergence speed of the algorithm, so as to ensure the excellent performance of the obtained interlayer hybrid laminate structure and improve the efficiency of obtaining the optimal structure.

[0006] The technical solution provided by the present invention is as follows:

[0007] A multi-objective optimization method for the low-velocity impact performance of hybrid composite materials, comprising the following steps:

[0008] Establish a damage model of hybrid fiber composite materials;

[0009] Taking the ply material and ply angle of each layer in the laminate as design variables, a laminate structure sample is constructed to obtain a hybrid fiber laminate structure sample library;

[0010] According to the damage model, determine the maximum impact force, maximum displacement, and energy absorption of each sample in the sample library;

[0011] Extract multiple samples from the sample library, and construct a relationship model between the ply material, ply angle, maximum impact force, maximum displacement, and energy absorption based on the extracted samples;

[0012] Determine that the optimization objective and optimization constraint conditions of the laminate structure are respectively:

[0013]

[0014] Where x represents the laminate structure; f D (x) is the laminate displacement function, f F (x) is the impact force function, f E (x) is the energy absorption function, f M (x) is the mass function;

[0015] Solve the laminate structure optimization problem according to the relationship model, the optimization objective, and the optimization constraint conditions to obtain the optimal hybrid fiber laminate structure.

[0016] Preferably, the ply material is carbon fiber or basalt fiber, and the ply angle is 0°, 45°, 90°, or -45°.

[0017] Preferably, the Latin hypercube sampling method is used to extract multiple samples from the sample library, and the kriging approximation model toolbox is used to construct a relationship model between the ply material, ply angle, maximum impact force, maximum displacement, and energy absorption.

[0018] Preferably, the number of samples extracted from the sample library using the Latin hypercube sampling method is at least 200.

[0019] Preferably, the multi-objective optimization method for the low-velocity impact performance of the hybrid composite material further includes:

[0020] Using the coefficient of determination R 2 Evaluate the constructed relationship model, and the constructed relationship model satisfies R 2 Greater than 0.9.

[0021] Preferably, solving the laminate structure optimization problem includes the following steps:

[0022] Step 1: Randomly generate a parent population and calculate the fitness t of each individual in the parent population;

[0023]

[0024] Among them, each laminate structure corresponds to an individual, f i (x) is the objective function value of the individual, g j (x) is the penalty value for individuals violating optimization constraints;

[0025] Step 2: Select K individuals with the highest fitness, and perform crossover and mutation operations on the selected individuals in turn to generate the offspring population;

[0026] Step 3: After merging the offspring population with the parent population, non-dominated sorting is performed from best to worst according to the objective function values ​​of the individuals, and individuals of the same non-dominated level are arranged in descending order according to the crowding distance; multiple individuals with the highest sorting are selected as the new parent population;

[0027] Step 4: Randomly select an individual from the individuals with the highest non-dominated level in the new parent population as the global optimal individual, and initialize the i-th individual in the new parent population as the historical optimal individual;

[0028] Iterate steps 2 to 4 until the maximum number of iterations N is reached. max , we get the Pareto solution set;

[0029] Among them, when the number of iterations N≤N max / 2, the variation formula is:

[0030]

[0031] In the formula, x max 、x min is the boundary value of the laminate structure, δ is the coefficient of variation, η is 20, and r is a random number;

[0032] When the number of iterations N>N max / 2, the variation formula is:

[0033]

[0034] Where x_gbest N is the global optimal individual in the parent population in the Nth iteration, is the historical optimal individual in the Nth iteration, c1 is the individual learning weight, c2 is the population learning weight, r1 and r2 are random numbers;

[0035] Step 5: Select the optimal solution from the Pareto solution set;

[0036] Among them, the laminate structure corresponding to the optimal solution is the optimal mixed fiber laminate structure.

[0037] Preferably, in the third step, the crowding distance is calculated by the following formula:

[0038]

[0039] In the formula, n di is the crowding distance of individual i, f j (i + 1) and f j (i - 1) are respectively the j-th objective function values of the two individuals adjacent to individual i, is the maximum value of the j-th objective function in the population, is the minimum value of the j-th objective function in the population.

[0040] Preferably, in the fifth step, the optimal solution is selected from the Pareto solution set by the method of grey relational analysis, including:

[0041] Normalize the objective function values of the individuals in the Pareto solution set:

[0042]

[0043] In the formula, x i (k) represents the k-th objective function value of the i-th individual in the Pareto solution set, maxx i (k) and minx i (k) respectively represent the maximum and minimum values of the k-th objective function value of the i-th individual in the Pareto solution set;

[0044] Take the vector composed of the minimum impact force and the minimum displacement in the Pareto solution set as the ideal solution, and calculate the correlation coefficient between each individual in the solution set and the ideal solution:

[0045]

[0046] In the formula, Δ i (k) is the difference between the k-th objective function value of the i-th individual in the Pareto solution set and the k-th objective function of the ideal solution, min i min k Δ i (k) and max i max k Δ i (k) respectively represent the minimum and maximum values of the difference between the k-th objective function value of the i-th individual in the Pareto solution set and the k-th objective function of the ideal solution, and δ is the identification coefficient;

[0047] Take the individual with the largest correlation coefficient with the ideal solution as the optimal solution.

[0048] The beneficial effects of the present invention are:

[0049] The multi-objective optimization method for the low-velocity impact performance of the hybrid composite material provided by the present invention takes the peak force and the maximum displacement under the low-velocity impact load as the optimization objectives, and the weight and the energy absorption as the constraints, and can obtain the optimal structure of the interlayer hybrid laminate.

[0050] The present invention uses the improved NSGA2 algorithm to perform multi-objective optimization on the ply materials and ply angles of the laminate, which can enhance the global search ability and the convergence speed of the algorithm, thereby ensuring the excellent performance of the obtained interlayer hybrid laminate structure and improving the efficiency of obtaining the optimal structure. Brief Description of the Drawings

[0051] Figure 1 It is a schematic diagram of the bilinear progressive degradation model described in the present invention.

[0052] Figure 2 It is a flowchart of the ABAQUS three-dimensional progressive damage subroutine described in the present invention.

[0053] Figure 3 It is a schematic diagram of the ply of the hybrid fiber composite material described in the present invention.

[0054] Figures 4a - 4c It is a graph of the prediction accuracy of the relationship model described in the present invention.

[0055] Figure 5 It is a flowchart of the improved NSGA2 described in the present invention.

[0056] Figure 6 It is a schematic diagram of the Pareto solution set obtained by optimization in the embodiment of the present invention.

[0057] Figure 7 It is the simulated contact force-time curve of the optimal structure obtained in the embodiment of the present invention.

[0058] Figure 8 It is the simulated contact force-displacement curve of the optimal structure obtained in the embodiment of the present invention. Detailed Embodiments

[0059] The following further describes the present invention in detail with reference to the drawings, so that those skilled in the art can implement it according to the description in the specification.

[0060] As Figure 1 shown, the present invention provides a multi-objective optimization method for the low-velocity impact performance of a hybrid composite material, and the specific implementation process is as follows.

[0061] 1. Establish a damage model for the hybrid fiber composite material.

[0062] First, an in-plane damage model is established. The establishment of the in-plane damage model of the composite material is based on the three-dimensional constitutive model of the composite material, as shown in the following formula (1), where σ is the stress, ε is the strain, E is the Young's modulus, v is the Poisson's ratio, G is the shear modulus, and the subscripts 1, 2, and 3 represent the fiber direction, the in-plane direction perpendicular to the fiber, and the out-of-plane direction perpendicular to the fiber.

[0063]

[0064]

[0065] According to the theory of continuum damage mechanics, the in-plane failure of the composite material is due to the gradual reduction of the material stiffness caused by fiber fracture, matrix crack propagation, etc., until overall failure. Therefore, simulating the in-plane damage requires simulating two parts: damage initiation and damage evolution of the material.

[0066] The maximum strain criterion is selected to judge fiber failure, and the three-dimensional Hashin criterion is selected to judge matrix failure. The specific expressions are as follows:

[0067] Fiber tension (ε 11 ≥0):

[0068]

[0069] Fiber compression (ε 11 ≤0):

[0070]

[0071] Matrix tension (ε 22 +ε 33 ≥0):

[0072]

[0073] Matrix compression (ε 22 +ε 33 ≤0):

[0074]

[0075] Among them, are the initial damage variables characterizing fiber tension and compression, matrix tension and compression. X' t , X' c , Y' t , Y' c , S' are the equivalent strength parameters calculated from the material strength limit and the stiffness matrix coefficients, and their calculation formula is as (6).

[0076]

[0077] When the damage initial variable reaches 1, the material begins to be damaged.

[0078] The bilinear progressive degradation method based on the fracture toughness of the material is adopted to simulate the stiffness degradation process of the material, and the degree of stiffness degradation is represented by the damage state variable d ij . As Figure 1 shown, ε0 and σ0 are respectively the initial damage strain and equivalent strength when reaching 1, and ε f is the strain when the material completely fails. The area of the constitutive triangle formed by ε f and σ0 is the fracture toughness G ij of the material. It can be known from Figure 1 that the complete failure strain ε f can be calculated by the following formula (7). L c is the characteristic length of the element. For solid elements, the characteristic length is the cube root of the element volume.

[0079]

[0080] The damage state variable d ij of the composite material is calculated as follows. d ft , d fc , d m are the damage state variables of fiber tension, fiber compression, matrix tension, and matrix compression respectively.

[0081]

[0082] After obtaining the damage state variable, the stiffness matrix of the composite material is linearly reduced, and the stiffness degradation matrix is as follows:

[0083]

[0084] d f = 1 - (1 - d ft )(1 - d fc )d m = 1 - (1 - d mt )(1 - d mc )d s = 1 - (1 - d m )(1 - d f )

[0085] In ABAQUS / Explicit, if you want to introduce the above material damage scheme, you need to write a VUMAT user subroutine. ABAQUS / Explicit is an explicit solver. The main principle of the VUMAT subroutine is to call the solution variables of the previous increment step from the ABAQUS / Explicit main program, such as stress and strain, user-defined state variables, and combine them with the strain increment of the current increment step and the variable values involved in other damage criteria. After calculation by the subroutine, it is returned to the ABAQUS / Explicit main program to update the stress and state variables of the current increment step as the basis for the next increment step. This cycle continues until the calculation is completed. Based on the above theory, a three-dimensional composite progressive damage subroutine was written using Fortran language and combined with ABAQUS for simulation. The subroutine flow chart is as Figure 2 shown.

[0086] Then, an interlaminar damage model was established. The delamination damage of the composite material was simulated using the cohesive element built into ABAQUS. The cohesive element also adopted a bilinear constitutive model, as shown in Equation (10). Here, K is the stiffness coefficient of the cohesive element.

[0087]

[0088] The quadratic stress criterion was used to define the damage initiation of the cohesive element, as shown in Equation (11) below. Here, N, S, and T are the interlaminar strength values when the laminate undergoes pure mode I opening, mode II slip, and mode III tearing.

[0089]

[0090] The damage evolution criterion of the cohesive element adopted the energy-based mixed-mode B-K criterion, and the expression was as shown in Equation (12):

[0091]

[0092] Among them, G c is the fracture toughness under the mixed mode, G s , G t , G n are the energy release rates when the cohesive element undergoes three failure modes, is the critical strain energy release rate of the normal and tangential directions, and η is a material parameter.

[0093] The maximum impact force (maximum contact force), maximum displacement, and energy absorption of the laminate structure were obtained through the damage model.

[0094] II. Establish a structural optimization design scheme

[0095] The hybrid fiber composite laminate uses a symmetric layup, and four sub-layers are studied as a whole. The layup schematic diagram is as shown in Figure 3 Figure 2s Take the layup structure [CCBB] as an example, where C is carbon fiber and B is basalt fiber. Starting from the laminate surface, four layers are laid in the order of C, C, B, B, and after repeating the laying twice, symmetric layup is carried out.

[0096] Using the above layup form, the layup material and layup angle of each sub-layer are used as design variables, and real number coding is used for optimization at the same time. There are two layup materials, carbon fiber and basalt fiber. Four layup angles, 0°, 45°, 90°, and -45°, are used. Real numbers 1-4 represent carbon fiber with layup angles of 0°, 45°, -45°, and 90° respectively, and 5-8 represent basalt fiber with layup angles of 0°, 45°, -45°, and 90°. Their corresponding relationships are shown in Table 1.

[0097] Table 1 Schematic diagram of layup coding

[0098]

[0099] Take the energy absorption and weight of the laminate as constraints in the optimization process. It is stipulated that there is at least one layer of carbon fiber in the large layer composed of four layers as shown in Figure 3 Figure. The constraint value of weight is set to 109.2 g, and the constraint value of energy absorption is set to 8.5 J.

[0100] Take the layup material and layup angle as optimization variables.

[0101] Take the peak force and maximum displacement under 20 J impact energy as optimization objectives.

[0102] Establish an optimization mathematical expression

[0103]

[0104] Among them, x is the design variable, that is, the layup form of each layer, f D (x) is the laminate displacement function, f F (x) is the impact force function, f E (x) is the energy absorption function, f M (x) is the mass function.

[0105] III. Sample the original variable space:

[0106] 200 groups of sample points were extracted by the optimal Latin hypercube sampling method and brought into the low-velocity impact finite element model for simulation. Some of the obtained responses are shown in Table 2, where the real numbers 1 - 4 in the ply code represent carbon fibers with ply angles of 0°, 45°, -45°, and 90°, and 5 - 8 represent basalt fibers with ply angles of 0°, 45°, -45°, and 90°.

[0107] Table 2 Optimal Latin hypercube experimental design table

[0108]

[0109]

[0110] Continued Table 2

[0111]

[0112] IV. The approximation models for the maximum displacement, peak force, and energy absorption were constructed using the kriging approximation model toolbox in MATLAB.

[0113] V. Ten groups of sample points were selected to evaluate the accuracy of the approximation model. The evaluation used the coefficient of determination method (R 2 ), and its calculation formula is shown in Equation (14), where y and are the true response and predicted value of the sample point, and is the expected value of the true response of the sample point:

[0114]

[0115] R 2 The closer it is to 1, the higher the accuracy of the approximation model. For most engineering problems, it is required that R 2 is greater than 0.9. The fitting accuracies of the approximation models for the maximum displacement, impact force, and energy absorption are as shown in Figures 4a - 4c , and their R 2 values are 0.912, 0.908, and 0.911 respectively. It can be seen that the accuracy of the approximation model can meet the requirements.

[0116] VI. Since the optimization design variables are discrete variables, the improved NSGA2 algorithm was used to solve the optimization problem. As shown in Figure 5 , the improved NSGA2 algorithm uses the NSGA2 algorithm as the basic framework and divides the optimization process into two parts according to the set population iteration times N max . When the iteration times N ≤ N max / 2, the global exploration of the design variables is carried out using the evolutionary method of NSGA2. When the iteration times N > N maxAfter / 2, introduce the population update method of the particle swarm algorithm into the NSGA2 algorithm and evolve in the direction of the optimal individual.

[0117] 1. Generate the parent population:

[0118] Initialize the population according to the set population size, and calculate the fitness value t of each individual according to the following formula, where f i (x) is the objective function value of the individual, that is, the impact force and displacement value of the laminated plate (different i values represent different objective functions), and g j (x) is the penalty value for the individual violating the constraint, that is, the difference between the energy absorption, weight of the laminated plate and the set limit (different j values represent different constraint conditions). The population at this time is the parent population.

[0119]

[0120] 2. Select individuals using the random tournament method, that is, sort the fitness of all individuals and select the K individuals with the highest fitness to enter the next generation population, where K is a fixed value.

[0121] 3. Perform crossover operations on the selected individuals. The formula is shown in (16), where p1 and p2 are parent individuals, c1 and c2 are offspring individuals, β is the propagation factor, which can be determined by formula (17), r is a random number, and ο is 20.

[0122]

[0123]

[0124] 4. To increase the diversity of individuals, perform polynomial mutation operations on the individuals. The formula is as follows (18). Among them, x max , x min are the boundary values of the variable (laminated plate structure) encoding, x max = [8, 8, 8, 8], x min = [1, 1, 1, 1], δ is the mutation coefficient, and η is 20:

[0125]

[0126] 5. Merge the parent and offspring populations and perform non - dominated sorting. When all the objective function values of a design variable x1 are not worse than those of x2, it is said that x1 has a dominance relationship with x2.

[0127] First, compare the dominance relationship between each individual and all other individuals. If there exists an individual x that is not dominated by any other individual, mark it as a non-dominated individual, and its non-dominance level is 1. After traversing all individuals, ignore the individuals with a non-dominance level of 1, compare the dominance relationship among the remaining individuals, and record the non-dominated individuals in this round as level 2, and so on, until all individuals in the population are assigned non-dominance levels.

[0128] 6. Sort the individuals in the population according to the magnitude of each objective function in turn, and calculate the crowding degree of the individuals. The calculation formula is shown in (19), where n di is the crowding distance of the individual ranked at the i-th position, is the maximum value of the j-th objective function in the population, is the minimum value of the j-th objective function in the population.

[0129]

[0130] 7. Generate a new parental population from high to low according to the non-dominance levels of the individuals. If the individuals at a certain non-dominance level cannot all be placed in the new population, sort the individuals at this non-dominance level according to the crowding degree, and select the individuals with a higher crowding degree to be placed in the new population.

[0131] 8. After generating the new parental population, introduce the concepts of the global best position and the individual best position in the multi-objective particle swarm algorithm. Randomly select an individual from the individuals with the highest non-dominance level in the new population as the global best individual, initialize the i-th individual in the new population as the historical best individual, and record its fitness. Compare and update the historical best individual in the next iteration.

[0132] 9. Perform selection, crossover, and mutation operations on the new parental population again to generate the offspring population. Different from initializing the parental population, when the iteration number N < N / 2, the mutation still proceeds according to formula (18). When the iteration number N > N / 2, the mutation proceeds according to formula (20), where x_gbest N is the global best individual in the parental population in the N-th iteration, is the historical best individual at the i-th position in the N-th iteration, w is the inertia weight, c1 is the individual learning weight, c2 is the population learning weight, and r1, r2 are random numbers.

[0133]

[0134] 10. Repeat the operations of merging the parent and offspring populations and generating a new population until the maximum iteration number is reached. The Pareto solution set obtained by using the improved NSGA2 optimization is as Figure 6 shown.

[0135] The NSGA2 algorithm uses a random mutation method and has strong global search ability, but its convergence speed is slow. Compared with NSGA2, the particle swarm algorithm adjusts the evolution direction of the population according to historical information during evolution and has a faster convergence speed. The present invention takes the NSGA2 algorithm as the basic framework and divides the optimization process into two parts before and after according to the set population iteration number N. When the iteration number N < N / 2, the evolution method of NSGA2 is used to explore the global design variables. After the iteration number N > N / 2, the population update method of the particle swarm algorithm is introduced into the NSGA2 algorithm and evolved in the direction of the optimal individual. The improved NSGA2 algorithm combines the advantages of the NSGA2 algorithm and the particle swarm algorithm, has strong global search ability and a fast convergence speed at the same time.

[0136] 11. Determine a relatively optimal solution through the method of grey relational analysis.

[0137] When performing grey relational analysis, it is first necessary to normalize the data to unify the data into the same interval, as shown in formula (21).

[0138]

[0139] Among them, i represents the i-th individual in the Pareto solution set, and k represents the k-th objective function of the i-th individual.

[0140] Take the vector composed of the minimum impact force and the minimum displacement in the Pareto solution set as the ideal solution, and calculate the correlation coefficient between each point in the solution set and the ideal point, as shown in formula (22).

[0141]

[0142] Among them, Δ i (k) is the difference between the k-th objective function of the i-th point in the solution set and the k-th objective function of the ideal point, and δ is the identification coefficient, taking 0.5. After obtaining the correlation coefficient, the correlation degree can be calculated by formula (23).

[0143]

[0144] Take the solution with the largest correlation degree as the optimal solution.

[0145] In this embodiment, the Latin hypercube sampling data shown in Table 2 is optimized, and the finally obtained optimal solution is [4, 7, 5, 3], that is, the ply structure is [CBBC] 2s , and the ply angles are [90 / 45 / 0 / -45] 2s . Perform impact simulation on the optimized laminate, and the simulation contact force curve and simulation displacement curve are as Figure 7 、 Figure 8As shown, the comparison between the simulation response and the predicted response is shown in Table 3. The optimization results correspond well with the simulation results, indicating that the optimization algorithm adopted in the present invention has good accuracy.

[0146] Table 3 Comparison between the predicted value and the simulation value of the optimization result

[0147]

[0148] Apply the optimization result to the front anti-collision beam of the car. Conduct a collision simulation on the front anti-collision beam assembly according to the national standard and compare it with the steel front anti-collision beam. The results are shown in Table 4. The energy absorption, collision force and other indicators of the basalt-carbon fiber hybrid composite anti-collision beam are better than those of the steel anti-collision beam during low-speed collision, and the mass is reduced by 38.5% compared with the steel anti-collision beam.

[0149] Table 4 Comparison between the hybrid material front anti-collision beam and the steel front anti-collision beam

[0150]

[0151] Although the embodiments of the present invention have been disclosed as above, it is not limited to the applications listed in the specification and the embodiments. It can be fully applied to various fields suitable for the present invention. For those familiar with the field, additional modifications can be easily achieved. Therefore, without departing from the general concept defined by the claims and the equivalent scope, the present invention is not limited to the specific details and the examples shown and described here.

Claims

1. A multi-objective optimization method for the low-velocity impact performance of hybrid composite materials, characterized in that, The steps include: Establish a damage model for hybrid fiber composites; The laminate structure samples are constructed by taking the ply material and ply angle of each layer in the laminate as design variables, and a hybrid fiber laminate structure sample library is obtained; Determine the maximum impact force, maximum displacement and absorbed energy of each sample in the sample library according to the damage model; Extracting a plurality of samples from the sample library, and constructing a relationship model between ply material, ply angle, maximum impact force, maximum displacement, and energy absorption according to the extracted samples; The optimization objectives and optimization constraints of the laminate structure are determined as follows: Where x represents the laminated plate structure; f D (x) is the displacement function of the laminated plate, f F (x) is the impact force function, f E (x) is the energy absorption function, f M (x) is the mass function; The laminate structure optimization problem is solved according to the relationship model, the optimization target and the optimization constraint conditions to obtain an optimal hybrid fiber laminate structure.

2. The multi-objective optimization method for the low-speed impact performance of the hybrid composite material according to claim 1, wherein The ply material is carbon fiber or basalt fiber, and the ply angle is 0°, 45°, 90° or -45°.

3. The multi-objective optimization method for the low-velocity impact performance of the hybrid composite material according to claim 2, characterized in that A Latin hypercube sampling method is used to extract multiple samples from the sample library, and a kriging approximation model toolkit is used to construct a relationship model between ply material, ply angle and maximum impact force, maximum displacement, and energy absorption.

4. The multi-objective optimization method for the low-velocity impact performance of the hybrid composite material according to claim 3, characterized in that The number of samples drawn from the sample library using the Latin hypercube sampling method is at least 200.

5. The multi-objective optimization method for the low-velocity impact performance of the hybrid composite material according to claim 3 or 4, characterized in that Also includes: Use the coefficient of determination R 2 to evaluate the constructed relationship model, and the constructed relationship model satisfies R 2 greater than 0.

9.

6. The multi-objective optimization method for the low-velocity impact performance of the hybrid composite material according to claim 5, characterized in that Solving the laminate structure optimization problem includes the following steps: Step 1: randomly generate a parent population, and calculate the fitness t of each individual in the parent population; Among them, each laminate structure corresponds to an individual, and f i (x) is the objective function value of the individual, and g j (x) is the penalty value for the individual violating the optimization constraints; Step 2: Select K individuals with the highest fitness, and perform crossover and mutation operations on the selected individuals in turn to generate the offspring population; Step 3: After merging the offspring population with the parent population, non-dominated sorting is performed from best to worst according to the objective function values ​​of the individuals, and individuals of the same non-dominated level are arranged in descending order according to the crowding distance; multiple individuals with the highest sorting are selected as the new parent population; Step 4: Randomly select an individual from the individuals with the highest non-dominated level in the new parent population as the global optimal individual, and initialize the i-th individual in the new parent population as the historical optimal individual; Iteratively perform Step 2 to Step 4 until the maximum number of iterations N is reached max , and obtain the Pareto solution set; Among them, when the number of iterations N ≤ N max / 2, the mutation formula is: where x max , x min are the boundary values of the laminated plate structure, δ is the coefficient of variation, η is 20, and r is a random number; When the number of iterations N > N max / 2, the mutation formula is: where \(x_{gbest}\) N is the global optimal individual in the parental population in the \(N\)th iteration, is the historical optimal individual in the \(N\)th iteration, \(c1\) is the individual learning weight, \(c2\) is the population learning weight, and \(r1\), \(r2\) are random numbers; Step 5: Select the optimal solution from the Pareto solution set; Among them, the laminate structure corresponding to the optimal solution is the optimal mixed fiber laminate structure.

7. The multi-objective optimization method for the low-velocity impact performance of the hybrid composite material according to claim 6, characterized in that In step 3, the crowding distance is calculated by the following formula: where n di is the crowding distance of individual i, f j (i + 1) and f j (i - 1) are respectively the j-th objective function values of two individuals adjacent to individual i, is the maximum value of the j-th objective function in the population, is the minimum value of the j-th objective function in the population.

8. The multi-objective optimization method for the low-velocity impact performance of the hybrid composite material according to claim 7, characterized in that In the step 5, the optimal solution is selected from the Pareto solution set by using the grey correlation analysis method, including: Normalize the objective function values ​​of individuals in the Pareto solution set: where x i (k) represents the k-th objective function value of the i-th individual in the Pareto solution set, maxx i (k) and minx i (k) represent the maximum and minimum values of the k-th objective function value of the i-th individual in the Pareto solution set, respectively; The vector consisting of the minimum impact force and the minimum displacement in the Pareto solution set is taken as the ideal solution, and the correlation coefficient between each individual in the solution set and the ideal solution is calculated: where, Δ i (k) is the difference between the k-th objective function value of the i-th individual in the Pareto solution set and the k-th objective function of the ideal solution, min i min k Δ i (k) and max i max k Δ i (k) respectively represent the minimum and maximum values of the difference between the k-th objective function value of the i-th individual in the Pareto solution set and the k-th objective function of the ideal solution, and δ is the recognition coefficient; The individual with the largest correlation coefficient with the ideal solution is considered the optimal solution.

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