Structural lightweight optimization method based on multi-objective genetic algorithm

Abstract

The invention discloses a structure lightweight optimization method based on a multi-objective genetic algorithm, and belongs to the field of structure optimization. The method comprises the steps of layering of a macrostructure and optimization of geometric parameters of the microstructure. Under the constraint of the macroscopic structure configuration and the geometric parameters of the microcosmic cell elements, the geometric parameters of the microcosmic cell elements filled among different parts of the macroscopic structure are obtained through optimization, the matching of the rigidity and the relative density among different cell elements is realized, and the optimal balance between the rigidity and the quality of the optimized macroscopic structure is realized. In the optimization process, an interface of simulation software and a multi-target 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 multi-target genetic algorithm, and optimization of microscopic cell geometric parameters is carried out. Through coupling finite element simulation software and a multi-target genetic algorithm, collaborative optimization of macro and microstructure is realized, the problem that high-rigidity lightweight of a complex three-dimensional model is difficult is effectively solved, and the high-rigidity lightweight efficiency of a complex structure is improved.

Description

Technical Field

[0001] The present invention belongs to the field of structural optimization and relates to an optimization method for structural lightweighting based on a multi-objective genetic algorithm. Background Art

[0002] In actual engineering, the design of three-dimensional structures is very complex, involving a large number of geometric parameters and material distribution variables. Therefore, it is necessary to perform parametric modeling on the geometric shape for optimization design. However, the complex geometric shape and parametric modeling increase the design complexity and computational cost. The optimization problem is usually highly non-linear and non-convex, resulting in the optimization process being prone to falling into local optima and difficult to find the global optimal solution. In addition, searching for the best solution requires operations in a high-dimensional space, increasing the computational complexity and the difficulty of the optimization algorithm. Traditional optimization methods are difficult to effectively handle such a large design space. The optimization of three-dimensional structures also involves multiple conflicting objectives, and improving one objective usually comes at the expense of the deterioration of other objectives. Therefore, the optimization design not only needs to meet the design objectives and constraints, but also must consider the engineering practicability and manufacturability of the structure. Summary of the Invention

[0003] The main objective of the present invention is to provide an optimization method for structural lightweighting based on a multi-objective genetic algorithm, which optimizes complex three-dimensional structures based on the multi-objective genetic algorithm, including the layering of the macrostructure and the optimization of the geometric parameters of the microstructure. Under the constraints of the macrostructure configuration and the geometric parameters of the microcells, the geometric parameters of the microcells filled between different parts of the macrostructure are optimized to achieve the matching of stiffness and relative density between different cells, so as to achieve the best balance between the stiffness and mass of the optimized macrostructure. During the optimization process, an interface between the simulation software and the multi-objective genetic algorithm is established. The mechanical properties of the complex model are analyzed by the simulation software, and the simulation data is extracted and transmitted to the multi-objective genetic algorithm for the optimization of the geometric parameters of the microcells. By coupling the finite element simulation software and the multi-objective genetic algorithm, the collaborative optimization of the macro-micro structure is realized, effectively solving the problem of difficult high-stiffness lightweighting of complex three-dimensional models and improving the efficiency of high-stiffness lightweighting of complex structures.

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

[0005] An optimization method for structural lightweighting based on a multi-objective genetic algorithm discloses that a complex three-dimensional model is imported into finite element analysis software, and the macroscopic structure is split into a skin and an internal structure. Different modules are divided according to the force on the macroscopic structure in the finite element analysis software, and a mapping relationship between the geometric parameters of the microscopic cell and the Young's modulus is established through the elastic theory. With the limitations of the macroscopic structure configuration and the geometric parameters of the microscopic cell in the multi-objective genetic algorithm, an optimization objective function of stiffness and mass is established. Through the domination and non-domination relationship, the relationship between the optimized cell geometric parameters and the macroscopic structure stiffness is established. An interface between the finite element analysis software and the multi-objective genetic 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 multi-objective genetic algorithm. Microscopic structures with different geometric parameters are filled between different macroscopic modules to achieve the matching of stiffness and relative density between different modules, and the best balance relationship between stiffness and mass is achieved. In the multi-objective genetic algorithm, with stiffness and mass as the objective functions, an initial population of microscopic cell geometric parameters is generated. Through the mapping relationship between the geometric parameters and the Young's modulus, the corresponding finite element model of the macroscopic structure is established, and the stiffness of the whole macroscopic structure is calculated in the simulation software, and the calculated stiffness value is transmitted to the multi-objective genetic algorithm as the first optimization objective of the multi-objective genetic algorithm. The mass of the macroscopic structure under the initial population is calculated as the second optimization objective of the multi-objective genetic algorithm. The population is quickly non-dominated sorted, and appropriate parent individuals are selected based on the sorting result and the crowding distance. Through the crossover and mutation operations of the multi-objective genetic algorithm, an offspring population is generated. The current population and the offspring population are merged to form a new population, and non-dominated sorting and crowding distance calculation are performed again. In each round of iteration, by combining the finite element analysis and the multi-objective genetic algorithm, the population is continuously optimized, gradually approaching or reaching the optimization of multiple optimization objectives. The finally obtained Pareto optimal solutions are non-dominant to each other during the optimization process and present the best balance relationship between stiffness and mass, that is, structural lightweighting is realized based on the multi-objective genetic algorithm.

[0006] An optimization method for structural lightweighting based on a multi-objective genetic algorithm disclosed by the present invention includes the following steps:

[0007] Step 1: The equivalent mechanical properties of the 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 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 cell and the equivalent mechanical properties of the macroscopic structure, and the mechanical properties of the material of the equivalent entity are obtained. Using the equivalent parameters of the lattice structure as the material input, the mechanical properties of the external structure are calculated and analyzed at the macroscopic scale, and by adjusting the geometric parameters of the cell, the best balance relationship between stiffness and mass is achieved.

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

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

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

[0011]

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

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

[0014] Δ1 = δ 11 M1 + Δ 1F

[0015] According to the structural symmetry, the structural rotational 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 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 rod 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 rod AB are respectively:

[0023]

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

[0025]

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

[0027]

[0028] F N =-Fsinθ,

[0029] F S =Fcosθ

[0030] When a unit force F = 1 is applied along the Y direction at point A, the bending moment axial force and shear force on rod AB are respectively:

[0031]

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

[0033]

[0034] It is obtained that:

[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,

[0037] μ = 0.3, the shear shape factor of the circular cross-section The Young's modulus E of the structure in the Y direction Y is:

[0038]

[0039] The relative density of the micro cell is:

[0040]

[0041] where ρ s is the density of the base material, and L is the cell length size.

[0042] Step 2: Import the 3D model to be optimized into the finite element analysis software to calculate the structural response. Shell the macrostructure into an external skin and an internal structure. According to the force condition of the load, divide the internal structure into blocks in the simulation software, assign different equivalent solid materials to different regions, add structural boundary conditions, apply displacement loads, set force extraction reference points, divide the mesh, set history output and field output, and then solve for the stiffness of the macrostructure based on the magnitude of the reaction force extracted under the applied displacement load.

[0043] As an optimization, the finite element analysis software selected in Step 2 is Abaqus.

[0044] Step 2.1: Import the 3D model to be optimized into Abaqus; shell the macrostructure into an external skin and an internal structure; the division of the model to be optimized into blocks is for the multi-objective design of the macrostructure, and different regions of the internal structure are divided according to the force condition of the macrostructure.

[0045] Step 2.2: According to the division of the macro internal structure, 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 corresponding microcells are different; by arranging microcells with different geometric parameters in the macro internal structure, the stiffness and relative density of different regions of the macrostructure are changed to achieve the best balance relationship between the stiffness and mass of the overall macrostructure.

[0046] Step 2.3: Set boundary conditions for the macrostructure in Abaqus; bond the internal structure to the external skin; to facilitate the extraction of the response of the entire macrostructure, couple the upper surface of the structure to the node set "M_SET-1" and apply a displacement load in the horizontal direction to this point, and fix the lower surface of the structure; divide the mesh of the macrostructure and set history output and field output to obtain a finite element analysis model.

[0047] Step 3: Combine Abaqus with the genetic algorithm, and control the finite element analysis of Abaqus and optimize the design parameters through a Python script.

[0048] Step 3.1: Combine Abaqus with the genetic algorithm, perform finite element analysis and extract the magnitude of the reaction force on the finite element model in Step 2 through a Python script, and use the magnitude of the reaction force as the first optimization objective.

[0049] Step 3.2: Through the analytical relationship between the micro geometric parameters and the relative density of the equivalent solid established in Step 1, combined with the volume of each module of the internal structure in Step 2, calculate the mass of the macrostructure, and use the mass as the second optimization objective.

[0050] Step 4: Perform fast non-dominated sorting on the population. Based on the sorting results and crowding distance, select appropriate parent individuals. Through the crossover and mutation operations of the multi-objective genetic algorithm, generate an offspring population. Merge the current population with the offspring population to form a new population, and re-perform non-dominated sorting and crowding distance calculation. In each iteration, utilize the combination of finite element analysis and the multi-objective genetic algorithm to continuously optimize the population, gradually approaching or achieving the optimization of multiple optimization objectives, and obtain the Pareto optimal solutions. The Pareto optimal solutions are the combinations of the micro-cell radii corresponding to the best balance relationship between stiffness and mass. The Pareto optimal solutions are non-dominated by each other during the optimization process and exhibit the best balance relationship between stiffness and mass.

[0051] Step 4.1: Take the internal structure in Step 2.1 as the optimization region, and take the geometric radius of the micro-cell to be optimized as the optimization parameter. The optimization parameter is a set of design vectors Xn = [R1, R2, …, R N ; Equivalent the different regions in Step 2.2 to the Young's modulus En = [E1, E2, …, E N of the solid material; Set the population size pop_size, the maximum number of iterations max_gen, and the value range RX_BOUND of the geometric parameters of the micro-cell; Encode the geometric radius of the micro-cell in a real-number encoding manner to establish the initial population Pt.

[0052] Step 4.2: Randomly generate pop_size individuals s1, s2, …, sp in RX_BOUND, that is, the micro-cell radii in different regions, and obtain pop_size groups of Young's modulus {E1, E2, …, E N} of the equivalent solid materials through Step 1 to form the initial population Pt = {s1, s2, …, sp}; Calculate the two optimization objectives of the multi-objective genetic algorithm through Steps 3.1 and 3.2.

[0053] Step 4.3: According to the optimization objectives obtained in 4.2, perform fast non-dominated sorting on the initial population Pt to determine the sorting levels of each individual and the crowding distance of the individuals within each level. Based on non-dominated sorting and crowding distance, select parent individuals for reproduction; According to the crossover and mutation in the multi-objective genetic algorithm, randomly change the radius R of a single cell in its population to generate an offspring population Qt, and combine the two populations to form a population Rt with a size of 2 * pop_size.

[0054] Step 4.4: Perform fast non-dominated sorting on the new population Rt generated in Step 4.3. At the same time, calculate the crowding degree of each individual in the dominated layer, and select individuals based on the non-dominated relationship and individual crowding degree to form a new parental population Pt+1. Generate a new offspring population Qt+1 through the basic operations of the genetic algorithm, and merge Pt+1 and Qt+1 to form a new population Rt.

[0055] Step 4.5: Repeat the operation in 4.4 until the maximum number of iterations is reached to obtain the Pareto optimal solution set.

[0056] Beneficial effects:

[0057] 1. An optimization method for structural lightweighting based on a multi-objective genetic algorithm disclosed by the present invention optimizes complex structures based on the multi-objective 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 cells, the geometric parameters of the microscopic cells filled between different parts of the macroscopic structure are optimized to achieve the stiffness matching between different cells, so that the stiffness and mass of the optimized macroscopic structure reach the best balance, realizing the lightweight design of the structure.

[0058] 2. An optimization method for structural lightweighting based on a multi-objective genetic algorithm disclosed by the present invention establishes an interface between the finite element software and the multi-objective genetic algorithm during the optimization process. The mechanical properties of the complex model are analyzed by the finite element software, and the simulation data is extracted and transmitted to the multi-objective genetic algorithm for the optimization of the geometric parameters of the microscopic cells. By coupling the simulation software and the genetic algorithm, the collaborative design of the macro-micro structure is realized, the problem of difficult optimization of complex three-dimensional models is solved, and the optimization efficiency is improved.

[0059] 3. An optimization method for structural lightweighting based on a multi-objective genetic algorithm disclosed by the present invention generates an initial population of geometric parameters of the microscopic cells in the multi-genetic algorithm, and establishes a corresponding finite element model of the macroscopic structure through the mapping relationship between the geometric parameters and the Young's modulus. By introducing mechanisms such as non-dominated sorting and crowding distance, the multi-objective genetic algorithm can maintain the diversity of solutions, efficiently process multiple objective functions, and improve the efficiency and accuracy of structural optimization.

[0060] 4. An optimization method for structural lightweighting based on a multi-objective genetic algorithm disclosed by the present invention uses Python as a programming tool, which 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 extensibility, which can further enhance the parallel optimization ability and performance of the genetic algorithm, improve the optimization efficiency of complex three-dimensional structures, quickly obtain the Pareto optimal solution set, and complete the screening of the microscopic cell radius combination. Description of the Drawings

[0061] 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, without creative efforts, other drawings can also be obtained based on these drawings.

[0062] Figure 1 It is a flowchart of the joint simulation of the multi-objective genetic algorithm and Abaqus based on Python disclosed by the present invention;

[0063] Figure 2 It is a deformation diagram of the rod when the BCC representative volume element disclosed by the present invention is stressed in the Y direction;

[0064] Figure 3(a) is the skin structure of the three-dimensional structure to be optimized;

[0065] Figure 3(b) is the internal structure of the three-dimensional structure to be optimized

[0066] Figure 4 Schematic diagram of the layering of the internal structure to be optimized;

[0067] Figure 5 It is the Pareto front solution for multi-objective optimization;

[0068] Figure 6 It is the reconstruction of the optimization model; Specific implementation manners

[0069] The following will clearly and completely describe the technical solutions of the present invention in combination with the drawings of the present invention and specific embodiments. The specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0070] As Figure 1 shown in the flowchart, an optimization method for structural lightweighting based on a multi-objective genetic algorithm disclosed in this embodiment is specifically implemented as follows:

[0071] The specific implementation method of step one is:

[0072] In this example, the BCC structure is used as the filling cell, and the geometric parameters of the cell are as Figure 2 shown. The cell length is L = 8 mm, and the value range of the radius R is 0.25 - 3.4 mm. The selected material is AlSi10Mg, with Young's modulus Es = 71000 MPa and Poisson's ratio μ = 0.3. The analytical formula for the equivalent mechanical properties of the BCC structure is derived based on the energy method.

[0073] Considering the overlapping effect between the rods, the effective length l of the cell rods is obtained E :

[0074]

[0075] Where: l is the length of the cell member, R is the cell radius, ψ is the angle between the member radius and the connecting surface, and the coefficient is a semi-empirical coefficient;

[0076] Under the action of the external force F, the rotational displacement of point A along the M1 direction is Δ 1F , and under the bending moment M1 = 1, the rotational displacement of point A along the M1 direction is δ 11 , so under the combined action of the external force F and M1, the rotational displacement Δ1 of point A along the M1 direction is:

[0077] Δ1 = δ 11 M1 + Δ 1F

[0078] According to the structural symmetry, the structural rotational displacement is 0, and the deformation compatibility equation is obtained:

[0079] δ 11 M1 + Δ 1F = 0

[0080] Under the action of the statically determinate system, under the condition of 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:

[0081] M(x) = Fxcosθ,

[0082] F N (x) = -Fsinθ,

[0083] F S (x) = Fcosθ

[0084] θ is the angle between the cell member and the horizontal direction;

[0085] 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 on the rod AB axial force and shear force are respectively:

[0086]

[0087] According to the deformation compatibility equation, the obtained bending moment is:

[0088]

[0089] The actual force condition of the rod AB is:

[0090]

[0091] F N = -Fsinθ,

[0092] F S = Fcosθ

[0093] Apply a unit force F = 1 along the Y direction at point A, and the bending moment, axial force and shear force on the rod AB are respectively::

[0094]

[0095] Then the displacement ΔY of point A in the vertical direction is::

[0096]

[0097] Obtain::

[0098]

[0099] 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 The Young's modulus E of the structure in the Y direction Y is::

[0100]

[0101] The relative density of the microcellular unit is::

[0102]

[0103] where ρ s is the density of the base material, and L is the cell length size.

[0104] Step 2: Import the 3D model to be optimized into the finite element analysis software to calculate the structural response. Shell the macrostructure into an external skin and an internal structure. According to the loading conditions, divide the internal structure into blocks in the simulation software, assign different equivalent solid materials to different regions, add structural boundary conditions, apply displacement loads, set the force extraction reference points, divide the mesh, set the history output and field output, and then solve for the stiffness of the macrostructure based on the magnitude of the reaction force extracted under the applied displacement load.

[0105] As an optimization, the finite element analysis software selected in Step 2 is Abaqus.

[0106] Step 2.1: Import the model to be optimized into Abaqus. The partitioning of the model to be optimized is for the multi-objective design of the macrostructure. In this example, the selected structure is a complex three-dimensional stent structure. First, extract the outer skin of the structure and divide the internal structure into modules. The skin and the internal structure are respectively called Part-1 and Part-2, as shown in Figure 3. Divide different regions according to the force conditions of the macrostructure. Part-2 is layered as Figure 4 shown. The mechanical properties of the materials of the equivalent entities in different regions are different, that is, the geometric parameters between the corresponding micro-cells are different. Assign the initial material properties E1 to E5 respectively, and use these material properties as the optimization design variables. Different material properties correspond to different cell size radii and different relative densities. The material of Part-1 is selected as AlSi10Mg, where the Young's modulus Es = 71000 MPa and the Poisson's ratio μ = 0.3, which are not used as optimization design variables. After measurement, the area of each region of the structure to be optimized is V1 = 281680.72 mm 3 , V2 = 44958.70 mm 3 , V3 = 619735.94 mm 3 , V4 = 364321.56 mm 3 , V5 = 178578.39 mm 3 , V6 = 46022.72 mm 3 .

[0107] Step 2.2: Set different material properties in Abaqus according to the partitioning of the macrostructure. Different regions are assigned the Young's modulus E of different equivalent entity materials obtained in Step 1, that is, the geometric parameters between the corresponding micro-cells are different; by arranging micro-cells with different geometric parameters in the macro internal structure, the stiffness and relative density of different regions of the macrostructure are changed to achieve the best balance relationship between the stiffness and mass of the overall macrostructure. Y

[0108] Step 2.3: Set boundary conditions for the macrostructure in Abaqus. To facilitate the extraction of the response of the entire structure, couple the upper surface of the structure to the node set "M_SET-1" and apply a 1-mm displacement load in the horizontal direction to this point. Fix the lower surface of the structure, and set the bonded contact between Part-1 and Part-2. Mesh the macrostructure and set the history output and field output to obtain the finite element analysis model.

[0109] Step 3: Combine Abaqus with the genetic algorithm to control the finite element analysis of Abaqus by a Python script and optimize the design parameters.

[0110] Step 3.1: Combine Abaqus with the genetic algorithm. Use Python scripts to perform finite element analysis on the finite element model in Step 2 and extract the magnitude of the reaction force. Take the magnitude of the reaction force as the first optimization objective and set it as function1.

[0111] Step 3.2: Based on the analytical relationship between the microscopic geometric parameters and the equivalent solid relative density established in Step 1, and combined with the volume of each module of the internal structure in Step 2, calculate the mass of the macroscopic structure. Take the mass as the second optimization objective and set it as function2.

[0112] Step 4: Perform a fast non-dominated sorting on the population. Based on the sorting results and the crowding distance, select appropriate parent individuals. Generate the offspring population through the crossover and mutation operations of the multi-objective genetic algorithm. Combine the current population and the offspring population to form a new population, and re-perform non-dominated sorting and crowding distance calculation. In each iteration, utilize the combination of finite element analysis and the multi-objective genetic algorithm to continuously optimize the population, gradually approaching or achieving the optimization of multiple optimization objectives, and obtain the Pareto optimal solutions. The Pareto optimal solutions are the combinations of microscopic cell radii corresponding to the best balance relationship between stiffness and mass. The Pareto optimal solutions are non-dominant to each other during the optimization process and present the best balance relationship between stiffness and mass.

[0113] Step 4.1: Take the internal structure in Step 2.1 as the optimization region, and take the geometric radius of the microscopic cell to be optimized as the optimization parameter. The optimization parameter is a set of design vectors Xn = [R1, R2, …, R5]; Equivalent the different regions in Step 2.2 to the Young's modulus En = [E1, E2, …, E5] of the solid material; Set the population size pop_size = 30, the maximum number of iterations max_gen = 15, and the value range of the microscopic cell geometric parameters RX_BOUND = [0.25, 3.4].

[0114] Step 4.2: Thirty individuals s1, s2, …, s30 in [0.25, 3.4], that is, the microscopic cell radii of different regions, obtain pop_size = 30 sets of Young's moduli [E1, E2, …, E5] of the equivalent solid materials through Step 1, and form the initial population Pt = {s1, s2, …, s30}; Calculate the two optimization objectives of the multi-objective genetic algorithm through Steps 3.1 and 3.2.

[0115] Step 4.3: According to the optimization objectives obtained in 4.2, perform fast non-dominated sorting on the initial population Pt to determine the sorting levels of each individual and the crowding distance of individuals within each level. Based on non-dominated sorting and crowding distance, select parent individuals for reproduction; according to the crossover and mutation in the multi-objective genetic algorithm, randomly vary the radius R of a single cell of its population to generate the offspring population Qt, and combine the two populations to form a population Rt with a size of 2*pop_size;

[0116] Step 4.4: Perform fast non-dominated sorting on the new population Rt generated in Step 4.3, and at the same time calculate the crowding degree of individuals in each dominated layer. Select individuals according to the non-dominated relationship and individual crowding degree to form a new parent population Pt+1; generate a new offspring population Qt+1 through the basic operations of the genetic algorithm, and merge Pt+1 and Qt+1 to form a new population Rt;

[0117] Step 4.5: Repeat the operation in 4.4 until the maximum number of iterations is reached to obtain the Pareto optimal solution set. The obtained Pareto solution set is as shown in Figure 5 shown. According to the Pareto solution set, select the design variables with the overall structure mass under 1.557 kg for model verification. At this time, the design variables [R1, R2, R3, R4, R5] are [1.256, 0.976, 0.742, 1.085, 1.142]. According to the theory, the corresponding material properties [E1, E2, E3, E4, E5] can be obtained as [4228.36, 1316.63, 385.74, 2138.21, 2709.91]. The model reconstruction obtained according to the geometric parameters is as shown in Figure 6 shown. After verification, it shows that the homogenized stiffness of the equivalent geometric parameters is 554.54 MPa, and the stiffness of the model reconstruction is 467.48 MPa. The error between the two is 15.1%, indicating the effectiveness of the structural lightweight optimization method based on the multi-objective genetic algorithm and improving the optimization efficiency to meet the requirements of structural lightweight.

[0118] The above are only the preferred embodiments of the present invention and are not used to limit the present invention. For those skilled in the art, the present invention can have various changes and modifications. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention are all included within the protection scope of the present invention.

Claims

1. An optimization method for structural lightweighting based on a multi-objective genetic algorithm, characterized in that: It includes the following steps: Step 1: Based on the cell type and the periodic arrangement of cells in space, perform homogenization calculations to establish an analytical relationship between the microscopic geometric parameters, the Young's modulus of the equivalent solid material, and the relative density; through the analytical relationship between the microscopic geometric parameters and the Young's modulus of the equivalent solid material, 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; perform shelling on the macroscopic structure, which is divided into an external skin and an internal structure; divide the structure in the finite element analysis software, and different regions are given the Young's modulus of different equivalent solid materials obtained in Step 1; Add structural boundary conditions, set force extraction reference points, divide the mesh, set history output and field output to obtain a finite element analysis model; Step 3: Combine Abaqus with the genetic algorithm, perform finite element analysis on the finite element model in Step 2 and extract the magnitude of the reaction force through a Python script, and use the magnitude of the reaction force as the first optimization goal; through the analytical relationship between the microscopic geometric parameters and the relative density of the equivalent solid established in Step 1, combined with the volume of each module of the internal structure in Step 2, calculate the mass of the macroscopic structure, and use the mass as the second optimization goal; Step 4: Encode the radius R of the microscopic cells in different regions in a real number coding manner and randomly generate an 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, and obtain the magnitude of the reaction force and the mass of the macroscopic structure through Step 3, which are the two optimization goals in the multi-objective genetic algorithm; according to the optimization goals, perform fast non-dominated sorting on the initial population, and select parent individuals based on the sorting results and crowding distance; generate an offspring population through the crossover and mutation operations of the multi-objective genetic algorithm; merge the current population with the offspring population to form a new population, and re-calculate the non-dominated sorting and crowding distance; after multiple rounds of iteration, obtain the Pareto optimal solution, and the Pareto optimal solution is the combination of microscopic cell radii corresponding to the best balance relationship between stiffness and mass.

2. The optimization method for structural lightweighting based on a multi-objective genetic algorithm according to claim 1, characterized in that: It also includes Step 5: According to the Pareto optimal solution set obtained in Step 4, select a set of parameters in the Pareto optimal solution set to reconstruct the macroscopic structure in Hypermesh, establish a macroscopic structure containing microscopic cells with different radii according to the optimization, and import the macroscopic structure into Abaqus for verification, verify and screen out the macroscopic structure that meets the preset optimization goals, so that the stiffness and mass of the optimized macroscopic structure reach the best balance.

3. The optimization method for structural lightweighting based on a multi-objective genetic algorithm according to claim 1, characterized in that: The microscopic cell described in Step 1 is a BCC structure without transverse bars.

4. The optimization method for structural lightweighting based on a multi-objective genetic algorithm according to claim 1, 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 connecting surface, and 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 corner is 0, and the deformation coordination equation is obtained: δ 11 M1 + Δ 1F = 0 Under the action of a statically determinate system, under the condition of an external force F acting at point A, the bending moment M, axial force F N , and shear force Fs on rod AB are respectively: M(x) = Fxcosθ, F N (x) = -Fsinθ, F S F(x) = F cos θ θ is the angle between the cell bar and the horizontal direction; Under the action of a statically determinate system, when the unit virtual moment M = 1 acting at point A, the bending moment axial force and shear force on member AB are respectively According to the deformation coordination 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 bending moment axial force and shear force on the rod AB are respectively:: 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: The relative density of the microscopic cell is: where ρ s is the density of the substrate, and L is the cell length size.

5. The optimization method for structural lightweighting based on a multi-objective genetic algorithm according to claim 1, characterized in that: The finite element analysis software selected in Step 2 is Abaqus; the implementation method of Step 2 is as follows: Step 2.1: Import the 3D model to be optimized into Abaqus; perform shelling on the macroscopic structure, which is divided into an external skin and an internal structure; the division of the model to be optimized into blocks is for the multi-objective design of the macroscopic structure, and different regions are divided for the internal structure according to the force-bearing conditions of the macroscopic structure. Step 2.2: According to the segmentation of the macroscopic internal structure, different regions are given the Young's modulus E of different equivalent entity materials obtained in Step 1 Y , that is, the geometric parameters between the corresponding microscopic cells are different; by arranging microscopic cells with different geometric parameters in the macroscopic internal structure, the stiffness and relative density of different regions of the macroscopic structure are changed to achieve the best balance relationship between the stiffness and mass of the overall macroscopic structure. Step 2.3: Set boundary conditions for the macroscopic structure in Abaqus; bind the internal structure to the external skin; in order to facilitate the extraction of the response of the entire macroscopic structure, couple the upper surface of the structure to the node set "M_SET-1", and apply a displacement load in the horizontal direction to this point, and 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.

6. The optimization method for structural lightweighting based on a multi-objective genetic algorithm according to claim 1, characterized in that: The implementation method of Step 3 is as follows: Step 3.1: Combine Abaqus with the genetic algorithm, perform finite element analysis on the finite element model in Step 2 and extract the magnitude of the reaction force through a Python script, and use the magnitude of the reaction force as the first optimization objective. Step 3.2: Based on the analytical relationship between the microscopic geometric parameters and the equivalent solid relative density established in Step 1, and combined with the volume of each module of the internal structure in Step 2, calculate the mass of the macroscopic structure, and use the mass as the second optimization objective.

7. The optimization method for structural lightweighting based on a multi-objective genetic algorithm according to claim 1, characterized in that: The implementation method of Step 4 is as follows: Step 4.1: Take the internal structure in Step 2.1 as the optimization region, and take the geometric radius of the micro-cell to be optimized as the optimization parameter. The optimization parameter is a set of design vectors Xn = [R1, R2, …, R N ; Equivalent the different regions in Step 2.2 to the Young's moduli En = [E1, E2, …, E N of the solid materials; Set the population size pop_size, the maximum number of iterations max_gen, and the value range RX_BOUND of the geometric parameters of the micro-cell; Encode the geometric radius of the micro-cell in a real-coded manner to establish the initial population Pt; Step 4.2: Randomly generate pop_size individuals s1, s2, …, sp in RX_BOUND, that is, the microcell radii in different regions, and obtain pop_size groups of Young's moduli {E1, E2, …, E N} of the materials of the equivalent entities through Step 1 to form the initial population Pt = {s1, s2, …, sp}; calculate the two optimization objectives of the multi-objective genetic algorithm through Steps 3.1 and 3.2; Step 4.3: According to the optimization objectives obtained in 4.2, perform fast non-dominated sorting on the initial population Pt, determine the sorting levels of each individual and the crowding distance of individuals within each level, select parent individuals for reproduction based on non-dominated sorting and crowding distance; according to the crossover and mutation in the multi-objective genetic algorithm, randomly vary the radius R of a single cell of its population to generate an offspring population Qt, and combine the two populations to form a population Rt with a size of 2*pop_size. Step 4.4: Perform fast non-dominated sorting on the newly generated population Rt in Step 4.3, and calculate the crowding degree of individuals in each domination layer at the same time. Select individuals according to the non-dominated relationship and individual crowding degree to form a new parent population Pt+1; generate a new offspring population Qt+1 through the basic operations of the genetic algorithm, and merge Pt+1 and Qt+1 to form a new population Rt. Step 4.5: Repeat the operation in 4.4 until the maximum number of iterations is reached to obtain the Pareto optimal solution set.

8. The optimization method for structural lightweighting based on a multi-objective genetic algorithm according to claim 1, characterized in that:

Images