Optimization method for mixed lattice structure parameters
By establishing an initial model of hybrid lattice structure and using firefly algorithm to optimize single cell species, porosity and relative volume, combined with finite element modeling and simulation analysis, the slow speed and low efficiency of hybrid lattice structure optimization design in the existing technology are solved. The problem of efficient energy absorption capacity and mechanical performance improvement has been achieved.
Patent Information
- Application Number
- CN202411119744.5
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-08-15
- Publication Date
- 2024-12-13
AI Technical Summary
In the prior art, the optimization design speed of hybrid lattice structures is slow, the optimization efficiency is low, and it is difficult to adapt to complex mechanical environments. There are few researches on hybrid lattice structures with different relative volumes of cell and porosity.
By establishing an initial model of a hybrid dot matrix structure, combining the results of mechanical simulation calculations, the model is optimized using the firefly algorithm, the objective function and fitness function are established, the cell species, porosity and relative volume are optimized, the energy absorption capacity is improved, and the finite element construction is constructed Model and simulation analysis, automated simulation analysis process to improve optimization efficiency.
It realizes efficient hybrid lattice structure optimization, improves the energy absorption capacity and mechanical properties of the structure, adapts to complex mechanical environments, has clear processes, high computing efficiency, and good global convergence.
Smart Images
Figure CN119129313A_ABST
Abstract
Description
Technical Field
[0001] The invention relates to the field of lattice structure optimization design, and in particular to a method for optimizing parameters of a hybrid lattice structure. Background Art
[0002] The lattice structure is composed of a periodic arrangement of unit cells consisting of pillars and nodes. It has good mechanical properties such as high specific modulus, high specific strength and high specific surface area, as well as excellent energy absorption performance. It has broad application prospects in the fields of aerospace, automobiles, ships and other transportation equipment. In recent years, the rapid development of selective laser melting technology has provided an effective means for the preparation of complex metal lattice structures. Compared with traditional casting, forging and other technologies, SLM shows higher manufacturing flexibility and material utilization in the manufacture of metal lattice structures. The mechanical properties of the lattice structure are mainly determined by factors such as raw material properties, geometric configuration and relative density. Therefore, the performance of the lattice structure can be improved by optimizing the geometric configuration and innovative design.
[0003] However, the lattice structure design in related technologies is mostly the optimization design of a single cell structure, with relatively simple mechanical properties, and it is difficult to adapt to complex mechanical environments. Currently, there is little research on the optimization of mixed lattice structures. The existing mixed lattice structure optimization design methods are slow and have low optimization efficiency. There is no research on mixed lattice structures with different relative volume cells and porosities. Summary of the invention
[0004] Purpose of the invention: The purpose of the present invention is to provide a method for optimizing the parameters of a hybrid lattice structure, which can effectively improve the energy absorption capacity of the structure by optimizing the hybrid lattice structure using a parameter optimization model of the hybrid lattice structure.
[0005] Technical solution: The optimization method of the hybrid lattice structure parameters of the present invention establishes an initial model of the hybrid lattice structure, combines the mechanical simulation calculation results, and establishes the objective function P and the fitness function F according to the maximum energy absorption capacity as the optimization target. f The simulation analysis system built imports the model optimized by the firefly algorithm into the simulation software for mechanical analysis. Through the fitness function and calculation results, the relationship between the unit cell type, unit cell porosity, relative volume and optimization target in the mixed lattice structure is established. Through the continuous iteration of the firefly algorithm, the optimal structure is selected.
[0006] The method comprises the following steps:
[0007] Establishing an optimization model with the unit cell type, porosity, and relative volume in the hybrid lattice structure as design variables, introducing structural strength and stiffness as constraints, and maximizing energy absorption capacity as the goal; initial lattice structure, using modeling software to perform finite element modeling on the hybrid lattice structure;
[0008] Based on the constructed hybrid lattice structure model, the mesh at the connection of the hybrid lattice structure is locally encrypted to ensure the accuracy and effectiveness of the finite element calculation.
[0009] Build an automated simulation analysis process system that can integrate modeling software with simulation software. The system automatically imports the model into the simulation software to analyze the mechanical properties. The system automatically extracts key parameters from the simulation results, thereby significantly improving the efficiency of hybrid lattice structure optimization.
[0010] Based on the initial structural parameters, the corresponding variable parameter group of the hybrid lattice structure design scheme is loaded on the fireflies. The position and brightness of the fireflies are represented by the corresponding parameter group, which includes the unit cell type, porosity, relative volume and energy absorption capacity in the hybrid lattice structure. The firefly population is initialized based on different structural parameters and the simulation analysis system is established. The models of different structures are imported into the finite element simulation software to analyze their mechanical properties. The strain and stress of the hybrid lattice structure are calculated to evaluate its corresponding fitness. The optimal solution is searched in the solution space by updating the position and brightness of the fireflies, that is, different parameter combinations are used to achieve hybrid lattice structure optimization.
[0011] The firefly algorithm described in the present invention is a heuristic optimization algorithm based on the luminous behavior of fireflies in nature. In the firefly algorithm, each firefly represents a potential solution in the solution space, and the brightness of the firefly is proportional to the quality of its solution. The algorithm updates the position of the solution by simulating the mutual attraction between fireflies. Fireflies with higher brightness will attract fireflies with lower brightness to move toward them. The attraction usually decreases with the increase of the distance between fireflies, which can be simulated by a decay function. The algorithm continuously updates the position of the fireflies through an iterative process. In each iteration, the fireflies will adjust their positions according to the brightness and attraction of other fireflies. The position update problem of multiple fireflies can be handled at the same time. Therefore, the firefly algorithm is used to optimize the above parameters. With the assistance of finite element simulation results, the optimal hybrid lattice structure solution is obtained through multiple iterations.
[0012] Furthermore, the selected mixed lattice structure is composed of at least two unit cells out of five common unit cells, the five optional unit cell structures are (Bcc, Fcc, Diamond, Octet, Hcp), the porosity is 0.1 to 0.9, and the relative volume is 0.2 to 0.8.
[0013] Furthermore, the energy absorption capacity is evaluated by the energy absorption per unit volume W:
[0014]
[0015] In the formula, ε dis any strain; σ is the compressive stress; ε is the compressive strain corresponding to the compressive stress.
[0016] Furthermore, the key parameters include stiffness, stress distribution and / or strain of the hybrid lattice structure.
[0017] Furthermore, the present invention obtains the optimal variable combination including unit cell type, porosity, and relative volume through the obtained parameter group under the constraints of strength and stiffness, so as to maximize the energy absorption capacity of the hybrid lattice structure after parameter optimization.
[0018] Furthermore, the position and brightness of the fireflies are represented by a corresponding parameter group, and the corresponding parameters include the type of single cell in the mixed lattice structure, porosity, relative volume and energy absorption capacity, and the optimization formula is:
[0019] I i =f(X i ),X i =[x i1 ,x i2 ,…,x in ]
[0020] n=1,2…,n
[0021] σ max ≤σ s
[0022] k s ≥k min
[0023] The penalty function and fitness formula are as follows:
[0024] P=ω1·max(0,σ s -σ max )+ω2·max(0,k s -k min )
[0025] F f =f(X i )-P
[0026] In the formula, I i is the absolute brightness of individual i; f(X i ) is the objective function value of individual i; X i is the optimization variable set; n is the number of variables. i1 ,x i2 ,…,x in For X i Each variable in, ω1 and ω2 are weight coefficients, σ max is the structural stress, σ s is the yield strength of the material, ks is the structural stiffness, k min is the minimum stiffness requirement. P is the penalty function, F f is the fitness function, and the variables include unit cell type, porosity and relative volume.
[0027] Furthermore, the expression of the brightness of the firefly is as follows:
[0028]
[0029] In the formula, I i,j is the relative brightness of individual i and individual j, I0 is the maximum brightness of the firefly, r i,j is the Euclidean distance between individual i and individual j, x i and x j is the spatial position of fireflies i, j, γ is the light intensity attraction coefficient, d is the spatial position dimension, x i,k represents the kth component of firefly i in the d-dimensional space.
[0030] Furthermore, initializing the firefly population includes: taking the initial structure obtained in the first step as a benchmark, generating individual structural parameter values of the initial population and their corresponding finite element models, calculating the corresponding firefly brightness and position, and taking the strength and stiffness of the mixed lattice structure as constraints.
[0031] Furthermore, based on the established simulation analysis system, each individual is imported into the simulation software for mechanical property analysis to obtain its corresponding fitness. If the fitness meets the expected value or the number of iterations reaches the maximum value, the individual with the largest fitness in the population, that is, the largest energy absorption capacity, is the optimal structure.
[0032] Furthermore, the attractiveness formula of the firefly algorithm is:
[0033]
[0034] In the formula, β i,j is the relative attraction between individuals i and j, β0 is the maximum attraction, γ is the light intensity attraction coefficient, r i,j is the Euclidean distance between individuals i and j.
[0035] Furthermore, the formula for updating the position of fireflies is as follows:
[0036] x i =x j +β·(x j -x i )+α·rand
[0037] In the formula, β is the attraction, x i and x jis the spatial position of fireflies i, j, α is the step factor, the value interval is [0,1], and rand is a Gaussian distributed, uniformly distributed random number variable.
[0038] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages: (1) A lattice structure with high strength and good energy absorption capacity is obtained by combining different unit cells to adapt to complex mechanical environments; (2) The firefly algorithm is combined with the lattice structure optimization design process, which requires fewer parameters to be adjusted, has a clear process, high calculation efficiency, and good global convergence. BRIEF DESCRIPTION OF THE DRAWINGS
[0039] Figure 1 It is a structural schematic diagram of the hybrid lattice;
[0040] Figure 2 A flow chart of the optimization method for the hybrid lattice structure;
[0041] Figure 3 Schematic diagram of finite element simulation results of hybrid lattice structure. DETAILED DESCRIPTION
[0042] The technical solution of the present invention is further described below in conjunction with the accompanying drawings.
[0043] Example
[0044] like Figure 1 The figure shows the initial mixed lattice structure of the present invention, which is composed of 5mm×5mm×5mm Bcc and Fcc unit cells, and the material is 316 stainless steel. The whole mixed lattice structure is divided into two layers of space, each layer has a size of 20mm×20mm×20mm×V (relative volume), wherein the relative volume and porosity of bcc are 0.5 and 80% respectively, and the relative volume and porosity of Fcc are 0.5 and 80% respectively, and the two selected unit cell lattice structure types are L1 and L2, and their relative volumes are V1 and V2, and their porosities are P1 and P2 respectively.
[0045] based on Figure 1 The hybrid lattice structure shown uses professional simulation software to perform quasi-static compression performance analysis based on the actual structural characteristics of the hybrid lattice structure. This step is the basis of the entire optimization process, ensuring that the model can accurately reflect the physical characteristics of the structure. Through the simulation results, key performance data is collected, including the stiffness, stress distribution, and strain of the structure.
[0046] The specific implementation steps of the hybrid lattice structure parameter optimization design method for additive manufacturing are as follows (the flow chart is as follows Figure 2 shown):
[0047] Step 1: According to the initial hybrid lattice structure, build its 3D model in SolidWorks, dimension the parameters to be optimized, build geometric relationships, and build the objective function and fitness function;
[0048] Step 2: Import the initial hybrid lattice structure obtained in step 1 into the simulation software nTop, and combine it with the mechanical analysis module. Using the nTop mechanical analysis module, set the upper and lower panels as rigid bodies, set the lower panel to be completely fixed, set the upper panel load to a constant downward displacement rate, and encrypt the local mesh.
[0049] Step 3: Use Python to write programs to build a simulation analysis process automation platform.
[0050] The specific implementation method of step 3 includes the following steps:
[0051] Step 3.1: Establish the connection between modeling software and platform.
[0052] Soildwork is used to build the hybrid lattice structure model, generate the corresponding .STP file, and use the program written in Python to read the .STP file. Specifically, the structural parameters marked in the .STP file are read, and the parameters can be modified to generate the .STP file of the new hybrid lattice structure.
[0053] Step 3.2: Establish the connection between simulation software and platform.
[0054] A program written in Python is used to read the finite element model in the .STP file in nTop, automatically perform meshing, add load conditions and simulation calculations according to the program design, and read the .ODB file generated by the nTop simulation after the simulation is completed, and extract the maximum stress and strain results from the file.
[0055] Step 4: Based on the initial structural parameters, the corresponding variable parameter group of the hybrid lattice structure design scheme is loaded on the fireflies. The position and brightness of the fireflies are represented by the corresponding parameter group, which includes the type of single cell, porosity, relative volume and energy absorption capacity in the hybrid lattice structure. The firefly population is initialized based on different structural parameters. Based on the simulation analysis system established in step 3, the models of different structures are imported into the finite element simulation software to analyze their mechanical properties. By calculating the strain and stress of the hybrid lattice structure, its corresponding fitness is evaluated. By updating the position and brightness of the fireflies, the optimal solution is searched in the solution space, that is, different parameter combinations are used to achieve hybrid lattice structure optimization.
[0056] The specific implementation method of step 4 includes the following steps:
[0057] Step 4.1: The position and brightness of the fireflies are represented by a corresponding parameter group, which includes the type of single cell in the hybrid lattice structure, porosity, relative volume and energy absorption capacity. The optimization formula is:
[0058] I i =f(X i ),X i =[x i1 ,x i2 ,…,x in ]
[0059] n=1,2…,n
[0060] σ max ≤σ s
[0061] k s ≥k min
[0062] The penalty function and fitness formula are as follows:
[0063] P=ω1·max(0,σ s -σ max )+ω2·max(0,k s -k min )
[0064] F f =f(X i )-P
[0065] Where: I i is the absolute brightness of individual i; f(X i ) is the objective function value of individual i; X i is the optimization variable set; n is the number of variables. i1 ,x i2 ,…,x in For X i Each variable in, ω1 and ω2 are weight coefficients, σ max is the structural stress, σ s is the yield strength of the material, k s is the structural stiffness, k min is the minimum stiffness requirement. P is the penalty function, F f is the fitness function, and the parameters include single cell type, porosity, and relative volume.
[0066] The energy absorption capacity needs to be evaluated by the energy absorption per unit volume W:
[0067]
[0068] In the formula, ε dis any strain; σ is the compressive stress; ε is the compressive strain corresponding to the compressive stress. The energy absorption per unit volume depends on the area enclosed by the stress-strain curve and the X-axis.
[0069] Step 4.2: Initialize the firefly population, take the initial structure in step 1 as the benchmark, generate the individual structural parameter values of the initial population and its corresponding finite element model, calculate the corresponding firefly brightness and position, and use the strength and stiffness of the mixed lattice structure as constraints. The structural parameters include: five optional unit cell structures (Bcc, Fcc, Diamond, Octet, Hcp), with a porosity of 0.1 to 0.9 and a relative volume of 0.2 to 0.8.
[0070] The expression for the brightness of the firefly is:
[0071]
[0072]
[0073] Where: I i,j is the relative brightness of individual i and individual j, I0 is the maximum brightness of the firefly, r i,j is the Euclidean distance between individual i and individual j, x i and x j is the spatial position of fireflies i, j, γ is the light intensity attraction coefficient, which usually takes a value in the range of (0, 1), d is the spatial position dimension, x i,k represents the kth component of firefly i in the d-dimensional space.
[0074] Step 4.3: Based on the simulation analysis system established in step 3, each individual is imported into the simulation software for mechanical performance analysis to obtain its corresponding fitness. If the fitness meets the expected value or the number of iterations reaches the maximum value, the individual with the largest fitness in the population, i.e., the largest energy absorption capacity, is the optimal structure. The attractiveness formula of the firefly algorithm is:
[0075]
[0076] In the formula, β i,j is the relative attraction between individuals i and j, β0 is the maximum attraction, γ is the light intensity attraction coefficient, r i,j is the Euclidean distance between individual i and individual j. The formula for updating the firefly position is as follows:
[0077] x i =x j +β·(x j -x i )+α·rand
[0078] In the formula, α is the step size factor, the value range is [0,1], β is the attraction, and rand is a Gaussian distribution, a uniformly distributed random number variable.
[0079] After applying the above optimization method in this embodiment, the results are as follows: Figure 3 shown.
[0080] like Figure 3 As shown in the figure, compared with the initial structure, the compressive strength of the optimized hybrid lattice structure increases from 467MPa to 518MPa, the energy absorption capacity is significantly enhanced, it has good mechanical properties under small compressive strain, and the energy absorption of the structure is improved under large compressive strain, indicating the effectiveness of the firefly algorithm in the optimization of hybrid lattice structures.
Claims
1. A method for optimizing hybrid lattice structure parameters, characterized in that: The following steps are involved: The unit cell type, porosity and relative volume in the hybrid lattice structure are used as design variables, structural strength and stiffness are introduced as constraints, and finite element modeling of the hybrid lattice structure is performed with the goal of maximizing energy absorption capacity; Based on the constructed hybrid lattice structure model, the mesh at the connection of the hybrid lattice structure is locally encrypted; Build an automated simulation analysis process system, which automatically imports the model into the simulation software to analyze the mechanical properties, and automatically extracts key parameters from the simulation results; Based on the initial structural parameters, the corresponding variable parameter group of the hybrid lattice structure design scheme is loaded on the firefly. The position and brightness of the firefly are represented by the corresponding parameter group, which includes the unit cell type, porosity, relative volume and energy absorption capacity. The firefly population is initialized based on different structural parameters and the simulation analysis system is established. The models of different structures are imported into the finite element simulation software to analyze their mechanical properties. The mechanical parameters of the hybrid lattice structure are calculated to evaluate its corresponding fitness. The optimal solution is searched in the solution space by updating the position and brightness of the firefly, that is, different parameter combinations are used to achieve hybrid lattice structure optimization.
2. The method for optimizing the hybrid lattice structure parameters according to claim 1, characterized in that: The energy absorption capacity is evaluated by the energy absorption per unit volume W: In the formula, ε d is any strain; σ is the compressive stress; ε is the compressive strain corresponding to the compressive stress.
3. The method for optimizing the hybrid lattice structure parameters according to claim 1, characterized in that: The selected mixed lattice structure includes at least two unit cell types, including body-centered cubic, face-centered cubic, diamond cubic, regular octahedral body-centered cubic or hexagonal close packing, the porosity is 0.1-0.9, and the relative volume is 0.2-0.
8.
4. The method for optimizing the hybrid lattice structure parameters according to claim 1, characterized in that: The key parameters include the stiffness, stress distribution and / or strain of the hybrid lattice structure.
5. The method for optimizing the hybrid lattice structure parameters according to claim 1, characterized in that: Through the obtained parameter group, under the constraints of strength and stiffness, the optimal variable combination including unit cell type, porosity, and relative volume is obtained, so as to maximize the energy absorption capacity of the hybrid lattice structure after parameter optimization.
6. The method for optimizing the hybrid lattice structure parameters according to claim 1, characterized in that: The optimization formula based on the firefly algorithm is as follows: I i =f(X i ),X i =[x i1 ,x i2 ,…,x in ] n=1,2…,n s max ≤σ s k s ≥k min The penalty function and fitness formula are as follows: P=ω1·max(0,σ s -s max )+ω2·max(0,k s -k min ) F f =f(X i )-P In the formula, I i is the absolute brightness of individual i; f(X i ) is the objective function value of individual i; X i is the optimization variable set; n is the number of variables, x i1 ,x i2 ,…,x in For X i Each variable in, ω1 and ω2 are weight coefficients, σ max is the structural stress, σ s is the yield strength of the material, k s is the structural stiffness, k min is the minimum stiffness requirement, P is the penalty function, and F f is the fitness function, and the variables include unit cell type, porosity and relative volume.
7. The method for optimizing the hybrid lattice structure parameters according to claim 1, characterized in that: The expression of the brightness of the firefly is as follows: In the formula, I i,j is the relative brightness of individual i and individual j, I0 is the maximum brightness of the firefly, r i,j is the Euclidean distance between individual i and individual j, x i and x j is the spatial position of fireflies i, j, γ is the light intensity attraction coefficient, d is the spatial position dimension, x i,k represents the kth component of firefly i in the d-dimensional space.
8. The method for optimizing the hybrid lattice structure parameters according to claim 1, characterized in that: Based on the simulation analysis process system, each individual is imported into the simulation software for mechanical performance analysis to obtain its corresponding fitness. If the fitness meets the expected value or the number of iterations reaches the maximum value, the individual with the largest fitness in the population, that is, the largest energy absorption capacity, is the optimal structure.
9. The method for optimizing the hybrid lattice structure parameters according to claim 1, characterized in that: The attractiveness formula of the firefly algorithm is: In the formula, β i,j is the relative attraction between individuals i and j, β0 is the maximum attraction, γ is the light intensity attraction coefficient, r i,j is the Euclidean distance between individuals i and j.
10. The method for optimizing hybrid lattice structure parameters according to claim 1, characterized in that: The formula for updating the firefly's position is as follows: x i =x j +β·(x j -x i )+a·rand In the formula, β is the attraction, x i and x j is the spatial position of fireflies i, j, α is the step size factor, the value interval is [0,1], and rand is a Gaussian distributed, uniformly distributed random number variable.