Multi-scale And Multi-objective Topological Optimization And Studies Of Mechanical Properties Of Functionally Graded Structures In Crashworthiness Design

The design of crashworthiness structure has very important significance in engineering design,and there are different requirements for energy absorption and bearing performance of crashworthiness structure in different designing occasions.In this paper,the structural stiffness and the negative Poisson’s ratio are used to measure the load-bearing capacity and energy absorption performance of the structure,and a multi scale and multiple topology optimization method of crashworthiness functional gradient structure is proposed.First,on the micro scale,the equivalent stiffness and equivalent negative Poisson’s ratio of periodic microstructure based on the energy homogenization method are deduced,and the relationship between the equivalent stiffness and the equivalent negative Poisson’s ratio of the element density is established by SIMP interpolation method,A micro-structure multi-objective topological optimization model with negative-Poisson’s ratio and stiffness is established.By applying the periodic boundary condition and the unit Test strain field to the micro-structure cells,the multi-objective optimization solution set under different weight ratios of different volume fractions is obtained by solving the finite element stiffness equation and an improved OC algorithm.The equation of equivalent stiffness and equivalent negative Poisson’s ratio of the optimal solution set under the same volume fraction is obtained by using the least squares polynomial fitting method.The analysis of results show that the change of weight proportion has good consistency with the equivalent stiffness and the equivalent negative Poisson’s ratio of topological optimization solution,which proves the correctness of this method in the design of microstructural topology optimization with the objective of negative-Poisson’s ratio and stiffness.Then,based on the concept of functionally gradient structure,this paper presents a method of multi-scale and multi-objective topology optimization.Selecting The topological optimization solution sets of micro-structure under the same volume fraction as the components,based on the finite element method and the equation of equivalent stiffness and equivalent negative Poisson’s ratio of microstructure under the same volume fraction,the relationship between the equivalent stiffness and the element stiffness matrix is deduced,A multi-objective optimization model is established with the equivalent stiffness of functionally graded structure and the equivalent negative Poisson ratio as the optimal target and the equivalent stiffness of the micro-structure cell as the design variable.the layered and layered microstructure of functionally graded structures under different weights are obtained by using multi-objective optimization function FGOALATTAIN of the MATLAB.The analysis of results show that the change of weight proportion and the change of equivalent stiffness and equivalent negative Poisson ratio of functionally graded structural optimization solutions are in good agreement,which proves the correctness of the proposed method.Finally,with the simulation analysis of FEM simulation and experimental research based on the representative optimization results,the mechanical properties of the functionally graded structures and lattice structure are studied.Results show that the lattice structure and functionally graded structure with high equivalent stiffness proved to have smaller negative Poisson’s ratio,less compression effect,more platform stress and more energy absorption,but it is prone to peak stress.The lattice structure and functionally graded structure with small equivalent stiffness proved to have lager negative Poisson’s ratio,more obvious pressure contraction effect,smaller platform stress and smaller energy absorption,but have more stable platform stress,and bigger energy absorption increment.In addition,there are obvious differences in mechanical properties between different layers of functionally graded structures,which are composed of different micro-structure cells,among them,the layers constituted with smaller stiffness and higher negative Poisson’s ratio cells showed more obvious internal contraction effect,smaller stress strain value and energy absorbing effect,but The stress strain value and the energy absorbing effect increment are bigger with the increase of plastic deformation,the layers constituted with the higher stiffness and smaller negative Poisson’s ratio cells showed smaller internal contraction effect,greater stress strain value and energy absorption effect,but the stress strain value and the energy absorption effect increment are smaller with the increase of plastic deformation.The analysis results further prove the correctness and validity of this proposed method.