The ESO Heuristic Algorithm For 3D Problems Based On Virtual Materials And Its Application In Engineering

With the continuous improvement of the degree of industrialization in China,the demand for cost efficiency,lightweight,high reliability and safety of complex equipment is very urgent.Because of the large number of factors to be considered in the complex structural designs,the traditional structural design method can't satisfy these demands.In this context,the modern optimization design method combined with computer technology and finite element method came into being.Evolutionary Structural Optimization(ESO)has become one of the focuses in the field of topology optimization because of its simple thinking,easy implementation and high computational efficiency.It has made great achievements in theoretical research and engineering application.Because of the lack of rigorous mathematical theory,ESO algorithm has been identified as a complete heuristic algorithm.Rozvany's Tie-beam algorithm has been used to attack the effectiveness of ESO algorithm.Since then,a large number of improved ESO algorithms for solving the example of Tie-beam have been emerging to repair the shortcomings of ESO algorithm.Among them,the ESO heuristic algorithm based on virtual material successfully solves the planar Tie-beam problem by detecting the integrity of the force path.In this paper,the ESO heuristic algorithm based on virtual material is extended from plane problem to 3D problem.The possible distributions of the adjacent units of the cells to be deleted on the three-dimensional spatial structure are analyzed,and the stress changes of the cells to be deleted are deduced in the four states of 0,1,2,3 adjacent units,and obtains the threshold of the stress change of the cells to be deleted,and makes the numerical calculation to verify of the threshold obtained by the theoretical derivation,and then constructs the ESO heuristic algorithm for3 D problems based on virtual material.The problem of Tie-beam failure optimization in three-dimensional space is successfully solved,and the algorithm is applied to general numerical examples.In order to solve the problem of lightweight design of flywheel satisfying certain moment of inertia and maximum stress constraint in three-dimensional space,this paper uses the inverse correlation between unit moment of inertia and unit stress to transform the multi-constraint problem into the single constraint problem.Then the ESO heuristic algorithm for 3D problems based on virtual material is successfully used to solve this problem,which shows that the algorithm is of certain engineering practical value.