Improved Approaches And Application Of Evolutionary Structural Optimization

The quest for performance of structure has been intensified in recent years due to the rapid development of science and technology.Especially the methods to obtain new design beyond engineering experiences are explored by researchers in the structural optimization fields.The topology of structures determines the main performance of structures,so in the configuration design and lightweight design of complex structures,topology optimization is more valuable than shape and size optimization.This paper focused focuses on the improved approaches and application of evolutionary structural optimization.The frustrated reason of traditional ESO method in some stiffness optimal topology design problems is analyzed and an improved ESO method is proposed.The improved ESO method is also applied in compliance optimization and thermal optimization. Not only the thermal dissipation problem but also the thermal insulation problem is considered.1.The thermal topology optimization method is proposed based on ESO by choosing the heat resistance as the design object,and element relative densities as design variables.To obtain the best performance of thermal dissipation and thermal insulation,the topology optimization results of a 2D square plate under different work conditions are presented.By this method,the heat performance of structures can be improved greatly.2.A Bi-Directional Evolutionary Structural Optimization(BESO) method for topology optimization of heat conduction structures is presented.In BESO method the elements are allowed to be added as well as removed.To improve the heat performance of structure,the additive criterion and rejection criterion are proposed respectively.With the limit volume of the high conductive material,the optimal layout of structure with high efficiency of heat dissipation and uniform temperature distribution can be obtained by BESO procedure.During the procedure of optimization,the re-mesh is avoided,which makes the BESO method more efficient,3.A new version of the additive evolutionary structural optimization(AESO) procedure based on sensitivity analysis for topology optimization of continuum structures is proposed. Illustrative examples have proved that the one-step AESO algorithm based on sensitivity analysis can't obtain good optimal results in the optimization of some continuum structures. The reason is pointed out as:the relationship of objective function and design variables can not be described accurately when the design variables are changed significantly(For example, from 0 to 1).And a new version of so called progressive AESO algorithm based on sensitivity analysis is proposed and is demonstrated by illustrative examples of topology optimization of heat conduction problems.The strategy of adding material in the bi-directional ESO algorithm based on sensitivity analysis is provided.4.The reason of failure of traditional ESO method in some topology design of structure stiffness problems is analyzed and an improved ESO method is proposed.The reason of failure of traditional ESO method in some cases is that sensitivity analysis is inaccurate.In traditional ESO method,the sensitivity of objective function(the difference between the objective function values at material densities of element being 1 and 0) is approximated as the derivative of the objective function with respect to the material density at the density being 1.This approximation may lead to large errors in sensitivity calculation in the case that the derivative of the objective function varies significantly with the change of material density of element from 1 to 0.Due to the large computational cost to improve the accuracy of the sensitivity analysis by the global difference method,a concept of singular element is introduced and a new improved ESO method is proposed.In this method,all the elements are divided into singular and ordinary elements based on the sensitivity of objective function.The sensitivities of objective function with respect to the densities of singular elements are calculated by the difference method.Numerical examples demonstrate the efficiency and validity of the method.5.The improved ESO method based on SIMP is presented,which is combination of ESO and SIMP.The step length of evolution is reduced so that the accuracy of sensitivity analysis can be improved.The SIMP method is employed to describe the relationship between the relative density and the stiffness of grey elements.With logical parameter the numbers of grey dements can be controlled,so the topology can be clearer and easier to manufacture. Topology optimization of continuum structures considering self-weight is carried out by this method,and more optimal results are obtained than those by traditional ESO method.