Topology Optimization Method And Application Of Continuum Structure Based On Element Differential Method

Topology optimization plays an important role in structural optimization methods for industrial design,which is widely adopted in aerospace,machinery,construction,automobile and etc.As the basis of the continuum topology optimization,the finite element method constructs the mechanical topology relationship of the optimization object,which has the advantages of efficient calculation,simple and easy to understand.However,limited by the size of the structural discrete grid,the accuracy of the finite element method lower than other,and it can’t meet the higher requirements of modern industrial design.In order to further improve the accuracy of topology optimization,the element differential method is studied,and a continuum structure topology optimization method based on element differential method is proposed.The main research work includes:Firstly,the evolution of the depicting model in the traditional continuum topology optimization is studied.The material interpolation scheme of SIMP and the methods to overcome numerical instabilities in calculation are deduced.At the same time,in order to improve the robustness of the topology optimization,the recommended settings of common parameters in topology optimization are analyzed and pointed out for the further research verification.S Secondly,it analyzes two optimization solution algorithms of continuum topology optimization.In order to eliminate porous and obtain clear structural in optimization results,a boundary sharpening sensitivity filtering method was proposed by combining the characteristics of structural boundaries and filter principles.Aiming at the problem that MMA(method of moving asymptotes)converges slowly in large-scale grid solution,the iterative solution process of MMA is optimized by combining MMA auxiliary convergence conditions and boundary sharpening sensitivity filtering method.Test cases verify the effectiveness and robustness of the method.Furthermore,for the problem of low accuracy of using finite element method in the continuum topology optimization,EDM(element differential method)which based on Lagrange isoparametric element and partial differential equilibrium equations is studied.Based on the element model and collocation balance equation in the mechanical response analysis of EDM,the adaptive collocation processing method of the element differential method is explored to simplify the method collocation process and analytical solution process.EDM exhibits higher accuracy in the grid of same scale,which provides a theoretical basis for achieving higher structural topology optimization performance.Finally,a continuum topology optimization method based on element differential method is proposed.In order to overcome the difference between the element differential method and finite element method,which makes it difficult to calculate the sensitivity in the numerical solution of continuum topology optimization,two optimization depicting models are proposed.And then the algorithm implementation and processing method of topology optimization model based on EDM are analyzed.On the contrast of the traditional continuum topology optimization method in the 2D cases such as sandwich beam,it is verified that the performances of optimized structures are improved in different application scenarios with both depicting models.