Structural Topology Optimization Method Based on Adaptive Finite Element Method

Abstract: For the existing problems of Structural Topology Optimization methods, such as mesh dependence, checkerboard , structure singularity and so on , some solutions are proposed, especially Bi-directional Evolutionary Structural Optimization based on adaptive finite element method.Firstly, after analysing and comparing all kinds of topology optimization methods, the simple and practical Evolutionary Structural Optimization is chosen as the base of this thesis .And the reasons due to the problems are analysed and summarized.Secondly, the solutions of problems are proposed:(1) For structure-singularity problem, the solution is given which can solve structure singularity problem and assure the topology optimization converging rapidly. For the checkerboard problem, the triangle element is used to replace quadrangle element as basic mesh of finite element method for triangle elements can compose random graphics, which can reduce checkerboard effectively.(2)For adaptive finite element method applying in topology optimization well, a improved Delaunay Triangle method is proposed, which can be adaptive to all kinds of static or dynamic complicated boundary multi-connected domain (3)For the mesh dependence problem, two methods are proposed: Bi-directional Evolutionary Structural Optimization basing on error estimator and Bi-directional Evolutionary Structural Optimization basing on adaptive finite element method .The former is easy to program and solve mesh dependence problem at a certain extent .The latter can solve mesh dependence problem well , though it is not easy to program relatively.Finally, the two methods of this thesis are compared to several kindsof topology optimization methods in order to show the methods validity andapplicability…
Key words: Topology Optimization; Error Estimation; Mesh Refinement; Adaptive Finite Element Method; Delaunay Triangle Method; Checkerboard; Mesh Dependence; Structure Singularity

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