Level Set Method In Topology Optimization Of Continuous Structure

Topology optimization had been used widely in the design of structures. Here, we introduced a new approach of topology optimization named level set method, which had advantage over traditional optimization in handling the topological transformation and no mesh dependency. We mainly discussed the basic theory of level set method, level set method in topology optimization and its improvement.In this thesis, based on the theory of level set method, we established level set model of the topology optimization, then discussed the solution of the level set equation, and gave the classical level set algorithm.The classical level set algorithm could not produce a new hole in the process of optimization, and had some requirements on the initial design. In order to solve this problem, we presented the theory of topological derivative, which combined with level set optimization yields a improved level set algorithm.At last, numerical examples, which were written in Matlab, were given to compare the classical level set algorithm and the improved level set algorithm. Results showed that the improved level set method was successful and effective.