Structural Optimization Techniques Based On Level Set Methods

Topology optimization of continuum structures has received more and more research attentions in the past twenty years, which is regarded as one of the most challenging research topics. The most popular approaches for topology optimization of continuum structures are homogenization approach and variable density approach. In this paper, the techniques for topology/shape optimization of continuum structures based on Level Set Method are studied.Level Set Method(LSM) was a numerical method for tracing the propagation of dynamic interfaces. Since proposed by Sethian and Osher in 1988, it has had extensive applications in many areas including image processing, fluid mechanics, etc. Sethian and Sethian introduced LSM into the field of structural optimization in 2000. Then it aroused high attention and much interest in researchers around the world for its special advantages. As Bendson said in one of his monographs in 2002, the research work about structural optimization based on LSM was in the initial stage.This thesis focuses on the techniques of structural optimization based on LSM, and by studying and fully utilizing the characteristics and advantages of LSM, we try to solve difficult problems in structural optimization for traditional approaches.In this thesis, topology/shape optimization under topology-dependent loads, which is hard to deal with by traditional approaches, is studied and good results are obtained by LSM. Furthermore simultaneous shape and topology optimization approach based on topology description functions is proposed. Because topological derivative is introduced into the topology optimization, the efficiency of computation is greatly improved. Then the rational evolution method in structural topology optimization is proposed in the frame of LSM, and it's proved to be stable and efficient by numerical results. Moreover Extended Finite Element Method is successfully implemented and integrated with LSM, and is adopted in our research work about shape optimization based on Euler description. Besides the approach based on topology description function is proposed for the design of the microstructures of composite materials with prescribed properties.As showed in our research work, LSM has unique advantages, which other approaches do not have in structural optimization, and is a valuable research topic.