Optimal Embedding Objects In The Topology Design Of Structure

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 optimization of continuum structures based on Level Set Method and variable density approach 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.The purpose of my paper is to study a new optimal embedding bodies problem in topology optimization. On the one hand, the new approach is developed in the use of level set method. By employing this method, the embedding bodies can be represented by a level set function implicitly, thus the optimization of structure topology is transferred to find the optimal level set function. On the other hand, the structure topology connecting the embedding bodies can be found by SIMP method. As a result, the difficulties associated with description of the embedding bodies can be overcome in an efficient and robust way. There are two core techniques in my paper. The first one is the use of the level set to descripe the embedding objects. The other one is the control of superposition of the embedding objects through the area of objects.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.