S-FEM Method

Level set methods are becoming an attractive design tool in shape and topology optimization for obtaining efficient and lighter structures. Since the boundary represented by the zero level set is moving across the elements of a fixed mesh, modelling of a moving local domain by the standard finite element method (FEM) becomes cumbersome due to the re-meshing involved to match the changing geometry.  

In our study, a dynamic implicit boundary-based moving superimposed finite element method (s-version FEM or S-FEM) is developed for structural topology optimization using the level set methods. A coarse fixed Eulerian mesh consisting of bilinear rectangular elements is used as a global mesh. The local mesh consisting of flexible linear triangular elements is constructed to match the dynamic implicit boundary captured from nodal values of the implicit level set function. The proposed moving S-FEM is applied to structural topology optimization and the normal velocity field of the boundary of the shape can be accurately predicted from the present moving S-FEM due to its local mesh refinement and consistent methodology. It is suggested that the present S-FEM can be a promising tool for shape and topology optimization using the level set methods.

1. Integration of the S-FEM method with both shape and topology optimization.

2. Improvement of computational efficiency of the S-FEM modeling via code optimization.

3. More flexible construction of the local FEM model.

4. Applications to other classical structural topology optimization problems.

5. Extensions to general problems with moving boundary.

• Research Grants Council (RGC) Competitive Earmarked Research Grant (CERG), Structural Shape and Topology Optimization Using Level-Set Methods (CUHK4164/03E).

• The Natural Science Foundation of China (NSFC). The Overseas Young Investigator Collaboration Award (50128503).

• Post-doctoral Fellowship grant from the Chinese University of Hong Kong (No. 03/ENG/12 and No. 04/ENG/1).