RBF-Level Set for Structural Optimization

In the level set-based structural topology optimization, it is required that the boundary be smooth enough such that the stable propagation of the front can be guaranteed and the numerical instabilities can be prevented. Since a fixed Eulerian mesh is usually adopted and only nodal values of the implicit level set functions are availabe, it is necessary to estimate the implicit boundary of the shape by approximation and interpolation. On the other hand, Radial Basis Functions (RBFs) are a modern and powerful tool which works well in general circumstances. RBFs are popular for interpolating scattered data to produce smooth surface/boundary. Therefore, it is very natural to develop a RBF-level set method for structural topology optimization.  

In our study, a new RBF-level set method is developed for structural topology optimization. The positive features of radial basis functions such as the unique solvability of the interpolation problem, the computation of interpolants, their smoothness and convergence have been integrated into the optimization procedure to improve the efficiency and accuracy of structural topology optimization using the level set methods.

1. Integration of the RBFs and level set methods with shape\topology optimization.

2. Appropriate separation of the unknowns in the level set transport equation via the RBFs.

3. Physically meaningful velocity extension and the collocation method.

4. Efficient heuristic update of the design variables and variation of the topology.

5. Introduction of the S-FEM method and a semi-Lagrangian approach.

• 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).