Material Nucleation and Topological
Derivatives in Solid Optimization

Topology optimization is at highest level in the field of structure optimization. The introduction of level set methods into this field is an important breakthrough. The powerful capability of level set methods has been demonstrated in this field. However, a congenital defect of the level set method is that it can easily emerge but can not create holes in the described domain. The nucleation of new holes in interior domain can only occur under the manual interposition but cannot produce with its own evolution.

Topological derivative approach is a recently developed procedure to overcome this problem. Topological derivative approach is a better way that can forecast the topology of structure and indicate the place to create new holes. It can enhance the efficiency of the level set method in topology optimization process. Topological derivative is a sensitivity measure that has been used by many researchers to solve topology optimization problems recently. Compared with the shape derivative, it can account for the sensitivity of creating a hole at the interior point of the design domain.

1. Geometry control in structural optimization.

2. Techniques of curvature diffusion in structural topology optimization.

• HKSAR Research Grants Council (RGC) Competitive Earmarked Research Grant (CERG), Design and Optimization of Heterogeneous Objects Using Multi-Phase Level-Set Models and Topological Derivatives (CUHK/416205).

• HKSAR 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.