Topology optimization with a penalty factor in optimality criteria

Topology optimization is one of the most important methods of reducing the weight of structure. Optimality Criteria method (OC) as a heuristic way can be used to deal with this problem efficiently. Popular SIMP method implements micro-structural density as the design variable. During the process of optimization, numerical instabilities are always observed; Moreover, higher penalty factor is not better for decreasing intermediate density elements. In this paper a penalty factor is imposed in OC method, and a relation between the filtering area and elements is also obtained. Meanwhile, the nodal density is used as design variable for more smoothing boundary. The results show that numerical stability can be obtained, checkerboard patterns haven't been observed, and the clear boundary of structure has been developed.