Topology optimization of structures using the generalized finite point method

In this paper, the procedure of topology optimization of continuum structures is combined with a meshfree method known as the Generalized Finite Point Method (GFPM). A density approach is employed to find the optimal material distribution in a continuum domain. GFPM is used to perform the structural response analysis as well as the sensitivity analysis. The optimization problem is solved by using the Method of Moving Asymptotes (MMA) where the objective function is the compliance energy and nodal densities are used as design variables. Optimization procedure is based on a sequential refinement strategy for the discritized field of design variables. A numerical example is presented to illustrate the feasibility of the proposed approach. It is observed that this method prevents some numerical instabilities such as appearance of checkerboard patterns and mesh-dependence phenomena

Keywords:

Topology optimization , mesh-free , Method of Moving Asymptotes , checkerboard pattern , mesh-dependence