Topology optimization of free vibrating continuum structures based on the element free Galerkin method

In this paper, the topology optimization design of the free vibrating continuum structures is formulated based on the element free Galerkin (EFG) method. Considering the relative density of nodes as design variable, and the maximization of the fundamental eigenvalue as an objective function, the mathematical formulation of the topology optimization model is developed using the solid isotropic microstructures with penalization (SIMP) interpolation scheme. The topology optimization problem is solved by the optimality criteria method. Finally, the feasibility and efficiency of the proposed method are illustrated with several 2D examples that are widely used in the topology optimization design.