Topology optimization method with direct coupled finite element-element-free Galerkin method

A topology optimization method, based on a direct coupled finite element (FE) and element-free Galerkin (EFG) method, is developed in this study, for reducing the computational cost of EFG-based topology optimization methods. Comparing with other coupling methods, the new coupling method can guarantee higher order continuity of the shape function in the coupling region and it can be implemented easily. A constrained centroidal Voronoi tessellation (CCVT) algorithm associated with density variable is developed to generate updated EFG nodes for the discretizing of EFG domain during the iterations which accelerates the optimization convergence. To reduce the computational cost, an adaptive multi-level Gauss quadrature scheme is introduced for numerical integration. Several examples are given to demonstrate the effectiveness of the proposed approach and the proposal shows advantages comparing with some other topology optimization methods.