Topology optimization of structures with coupled finite element - Element-free Galerkin method

A topology optimization, based on a coupling method of finite element and meshless method, is proposed for continuum structure. A reasonable arrangement of the meshless domain can guarantee the accuracy of the meshless methods and meanwhile keep the computational efficiency of the finite element method. Besides, as the coupling method is adopted, the displacement boundary conditions are applied to finite elements nodes by standard finite element method. A dual-level density approximant is carried out to approximate and interpolate a unified and continuous density field. An unstable nodes phenomenon is observed in the interface domain, leading to nonconvergence of the equilibrium iterations. A smooth blending function and an energy convergence criterion are used to circumvent the convergent difficulty. Three benchmark problems of topology optimization are given to demonstrate the effectiveness of the proposed approach. Neither islanding phenomenon nor other common numerical instabilities of the SIMP method occur in this approach.