Topology optimization of hyperelastic structure based on a directly coupled finite element and element-free Galerkin method

Meshless methods can solve large classes of problems where grid-based methods are awkward to handle, such as the discretizing of complicated structures, the remeshing in large displacement problems and so on. In this study, a meshless-based topology optimization is proposed for large displacement problems of nonlinear hyperelastic structure. In order to circumvent nonlinear numerical instabilities, the linear and nonlinear analyses are set in the low- and high-stiffness region, respectively. Thus, an interpolation scheme is adopted for hybridizing the linearity and nonlinearity in the structure analysis. A directly coupled finite element and meshless method is introduced to reduce the computational cost of meshless methods and an auto-coupling strategy is proposed for the adaptive arrangement of finite element and meshless regions. Several numerical examples are given to demonstrate the effectiveness of the proposed method.