Element subdivision technique for coupling-matrix-free iterative s-version FEM and investigation of sufficient element subdivision

In s-version finite element method (s-FEM), a local mesh is superposed on a global mesh, and they are solved monolithically. The local mesh represents the local feature such as a hole, whereas the global mesh does the shape of a structure. Since the two meshes are generated independently, mesh generation becomes very tractable. However, s-FEM has a difficulty that the generation of coupling stiffness matrices takes a lot of computational efforts. To overcome this difficulty, the authors proposed coupling-matrix-free iterative s-FEM. In this method, the coupling stiffness matrices are computed implicitly by stress integration on one mesh and stress transfer from one mesh to the other mesh. Converged solution is obtained by iteration. However, in practical cases, unnatural stress oscillations can occur with conventional Gaussian quadrature. In this paper, in order to smooth unnatural stress oscillations, element subdivision technique is applied. Element subdivision technique can deal with the discontinuity of discretized stress along element interfaces. The stress transfer scheme in coupling-matrix-free iterative s-FEM is designed to work harmoniously with element subdivision. Moreover, element subdivision strategy to obtain smooth stress distribution is investigated in the numerical experiments of a circular hole problem. We propose the element subdivision strategy as the following two items. First, at least 4 x 4 element subdivision should be adopted to obtain smooth stress distribution. Second, the local mesh should be fine enough to evaluate stress concentration accurately. To confirm this strategy, global and local meshes for elliptical hole problems are designed by following this strategy. Even in severe stress concentration problems, unnatural stress oscillations, which occur with conventional quadrature, is smoothed obviously with 4 x 4 element subdivision. In addition, stress concentration is evaluated accurately due to the second item of the strategy.