ABSTRACT
The scaled boundary finite element method (SBFEM) models the linear elastostatics problem excellently and out-performs the finite element method (FEM) when solving problems involving unbounded domains or stress singularities. This study enhances the classical energy norm based adaptive procedure by introducing new refinement criteria, based on the projection-based interpolation technique and the steepest descent method, to drive the mesh refinement. The technique is applied to /-adaptive procedure in this paper but an extension to other adaptive versions such as h- and hp-adaptivity is straightforward. The reference solution, which is the solution of the fine mesh formed by uniformly refining the current mesh, is used to represent the unknown exact solution. In the conventional adaptive approach, the optimum mesh is assumed to be obtained when each element contributes equally to the global error. In the new adaptive approach, the projection-based interpolation technique is developed for 2D in the scaled boundary finite element method and the projection-based interpolants are computed from different approaches. New refinement criteria are proposed. The optimum mesh is assumed to be obtained by maximizing the decrease rate of the projection-based interpolation error appearing in the reference solution. Numerical studies show that the new approach out-performs the conventional approach.
