Internal stress calculation using an iterative subdivision scheme in the boundary element method

An iterative subdivision scheme on a nearly singular integral boundary element developed for calculating the internal stress of a two-dimensional elastic solid near the boundary is presented. In the standard boundary element method, the stress field in the interior of a solid is computed from the stress boundary integral equation (SBIE) in terms of the obtained boundary displacements and tractions. In fact, numerical errors in SBIE formulation can arise when an internal point is very close to the boundary due to the involvement of a nearly singular kernel relation. An effective approach is presented here, where the internal stresses in the so-called ‘boundary layer’ regions can be accurately determined through the imposition of an iterative subdivision scheme. This scheme is merely employed over a boundary element which contains the evaluation of nearly singular integral. To validate the proposed scheme, some numerical examples have been calculated and compared with exact or other existing solutions.