Stress analysis of linear elastic structures by the fast multipole boundary element method

In this paper a fast multipole boundary element method (FMBEM) analysis of internal stress in twodimensional linear elastic structures is presented. The expansions of the potentials occurring in the stress integral equation are obtained by the differentiation of local series built for the displacement equation potentials, and application of the strain-displacement and stress-strain relations. Results of the analysis are presented. To illustrate the accuracy of the method a stress concentration problems are considered, which are a square plate with a circular hole under tension, and a gear. The application of the FMBEM can reduce the analysis time in relation to the conventional BEM case, providing similar accuracy. Presented method can be applied in the BEM analysis of non-linear structures, which requires the evaluation of internal strains or stresses.