Analytical integration and exact geometrical representation in the two-dimensional elastostatic boundary element method

Two ways of improving the accuracy of results in the boundary element method are considered. Since the geometries of many problems of practical interest are created from straight lines and circular arcs, errors caused by representing such geometries approximately using quadratic shape functions can be removed using exact geometrical representations for straight and circular boundaries. Besides, exact geometrical representations enable exact analytical integrations for some situations, thereby eliminating the errors caused by approximate numerical integration. The results of some simple test problems show that the use of exact representation of straight and circular geometries, and analytical integration in the situations where this is possible, offers worthwhile benefits in the boundary element analysis of two-dimensional elastostatics problems.