Accurate interior point computations in the boundary integral equation method

Abstract

This paper describes an implementation of the direct boundary integral equation method for problems of linear, elastostatic stress analysis. Isoparametric, quadratic boundary elements, with numerical integration of the kernel-shape function products, are employed for the numerical study. In the portion of a solid which is very close to a discretized surface, solutions generated with such boundary elements are subject to numerical error. A simple superposition procedure is described which eliminates the most inaccurate influence coefficients as well as the jump terms which arise when the interior point reaches the surface. This leads to accuracy in the near-surface area which is equal to that on the surface. The numerical integration effort is no greater than that required to generate the boundary solution. Both the interior body problem (a finite solid) and the exterior body problem (a cavity in an infinite solid) are analyzed and the method is demonstrated for the test problem of a spherical cavity in an infinite body. The procedure should be able to be implemented in most elastostatic boundary element programs which employ the conventional direct formulation and which integrate the kernel-shape function products numerically. As well, it is applicable in nonlinear problems and in other fields which use singular integral equations, such as elastodynamics.