Abstract
The purpose of this paper is to develop exact expressions for the evaluation of singular and finite-part integrals appearing in the stress analysis of elastic solids. A numerical solution is presented for the solution of problems in three dimensional elastostatics. The kernels of the integral equation solution are given in the case where the surfaces of the solid are discretized with flat triangular elements. Exact expressions are derived for the singular and finite-part integrals over a triangular domain. The availability of exact expressions for these integrals will increase the accuracy of the numerical results without the need of any cubature formulae. Finally, the example considered in the paper indicates the excellent approximation obtained by the method even when using only a few classical elements.
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