Analytic integration of kernel shape function product integrals in the boundary element method

In this paper, analytic integration procedures are presented for non-singular, nearly singular and nearly hyper-singular boundary element integrals in two-dimensional (2-D) elastostatics. Both curved and straight boundaries are considered for this purpose. In the former case, a series approximation is adopted and in the latter case the integrals are evaluated exactly. In the analytical results the geometry is kept in symbolic form. Integral result for a particular element can be obtained after giving appropriate numerical values to the analytical results. Convergence aspects of these analytical results are studied in detail. The analytical integral results are then used for analysis of 2-D structures in elasticity.