SYSTEMATIC DERIVATION OF CONTOUR INTEGRATION FORMULAS FOR LAPLACE ANDELASTOSTATIC GRADIENT BIES

A complete set of contour integrands is derived for the primary BIE's of elastostatics and potential flow. Because of surface-independent pr operties of vector potentials, these apply to non-planar surfaces and can be differentiated at the fixed point, producing contour integrands for both the so-called hypersingular and Cauchy singular parts of the gradient BIE. The results are applicable to 'far field', 'near field' and 'on surface' cases. Numerical examples demonstrate exact agreemen t with surface quadrature, and contour plots are given showing variati on of the hypersingular integrands in 'on surface' cases.