Revisit of the free terms of the dual boundary integral equations for elasticity

Abstract

Dual boundary integral equations for elasticity problems with a smooth boundary are derived by using the contour approach surrounding the singularity. Both two and three-demensional cases are considered. The potentials resulted from the four kernal functions in the dual formulation have different properities across the smooth boundary. The Hadamatd principal value or the so called Hadamatd finite part, is derived naturally and logically and is composed of two parts, the Cauchy principal value and the unbounded boundary term. After collecting the free terms, Cauchy principal value and unbounded termsm the dual boundart integral equations of the problems are obtained without infinity terms. A comparison between scalar (Laplace equation) and vector (Navier equation) potentials is also made.