ON THE NONSINGULAR TRACTION-BIE IN ELASTICITY

The work reported herein develops a generalized traction-BIE formulati on which involves only weakly singular integrals (in the three-dimensi onal problem) or totally regular integrals (in the two-dimensional pro blem). The first step deals with the terms in the Somigliana displacem ent identity, and then the derivatives of these terms. The only condit ions required for the existence of the traction-BIE and the related So migliana stress identity are weak continuity of the in-plane derivativ es of the surface displacements and of the surface tractions. It is sh own that the Cauchy Principal Value (CPV) interpretations so commonly used in BIE developments are unnecessary. The formulation is establish ed not only at a smooth boundary point, but also at a corner point. Th e extension of the non-singular formulation to discontinuous boundary tractions and tangential derivatives of the boundary displacements app licable to a generalized problem statement as well as the usual BEM im plementations is also shown. In the demonstrated formulation, the sour ce points are located directly at the boundary nodes and non-conformal elements are not needed.