On the nonsingular tractionBIE in elasticity
Abstract
The work reported herein develops a generalized tractionboundary integral equations (BIE) formulation which involves only weakly singular integrals (in the threedimensional problem) or totally regular integrals (in the twodimensional problem). The first step deals with the terms in the Somigliana displacement identity, and then the derivatives of these terms. The only conditions required for the existence of the tractionBIE and the related Somigliana stress identity are weak continuity of the inplane derivatives of the surface displacements and of the surface tractions. It is shown that the Cauchy principal value (CPV) interpretations so commonly used in BIE developments are unnecessary. The formulation is established not only at a smooth boundary point, but also at a corner point. The extension of the nonsingular formulation to discontinuous boundary tractions and tangential derivatives of the boundary displacements applicable to a generalized problem statement as well as the usual BEM implementations is also shown. In the demonstrated formulation, the source points are located directly at the boundary nodes and nonconformal elements are not needed.
 Publication:

International Journal for Numerical Methods in Engineering
 Pub Date:
 June 1994
 DOI:
 10.1002/nme.1620371204
 Bibcode:
 1994IJNME..37.2041H
 Keywords:

 Boundary Element Method;
 Elastic Properties;
 Integral Equations;
 Traction;
 Displacement;
 Stresses;
 Structural Mechanics