Validity conditions of the direct boundary integral equation for exterior problems of plane elasticity

TL;DR

This paper investigates the validity conditions of the direct boundary integral equation in plane elasticity exterior problems, proposing a new approach that relaxes restrictive assumptions, especially for cases with non-zero resultant forces.

Contribution

It introduces a modified formulation considering displacements relative to a finite point, broadening the applicability of the boundary integral method in elasticity.

Findings

Wider validity conditions for the boundary integral equation.

Effective handling of non-zero resultant forces.

Relaxation of asymptotic behavior hypotheses.

Abstract

Writing the boundary integral equation for an exterior problem of elasticity is subordinate so far to hypotheses on the asymptotical behaviour at infinity of solutions. The sufficient conditions met in the literature are too restrictive and do not notably cover the case when the loading has a non zero resultant force. This difficulty can be removed by considering the problem in displacements relatively to one point located at a finite distance from the loading. Finally, this auxiliary problem allows widening the conditions of validity of the usual formulation of the direct integral method.