Evaluation of in-boundary stress in 2D BEM for isotropic elasticity. A comparative study

The present work deals with the recovery of the in-boundary stress on smooth boundary parts in Boundary Element Method (BEM) in two dimensions. First, two Boundary Integral Representations (BIRs) of tangential derivative of boundary displacements, whose integral kernels multiplying either tangential derivative of displacements or displacements are smooth and bounded, are presented. Two procedures for an in-boundary stress recovery based on these BIRs are developed and analyzed. The first procedure, which directly uses the results obtained from a BEM analysis, displacements and tractions, requires the performing of integrations involved in these BIRs either over the real boundary of the solid or over a smooth approximation of the boundary part where the evaluation point is placed. The second procedure, which can be applied on a non-smooth (e.g. polygonal) approximation of the boundary, requires the use, in the first BIR introduced here, of an integral density which is previously smoothed by a local smoothing procedure. The third recovery procedure considered in this work is directly given by a local smoothing procedure of this kind. Results obtained by these three recovery procedures are compared in a series of numerical tests, the best results being obtained by the first procedure developed in this work.