Calculation of interior point stresses in two-dimensional boundary elementanalysis of anisotropic bodies with body forces

The true boundary integral equation, based on the so-called direct formulat ion of the boundary element method (BEM), for two-dimensional anisotropic e lasticity with body forces has only recently been reported in the literatur e. It involved transforming a volume integral term associated with the body forces into integrals around the surface of the domain. In the general cas e, this transformation for anisotropic elasticity gives rise to a series of line integrals along paths which traverse the domain, but their numerical evaluation does not pose any difficulties for the solution of the unknown b oundary displacements or tractions. Similarly, the displacements at interio r points of the anisotropic domain can be directly calculated using Somigli ana's identity for displacements. However, because of the presence of the e xtra line integrals in this identity as well, the strains, and hence the st resses, at these points cannot be obtained by simple direct differentiation of the identity. In this paper, the mathematical difficulties associated w ith the determination of interior point stresses for an anisotropic domain with body forces using the BEM are discussed and overcome. The correspondin g Somigliana's identity for strains is derived, from which the stresses at the interior point may be obtained. The veracity of the formulation is then demonstrated by three examples.