Application of the boundary element method to elastic orthotropic materials in 2D: Numerical aspects

A formulation of the Somigliana displacement and stress identities for plane orthotropic elastic bodies is introduced. Simple explicit formulae in complex variable of all the integral kernels and the free term tensor in the Somigliana displacement identity are presented. A BEM implementation of both identities is described and a comparative study of analytical and numerical integrations from the point of view of computational time and solution accuracy is performed. A study of error and convergence rate in stress computation at the center of linear elements by means of two approaches, a direct application of the hypersingular Somigliana stress identity and computing stresses directly from the nodal values of displacements and tractions, is performed. A similar study of stress computation inside the body and near the boundary is performed as well. Results of these two studies allow a deeper understanding of the so-called boundary layer effect in stress computation near the boundary for orthotropic materials.