Determination of interior point stresses in two dimensional BEM thermoelastic analysis of anisotropic bodies

In conventional boundary element method (BEM) analysis, the displacements and stresses at an interior point of an elastic body are obtained using the respective Somigliana's identities, after the boundary solutions for the displacements and tractions have been solved for. This paper presents the derivation of Somigliana's identity for the strains at any interior point of an anisotropic domain subjected to thermal effects. From these strains, the corresponding stresses at the interior point may be calculated directly using the Duhamel-Neumann relation. This identity is obtained in terms of integrals over the boundary of the solution domain only. Difficulties arising from the exact transformation of the volume integral term associated with thermal loading in BEM analysis into surface integrals in the anisotropic case are discussed and the procedures to overcome them are described. Three numerical examples are presented to demonstrate the veracity of the formulations developed.