Displacement and temperature discontinuity boundary integral equation and boundary element method for analysis of cracks in three-dimensional isotropic thermoelastic media

• The fundamental solutions for unit point displacement and temperature discontinuities are derived.
• The displacement and temperature discontinuity boundary integral equation method is developed.
• The displacement and temperature discontinuity boundary element method is proposed.
• The stress and heat flux intensity factors are derived in terms of displacement and temperature discontinuities.

The displacement and temperature discontinuity boundary integral equation and boundary element method are developed for the analysis of cracks in three-dimensional isotropic thermoelastic media. The fundamental solutions for unit point displacement and temperature discontinuities are derived, and the displacement and temperature discontinuity boundary integral equations are obtained for an arbitrarily shaped planar crack. The displacement and temperature discontinuity boundary integral equation method is developed to analyze singularities of near-crack border fields, and the stress and heat flux intensity factors are derived in terms of displacement and temperature discontinuities across crack faces. The fundamental solutions for a constant triangular element are obtained by integrating the fundamental solutions for unit point displacement and temperature discontinuities. On the basis of these solutions, the displacement and temperature discontinuity boundary element method is proposed. As an application, elliptical cracks are analyzed to validate the developed method.