Singularity analysis for 2D and 3D thermoelastic media containing V-notches

Abstract

ABSTRACTThe stress field and heat flux singularities at the vertex of two-dimensional (2D) and three-dimensional (3D) V-notches are, respectively, investigated. By introducing typical terms in the series asymptotic expansions of displacement and temperature fields near the notch tip, the thermoelastic governing equations and radial boundary conditions of a V-notched structure are transformed into characteristic ordinary differential equations with respect to the singular order. These equations can be solved by the interpolating matrix method developed earlier by part of the authors. The singular orders related to the stress field and heat flux can be derived simultaneously and can be specified by the corresponding characteristic angular functions in the present method. The singularities are compared between 2D and 3D thermoelastic specimen containing V-notches. It is found that one singular order will be discarded if a 3D medium is simplified into a 2D one.