Thermal stress analysis of a parabolic inhomogeneity under uniform remote heat flux and uniform temperature change

Abstract

We study the distributions of temperature and thermal stresses within a parabolic inhomogeneity when the surrounding matrix is subjected to a system of uniform remote heat flux. Our analysis indicates that: in general, the temperature and the thermal stresses inside the inhomogeneity are linear functions of the two in-plane Cartesian coordinates; and, in particular, the normal stress perpendicular to the axis of symmetry of the parabola is uniform within the inhomogeneity. When the inhomogeneity-matrix system undergoes a uniform temperature change, the normal stress parallel to the axis of symmetry of the parabola is uniform inside the inhomogeneity whereas the other two in-plane stress components are zero inside the inhomogeneity.