Two-dimensional Beltrami–Michell equations for a mixture of two linear elastic solids and some applications using the Airy stress function

Abstract

This paper presents the derivation of the Beltrami–Michell equations for plane stress and plane strain for a mixture of binary linear elastic solids. These equations are then used to solve the thin rotating circular disk and long rotating cylindrical rod problems by employing the Airy stress function, without neglecting the body forces of the constituents. The effect of the parameter α2 (the diffusive force coefficient) on the behavior of the mixture constituents is also investigated.