Axisymmetric Thermoelastic Response in a Semi-elliptic Plate With Kassir’s Nonhomogeneity in the Thickness Direction

Abstract

The main objective is to investigate the transient thermoelastic reaction in a nonhomogeneous semi-elliptical elastic plate heated sectionally on the upper side of the semi-elliptic region. It has been assumed that the thermal conductivity, calorific capacity, elastic modulus and thermal coefficient of expansion were varying through thickness of the nonhomogeneous material according to Kassir’s nonhomogeneity relationship. The transient heat conduction differential equation is solved using an integral transformation technique in terms of Mathieu functions. In these formulations, modified total strain energy is obtained by incorporating the resulting moment and force within the energy term, thus reducing the step of the calculation. The thermal deflection equation derived from the Berger approach is compared with Von Karman approaches, and its maximum normal stresses are determined. The numerical calculation is performed over the metal-metal based composite and graphically portrayed. Furthermore, by applying limiting conditions, the semi-elliptic region can be degenerate into a semi-circular plate. Results reveal that the highest tensile stress exists on the semi-circular core relative to the semi-elliptical core, suggesting the propagation of low heating due to insufficient heat penetration into the elliptic surface