Thermal Bending Stresses Analysis of a Clamped Elliptic Plate under Thermal Load

The present paper concerned with an analysis of the thermal bending stresses of a heated thin elliptical plate with clamped edges under transient temperature distribution using Berger's approximate methods. The prescribed surface temperature is on the top face of the plate while the bottom face is kept at zero temperature and the fixed circular edge is thermally insulated. In this study, the Laplace transform as well as the classical method has been used for the solution of heat conduction equation. The thermal moment is derived on the basis of temperature distribution, and its stresses are obtained using resultant bending moment and resultant forces per unit length.Thermally induced deflection results and its associated stresses are obtained in terms of Mathieu function of the first kind of order 2n by the quasi-static approach. Furthermore, aforementioned problems can be degenerated into the problems of the circular region by applying limiting conditions. The numerical results for temperature, deflection and bending stresses using thermal moment is verified by means of computational tools and illustrated graphically.