Thermoelastic Problems of Thin Circular and Rectangular Plates

In this paper an attempt is made to determine the temperature, displacement and stress functions of a thin circular plate by applying finite Hankel transform and Laplace transform techniques. This plate that is assumed to be in the plane state of stress is subjected to axisymmetric boundary conditions. As a further simplification, special cases of the third kind of boundary condition are used on the two plane surfaces, while zero temperature is maintained on the outer curved surface of the thin circular plate. A particular case of the boundary conditions is discussed in detail, and numerical results are presented graphically. A mathematically similar problem is that of determining temperature distribution, displacement and stress functions on an edge of a thin rectangular plate with the stated boundary conditions. The results are obtained by applying finite Marchi–Fasulo transform and Laplace transform techniques.