Axisymmetric thermo-elasticity field in a functionally graded circular plate of transversely isotropic material

Abstract

This paper presents a set of axisymmetric analytical solutions of the thermo-elasticity field induced by the external thermal load, in a heterogeneous circular plate. The plate can be either simply supported or clamped, and the properties of the transversely isotropic material are assumed to be functions of the thickness coordinate. Three typical types of thermal boundary conditions are considered and the corresponding temperature fields are determined. A direct displacement method is used to solve the governing equations for the elastic field in plate. The displacement functions pertinent to the current problem are solved by a step-by-step procedure of integration. The corresponding integral constants are determined by using the cylindrical boundary conditions in the Saint-Venant’s sense. In the present solutions, all of the material coefficients can vary independently and continuously along the thickness direction. Numerical calculations are performed to validate the present solutions and to show their applications to a heterogeneous model. The influence of the material heterogeneity is finally addressed. Since no ad hoc hypotheses on the elastic deformations of the plate are introduced, the present solution can be a nature benchmark to various plate theories and numerical codes.