On plane stress state and stress free deformation of thick plate with FGM interface under thermal loading

Abstract

This paper demonstrates the plane stress state and the stress free thermo-elastic deformation of FGM thick plate under thermal loading. First, the Sneddon-Lockett theorem on the plane stress state in an isotropic infinite thick plate is generalized for a case of FGM problem in which all thermo-mechanical properties are optional functions of depth co-ordinate. The proof is based on application of the Iljushin thermo-elastic potential to displacement type system of equations that reduces it to the plane stress state problem. Then an existence of the purely thermal deformation is proved in two ways: first, it is shown that the unique solution fulfils conditions of simultaneous constant temperature and linear gradation of thermal expansion coefficient, second, proof is based directly on stress type system of equations which straightforwardly reduces to compatibility equations for purely thermal deformation if only stress field is homogeneous in domain and at boundary. Finally, couple examples of application to an engineering problem are presented.