Analyzing a functionally graded pressurized cylinder of arbitrary material distribution subjected to thermal loading

Abstract

In this paper, a functionally graded long hollow cylinder of arbitrary material distribution under thermo-mechanical loading is studied analytically with the aim of briefing engineers by optimum design criteria. In order to solve the related elastic problem, the graded layer is divided into a number of sublayers; where in each sublayer the mechanical and thermal properties may appropriately be assumed to be constant. Based on this assumption an axisymmetric analytical elastic solution is presented for the coupled thermo-mechanical problem. Without loss of generality, numerical results are generated for a case in which the cylinder is assumed to be consisted of three layers; two homogeneous ceramic and metallic layers at the inner and outer surfaces and a functionally graded interlayer. By means of the presented elastic solution, the effect of thermal expansion coefficient, modulus of elasticity and material properties distribution is investigated. In addition, these parameters are set in a way to obtain minimum and smooth variation of stress inside the cylinder. In general, the results of this study show that in contrary to anticipations, the minimum and smooth stress variation case is met when the value of the material properties of the constituting phases of the graded layer are far from each other, which may be considered as the most important finding of this research. In addition, selecting a stiffer material as the ceramic phase at the inner surface results in lower stresses in the outer metal layer.