Thermo elastic analysis of a functionally graded cylinder under internal pressure using first order shear deformation theory

Abstract

Thermo elastic analysis of a functionally graded cylinder under mechanical and thermal loads is investigated analytically in the present paper. The first order shear deformation theory (FSDT) is employed for analysis of the problem. FSDT recognizes two components for definition of the deformation. Displacement of the mid-plane and rotation about that are two components of deformation. The modulus of elasticity is assumed to vary continuously along the thickness with a power function. Stress strain relation is developed in the cylindrical coordinate system with regarding the thermal strain. Necessary equations for solving the problem have been obtained by taking variation of the energy equation with respect to four assumed functions using Euler equations. The effect of the temperature rising on the distribution of the displacement and stress for different values of non-homogenous index (n) are investigated in the present paper. Evaluation of the axial displacement of cylinder can be presented as an important result of this paper. Furthermore, the present result is compared with results that were obtained using the plane elasticity theory. Key words: Thermo elastic, shell, temperature, cylinder, energy.