Nonlinear Thermo-Elastic Analysis of FG Cylinder with Temperature-Dependent Properties with Perturbation and Differential Quadrature Methods

In this article, thermo-elastic analysis of a thick hollow cylinder under internal pressure is investigated. The material properties are considered to be temperature-dependent and functionally graded in radial direction. This temperature dependency caused the heat conduction equations to be nonlinear. The perturbation theory is performed for solving nonlinear heat conduction equations of the cylinder. Arbitrary combined thermal boundary conditions containing temperature and temperature gradient are considered. As the temperature field is extracted, it can be used to solve decoupling thermal stress governing equations. These thermo-elastic equations and related boundary conditions are discretized in strong form using differential quadrature method. Numerical results extracted from the suggested semi-analytical approach in a linear regime are then compared to the existing results. It is depicted that the presented method benefits from the low computational and high convergence behavior. The stress distribution of the cylinder is computed by considering the approximation of the temperature in zeroth-order, one-order as well as second-order. In order to achieve proper accuracy, more terms of the perturbation approximation series should be considered for the higher temperature difference between the inner and outer surfaces of the cylinder.