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Abstract
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According to available literature, investigations on the thermo-elastic analysis of spherical shells are limited to single layered shells and without considering the temperature dependence of material properties. Also, most of these works are done based on Fourier heat transfer law. In this thesis, thermo-elastic analysis of multilayered spherical shells with functionally graded layers under axisymmetric thermo-mechanical loading is presented based on the elasticity theory. To consider the effects of finite speed of thermal wave propagation, the non-Fourier heat equation is employed to investigate the temperature distribution in the shell. In addition to convection heat transfer, the radiative boundary conditions at the inner and outer surfaces of shell are considered. The material properties are assumed to be temperature-dependent and have a continuous variation in the thickness direction. In order to accurately model the variation of the field variables across the thickness, the shell is divided into a set of mathematical layers. The differential quadrature method (DQM) as an accurate and computationally efficient numerical tool is adopted to discretize the governing differential equations of each layer together with the related boundary and compatibility conditions at the interface of two adjacent layers. The incremental differential quadrature method (IDQM) is adopted to discretize the governing differential equations in temporal domain. The Newton–Raphson method is used to solve the resulting nonlinear system of differential equations. In addition, the steady state thermo-elastic analysis of multilayered spherical shells with functionally graded layers surrounded by an elastic media is analyzed by the presented method. As a particular case, an analytical solution is presented for a FG single layer spherical shell. The presented formulation and method of solution are validated by showing their fast rate of convergence and by comparing the results with those avai
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