In this article, coupled thermoelasticity (without energy dissipation) based on Green-Naghdi model is applied to functionally graded (FG) thick hollow cylinder. The meshless local Petrov-Galerkin method is developed to solve the boundary value problem. The Newmark finite difference method is used to treat the time dependence of the variables for transient problems. The FG cylinder is considered to be under axisymmetric and plane strain conditions and bounding surfaces of cylinder to be under thermal shock loading. The mechanical properties of FG cylinder are assumed to vary across thickness of cylinder in terms of volume fraction as nonlinear function. A weak formulation for the set of governing equations is transformed into local integral equations on local subdomains by using a Heaviside test function. Nodal points are regularly distributed along the radius of the cylinder and each node is surrounded by a uni-directional subdomain to which a local integral equation is applied. The Green-Naghdi coupled thermoelasticity equations are valid in each isotropic subdomain. The temperature and radial displacement distributions are obtained for some grading patterns of FGM at various time instants. The propagation of thermal and elastic waves is discussed in details. The presented method shows high capability and efficiency for coupled thermoelasticity problems.

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