The use of functionally graded materials (FGM) has gained much popularity in recent years in extreme high temperature environment such a nuclear reactor and high speed spacecraft industries. Buckling is the most important in these structures. In this thesis thermal and mechanical buckling of FGM cylindrical shell in thermal environment, under axial and radial load are discussed. It is assumed that the shell is a mixture of metal and ceramic that his properties change continuously and smoothly through its thickness of shell, according to a power law distribution of volume fraction of constituents, temperature-dependent material properties are taken onto account. The governing equations are based on the first-order shell theory and the nonlinear strain-displacement relations of large deformation. based on Donnell’shell theory the equilbrium equation and stability equation of cylindrical shell are derived firstly, Then the results are presented for shell with simply supported boundary condition subjected to three types of thermal loading. Also stability state of FGM cylindrical shell is derived by applying the finite element method on the second variation of potential energy (Trefftz criterion). ABAQUS software was used to solve for instability problem, The analytical results are compared and validated using the finite element method. Finally thermal buckling under mentioned thermal conditions, in the two modes of temperature-dependent properties and properties independent of temperature has been investigated. Numerical results show various effects of power law exponent, temperature and dimensional parameters on buckling. Using the obtained results, the effect of variations of gradient index of material, the ratio radius to thickness and the ratio length to radius in critical buckling load are studied through pertinent computations. meanwhile, by taking into account the temperature-dependent material properties, various effects of the external thermal environments are also investigated. Numerical result show that axial buckling load decrease with an increase in the radius to thickness ratio, the increase in the length to radius ratio has no effect on buckling load, and it increases the wave number of the buckled shaped. Radial buckling load decreases with an increase in the radius to thickness ratio and length to radius ratio. Axial and radial buckling loads decrease with an increase of inhomogeneous parameter or power law exponent. Buckling temperature difference decreases as the material volume fraction exponent increases monotonically and increases linearly as the thickne to radius ratio increases. Keywords:Functionally graded material, buckling, cylindrical shell, temperature dependent properties
