Cylindrical shells are one of the most applicable constituents in various structures such as rockets, missiles, turbines, fluid transfer pipes, submarine industries, etc. Towards the improvement of these shells, Functionally Graded Materials (FGMs) are utilized for their enhanced behavior and properties. Their internal structure is non-homogeneous and their mechanical properties vary along the thickness direction consistently. The main components are usually ceramic and metal. The metal phase would strengthen the mechanical properties, and the ceramic phase would enhance thermal resistance of the structure. Depending on the application or the limitations, a cylindrical shell might be embedded in a tensionless elastic medium. In this case, its critical buckling load would be higher than the non-medium case, which is called unilateral buckling. In fact, the presence of a contact surface would confine the shell from buckling in usual sine waves. In unilateral buckling, the buckling mode has shorter wavelengths and the shell would be more rigid regarding the applied loads. In this thesis, unilateral buckling of FGM thin-walled cylinder embedded in tensionless elastic medium is investigated using Rayleigh-Rites method, for the first time. The effects of various parameters such as the order of FGM volumetric ratio function in constant thickness, the length to radius ratio, the radius to thickness ratio, and the presence of three different thermal environments on the unilateral and bilateral buckling loads are studied. The governing equations are extracted based on either the assumptions of Keywords: Unilateral buckling, Tensionless elastic medium, Thin-walled cylinder, Functionally Graded Material (FGM), Rayleigh–Ritz method
