In this thesis, the nonlinear vibrations of functionally graded graphene platelets reinforced composite (FG-GPLRC) toroidal panels and micro panels were investigated. The studied panels were in a thermal environment under static pressure, being in full contact with a nonlinear elastic media. Additionally, the rotation of the borders was restrained by rotational elastic springs. The shells consist of composite layers reinforced with graphene platelets (GPLs) that were assumed to be fully bonded together. A uniform distribution was considered for the GPLs in each layer, along with a random distribution for their direction. Moreover, with a slight change in the volume fractions of two adjacent layers, functionally graded (FG) distribution of platelets in the direction of shell thickness was created. The effective properties of each shell layer were estimated using the modified Halpin-Tsai model and the rule of mixtures. The nonlinear analysis of toroidal panels was performed based on the first-order shear theory (FSDT) under von Kármán geometric nonlinear hypotheses. Also, for the nonlinear analysis of toroidal micropanels, the above-mentioned theory and hypotheses were combined with the modified strain gradient theory (MSGT). In all cases, the finite element method with nine node elements and five degrees of freedom per node was applied to obtain the discrete motion equations in the spatial domain. Since the vibration takes place around the initial equilibrium state caused by the thermal environment and internal pressure, the nonlinear static analysis under thermo-mechanical loading was also done to specify this equilibrium state and obtain the initial stresses resulting from these loadings. In order to solve the system of nonlinear algebraic equations in the static equilibrium state, the Newton-Raphson method, and to extract the nonlinear frequencies, both the harmonic balance and direct iterative methods were employed. After examining the convergence of the method a