Mechanical Buckling of Ring-Supported Functionally Graded Cylindrical Shell with Material Properties Changing in the Length Direction using Third Order Shear Deformation Theory

In this paper, mechanical buckling of ring-supported functionally graded (FG) cylindrical shell under axial pressure load is investigated. The study carried out based on the third order shear deformation shell theory (TSDT) considering transverse shear strains. The rings are assumed to behave like a beam. The displacement field of the rings is based on the Euler-Bernoulli beam theory. The material properties continuously vary from the metal to the ceramic as a power form of the length coordinate variable x. The nonlinear strain-displacement relations are employed to obtain governing equations and using the variational method, the system of fundamental partial deferential equations is established. The simply supported boundary condition is assumed for both edges of the shell. The governing equations are solved by differential quadrature method (DQM). The obtained results for an isotropic shell are compared with those given in the literature. Then, FG power index, number of rings, and geometrical parameters effects on the critical buckling load are studied. The obtained results show the significant effect of rings on the buckling behavior of the shell.