Analytical solution for buckling analysis of FGM axisymmetric cylindrical shell under axial load using shear deformation theory and perturbation technique

This paper provides an analytical approach to determining the buckling load of an axisymmetric cylindrical shell made of functionally graded material (FGM) using utilizing the first-order shear deformation theory (FSDT) and von Karman relations. Nonlinear equilibrium equations are derived using the virtual work principle and solved with the perturbation technique. The stability equations are then obtained using the adjacent criterion method, resulting in a system of coupled linear differential equations with variable coefficients, which are solved analytically for the buckling load. A parametric study examines how various geometric and material properties influence the results. It is found that transitioning from homogeneous materials to FGMs increases the buckling load by 4–11%, depending on the shell dimensions. Additionally, finite element method (FEM) results are used to validate the analytical findings and are compared with existing literature.