Analytical Solution for Buckling Analysis of Axisymmetric Cylindrical Shell under Axial Load using Shear Deformation Theory

This paper determines the buckling load of an axisymmetric cylindrical shell of homogeneous and isotropic materials analytically using the first-order shear deformation theory (FSDT). To describe the kinematics of the shell, the FSDT, and von Karman relations are used. The equilibrium equations, which are a system of nonlinear coupled differential equations, are determined from the principle of virtual work. The nonlinear equilibrium equations are solved analytically using the perturbation technique and then the stability equations are derived from them by employing the adjacent criterion method. The resulting equations are a system of coupled linear differential equations with variable coefficients that are solved analytically to find the buckling load of the structure. The effects of geometrical properties have been investigated by a parametric study on buckling load results. Also, the buckling load is determined using the finite element method (FEM) and classical theory (Lorenz) and compared with the analytical solution results.