An Analytical Procedure for Buckling Load Determination of an Axisymmetric Cylinder with Non-Uniform Thickness Using Shear Deformation Theory

In this article, the buckling load of an axisymmetric cylindrical shell with a variable thickness is determined analytically by using the perturbation method. The loading is axial and the material properties are defined by the Hooke’s law. The displacement field is predicted by using the first order shear deformation theory and the nonlinear von-Karman relations are used for the kinematic description of the shell. The stability equations, which are the system of nonlinear differential equations with variable coefficients, are derived by the virtual work principle and are solved using the perturbation technique. Also, the buckling load is determined by using the finite element method and it is compared with the analytical solution results, the classical shell theory, and other references. The effects of linear and nonlinear shell profiles variation on the axial buckling load are investigated. Also, we studied the effects of geometric parameters on the buckling load results. The results show that the first order shear deformation theory is more useful for buckling load determination of thicker shells.