Analytical study on thermal buckling of cylindrical shells with non-uniform thickness

Abstract This paper presents an analytical study on thermal buckling of cylindrical shells with non-uniform thickness, which is common in engineering practice. Firstly, the shell thickness is assumed to be arbitrary in the axial direction. After solving the basic partial differential equations by the perturbation method, buckling temperature and modes in terms of thickness function and geometric sizes of the shell are obtained. Using the presented formulas, this paper deeply analyzes and discusses cosine distributed and stepwise thicknesses. For simple cosine distributed thickness, the classical Galerkin method is applied to derive buckling temperature factors, while stepwise thickness is verified by the finite difference method. Results from the Galerkin method and the finite difference method are in accordance with those by presented formulas in this paper. Furthermore, the influence of parameters in thickness functions and buckling modes on buckling temperature factors is discussed, and some interesting conclusions are drawn. The presented buckling temperature formulas can be applied to evaluate stability capacity of the cylinder used in thermal environment.