Computational p-element method on the effects of thickness and length on self-weight buckling of thin cylindrical shells via various shell theories

This paper is concerned with the development of a global p-element method for the analysis of self-weight buckling of thin cylindrical shells. Such buckling problems occur when cylindrical shells are subject to high-g acceleration, for instance the launching of rockets and missiles under high propulsive power. The cylindrical shells may have any combination of free, simply supported and clamped ends. A p-element computational method has been developed based on various thin shell theories including Donnell, Sanders and Goldenveizer-Novozhilov models. The strain energy for the global element during buckling is formulated and an eigenvalue equation is derived. Unlike the conventional buckling problem where the eigenvalue is directly solved, a pre-determined buckling parameter is fixed at the outset for a geometric-dependent stiffness and a recursive numerical procedure is developed to compute the effect of critical buckling length. The critical buckling length is found to be proportional to thickness to a power of approximately 0.9. The effects of shell thickness and length on buckling parameter are also investigated. Comparison of results from various shell theories indicates solutions of the Sanders and Goldenveizer-Novozhilov shell theories are in excellent agreement while the Donnel shell theory is good for buckling of short cylindrical shells.