Buckling Analysis of Moderately Thick Rotational Shells under Uniform Pressure Using the Ritz Method

Abstract

This paper is concerned with an application of the Ritz method for elastic, axisymmetric, buckling analysis of moderately thick, rotational orthotropic shells under uniform external pressure. In order to capture the effect of transverse shear deformation, which is significant for thick shells, the Mindlin shell theory is used. In applying the Ritz method, the displacement components of the shell are approximated by the product of one-dimensional polynomial functions, and the boundary equations are raised to the appropriate powers so as to ensure the satisfaction of geometric boundary conditions a priori. The validity of the method, convergence and accuracy of solutions are demonstrated using spherical shells, which is a special case of rotational shells, where closed-form solutions exist for some cases. A parametric study is conducted on spherical and parabolic shells, considering the effects of height-to-base-radius ratios, thickness-to-radius ratios, and different support conditions on the buckling solutions. The new solutions should be useful to researchers and engineers who are developing analytical tools and designs of shells.