Analytical modeling of variable thickness cylindrical shallow shells using extended Kantorovich method

Abstract

The objective of the current paper is to provide novel numerical and analytical solutions for the variable cross section shallow shells under static pressure loads. First, the governing equations and the corresponded boundary conditions of the system are derived using the principle of virtual work. Then using the extended Kantorovich method (EKM), the partial differential equations of the system are transformed into two sets of variable coefficient ordinary differential equations, which are solved iteratively using both a novel numerical finite difference scheme, as well as an analytical perturbation tool. The convergence of the developed finite difference scheme is analyzed and it is observed that considering 600 nodes in the normalized domain is sufficient for achieving highly accurate results. Similarly, analytical simulations reveal that a fourth order perturbation expansion leads to an error of less than 0.2% in calculating the pick transverse response. The convergence of the EKM is also investigated and it is observed that the maximum transverse displacement can be predicted with less than 0.01% error using only two iterates. Additionally, variations of the stress and strain components in the mid-surface are studied using contour plots. Finally, parametric studies are carried out to characterize the effect of the shell's aspect ratio on the maximum transverse deflection. The analytical and numerical findings reported in this paper are closely validated with FE results as well as other available data in the literature.