Deformation of a thin-walled cylindrical tube submerged in a liquid

Abstract

A long, thin, horizontal elastic cylindrical tube either fully or partially submerged in a liquid is considered. The tube supports a centered line load along its bottom and the load-carrying capacity of the tube is analysed. A nonlinear boundary value problem that takes into account the variable hydrostatic pressure is formulated. Perturbation solutions are obtained for the cases of small pressure gradients, especially in the neighborhood of the critical buckling pressure. Numerical solutions based on Newton's iteration and shooting methods are also obtained for general pressure gradients and for both the fully and partially submerged cases. The results show that, given a pressure gradient, there is an upper limit for the maximum load of the partially submerged tube. This maximum load decreases with depth when the shell is fully submerged and thus the corresponding equilibrium solution is unstable.