Buckling and collapse of heavy tubes resting on a horizontal or inclined plane

The buckling and collapse of empty and liquid-filled thin-wall cylindrical tubes resting on a horizontal or inclined plane is considered. The deflection is due to the action of gravity causing the tube to deform under the influence of its own weight, or due to a negative transmural pressure pushing the tube inward on the outside. Classical thin-membrane theory is used to formulate a boundary-value problem describing the shell deformation, and the results illustrate families of deformed shapes of inextensible shells with point or segment contact occurring between the shell and the supporting surface or between two collapsed sections of the shell. The computed two-dimensional deformed shapes are used to reconstruct the three-dimensional shape of a slowly collapsing fluid-conveying vessel in the absence of significant hydrostatic pressure variations over the cross section.