The equilibrium shapes of air-filled heavy membrane tubes resting on inclined planes

The equilibrium shapes of air-filled heavy thin-wall membrane tubes resting on an inclined plane are 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 transmural pressure. In the present study, an analytical approach for the nonlinear analysis of air-filled thin walled heavy membrane tubes resting on different inclined planes is developed. Geometric and equilibrium relations of the tube element are used to obtain the tube profile in an explicit closed form. The validity of the present analytical approach is confirmed by comparing the results with those obtained from the literature. It is shown that the present formulation is an appropriate method and a new approach to predict the nonlinear behavior of heavy membrane tubes with a good accuracy.