An exact solution for inflated orthotropic membrane tubes

Inflatable tubes must be pressurized before they are able to resist to external loadings. While there are many studies dedicated to the behavior of inflated tubes under bending or twisting, few results are available on the inflating stage when the beam is only submitted to the internal pressure. In this paper, an exact solution is proposed for a cylindrical tube made of an orthotropic membrane, with the orthotropy axes parallel to the circumferential and longitudinal directions of the cylinder, and undergoing finite deformations under internal pressure. The solution of the problem amounts to solving a cubic equation and analytical relations are given for the inflated geometry as well as the resultant stresses in the membrane. Numerical results are shown to compare very well with those obtained from a finite element code.