On the presence of bending stresses in inflated thin-walled structures

It is proposed that, in appropriate circumstances, membrane structures can experience bending moments. On uniformly inflating a thin sheet structure, which has a shape consisting of multiple curvatures, the structure will deform in such a way that the final shape will have a single radius of curvature, assuming that failure does not occur. It is the large change of shape from a multicurvature surface to a single curvature surface that causes bending moments to exist within a membrane. The validity of the hypothesis has been demonstrated using four finite element models, including an elliptical cylinder, an ellipsoid, a 'double' cone and a trileaflet heart valve.