Numerical analysis of partly wrinkled cylindrical inflated beams under bending and shear

This paper is aimed at assessing the nonlinear elastic response of an inflatable cylindrical beam through a simple mechanical model recently proposed by the authors for studying the equilibrium configurations of highly pressurised elastic membranes with general shapes. The attention is focused on beams loaded at mid-span with two different constraints, corresponding to simply-supported ends and built-in ends. The geometrical nonlinearities due to both the cross-sectional ovalization and wrinkling are carefully considered. In particular, the wrinkling of the membrane, clearly visible for load values much lower than the collapse load, is taken into account by means of an equivalent physical non-linearity. A two-states constitutive law for the material is assumed: when a fibre is stretched (the active state), its response is elastic, while when the fibre is contracted, no compressive force can be engendered in it (the passive state). The evolution of the cross-sectional ovalization, the size of the wrinkled regions and the magnitude of longitudinal and transverse stresses in the membrane are accurately determined for increasing levels of loads, up to collapse. The numerical results for the corresponding values of load and internal pressure, obtained through an expressly developed incremental-iterative algorithm, are compared with the experimental ones available in the literature.