Some new theoretical results for orthotropic inflatable beams

A so-called inflatable beam is a membrane tube which gains its stiffness only by a prescribed internal pressure. Such lightweight structures are useful in inflatable buildings and particularly in space industry, whenever rapidly deployable and easily transportable structures are required. An inflatable beam may look like a standard beam, but its mechanism is quite different and a specific mechanical study is necessary in order to establish its governing equations. The only way to correctly take account of the internal pressure – which is a follower load – is to carry out a complete nonlinear analysis before any possible linearization. This work aims to extend the analytical results for isotropic inflatable beams to the practical situation when the beam is made of an orthotropic fabric. It will be shown that the Timoshenko beam model combined with the finite rotation kinematics enables one to correctly account for all the nonlinear terms in the governing equations. A linearization will then be performed to study deformations about the pre-stressed reference configuration. Furthermore, it will be shown how to precisely compute the radius and the length of the inflated tube in the reference state, a very significant issue which is overlooked so far in the literature. All the proposed analytical results will be compared with the numerical ones obtained from a nonlinear 3D finite element code. NOMENCLATURE Coordinates systems (x,y,z) fixed orthonormal Cartesian basis (X ,Y,Z) reference Cartesian co-ordinates (r, φ , X) cylindrical co-ordinates (l, t , n) warp, weft, normal directions of the fabric (el,er,et ) the orthonormal local basis with vectors directed along the warp, normal and weft directions