Theoretical analysis of inflatable beams made from orthotropic fabric

A theoretical analysis of inflatable beam was performed. These circular cross-section beams are made from fabric of polyester fibers coated with PVC. Such fabric may be tailored to form an arch when inflated. In many analyses, the Saint Venant Kirchhoff hypothesis was used and the authors assumed that the beams are made from an isotropic fabric. In this paper, a 3D Timoshenko's beam with a homogeneous orthotropic fabric was proposed. The model took into account the geometric nonlinearities and the inflation pressure follower force effect. The analytical equilibrium equations were performed using the total Lagrangian form of the virtual work principle. As these equations were nonlinear, a linearization was performed at the prestressed reference configuration to obtain the equations devoted to linearized problems. As an example, the bending problem was investigated. Four cases of boundary conditions were treated and the deflection and rotation's results improved the existing models in the case of an isotropic fabric. The wrinkling load in every case was also presented.