Beam finite-element analysis of pressurized fabric tubes

Lightweight, portable air-pressurized beams and arches serve as primary load-carrying members for a number of civilian and military structures. These members are made from synthetic fibers that are woven or braided into a circular cross section. The pressurized air provides structural capacity by pretensioning the fabric and through its behavior as a confined gas. In this paper, a beam finite element is developed for the analysis of pressurized fabric beams based on virtual work principles. Work done by internal pressure due to deformation-induced volume changes is included in the formulation. A nonlinear moment-curvature relationship accounts for fabric wrinkling, and shear deformations are incorporated. A mixed-interpolation Timoshenko beam element is used to discretize the virtual work expression. A numerical method for determining the moment-curvature relationship of an inflated beam made from a fabric obeying a nonlinear stress-strain relationship is developed. Results of experiments on pressurized fabric beams loaded in three- and four-point bending are presented, and the finite-element model is shown to accurately predict experimentally observed load-deflection response for a range of pressures. Simulations demonstrate that in addition to prestressing the fabric, the pressurized air significantly increases beam capacity as the beam volume decreases due to deformation.