Deflections of highly inflated fabric tubes

Abstract

Inflatable beams made of modern textile materials with important mechanical characteristics can be inflated at high pressure. The aim of the paper is to present experimental, analytical and numerical results on the deflections of highly inflated fabric tubes submitted to bending loads. Experiments are displayed and we show that tube behaviour looks like that of inflatable panels (Thin-Walled Struct. 40 (2002) 523-536). Equilibrium equations are once again written in the deformed state to take into account the geometrical stiffness and the following forces. The influence of the shear stress cannot be neglected and Timoshenko's beam theory is used. A new inflatable tube theory is established and simple analytical formulas are given for a cantilever-inflated tube. Comparisons between analytical and experimental results are shown. A new inflatable finite tube element is constructed by use of algebraic operations, because the compliance matrix of the cantilever beam is not symmetric. Comparisons between experimental, analytical and numerical results prove the accuracy of this beam theory and on this new finite element for solving problems on the deflections of highly inflated tubes.

Finite element formulation for inflatable beams

“…Main et al [3,4] made experiments on a cantilever and improved Comer's theory. More recently, Wielgosz and Thomas [5,6] have derived analytical solutions for inflated panels and tubes by using the Timoshenko kinematics and by writing the equilibrium equations in the deformed state of the beam in order to take into account the follower force effect of the internal pressure. They have obtained new expressions for the deflection and shown that the limit load is proportional to the applied pressure and that the deflections are inversely proportional to the material properties of the fabrics and to the applied pressure, thus improving Fichter's theory.…”

Experimental research on tape spring supported space inflatable structures

“…(1) are 27 and 41 Nm when considering a 50 mm boom at 69 and 103 kNm -2 respectively. Other stiffening effects must also be considered having been observed in highly inflated structures [16] and analysed in detail by Davids (2008). This is caused by work done by pressure from deformation induced volume changes, such as boom bending and shearing, and can increase the structural capacity of inflatable booms beyond the 2M W limit predicted by Comer and Levy.…”

“…However there was increasing divergence between results at increased pressures. Experimental research by Thomas and Wielgosz (2004) [16] has shown highly inflated booms create pressure stiffening effects affecting the load-deflection response and increasing the load capacity of booms. Davids (2007) [17] formalised this by incorporating work done by pressure from deformation induced volume changes to a Timoshenko finite beam element model.…”

The interactive bending wrinkling behaviour of inflated beams

“…Fichter [7] published a paper in which the internal pressure appears in the deflection expression based on the minimization of total potential energy. By taking into account the deformed state of the beam, Wielgosz & Thomas [8,9] gave analytical expressions for inflated beams and panels using Timoshenko beam theory. In their approach, the force generated by internal pressure was treated as a follower force, which accounted for pressure stiffening effects.…”