Bending and buckling of inflatable beams: Some new theoretical results

• Published in: Thin-walled structures Vol. 43; no. 8; pp. 1166 - 1187
• Main Authors: Le van, A., Wielgosz, C.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.08.2005; New York, NY Elsevier Science; Elsevier
• Subjects: Bending; Buckling; Engineering Sciences; Exact sciences and technology; Follower force; Fundamental areas of phenomenology (including applications); Inelasticity (thermoplasticity, viscoplasticity...); Inflatable beam; Materials; Mechanics; Membrane structure; Physics; Solid mechanics; Static elasticity (thermoelasticity...); Structural and continuum mechanics; Thin-walled beam; Inflatable beam; Thin-walled beam; Bending; Follower force; Membrane structure; Buckling; Fold; Modeling; Cantilever beam; Finite element method; Linearized equation; Kinematics; Membrane; Cylindrical bending; Stretching; Linearization; Swelling; Prestress; Timoshenko beam; Mechanical properties; Large displacement; Inflatable structure; Thin walled beam; Non linear effect; Crush; Internal pressure
• ISSN: 0263-8231; 1879-3223
• DOI: 10.1016/j.tws.2005.03.005

The non-linear and linearized equations are derived for the in-plane stretching and bending of thin-walled cylindrical beams made of a membrane and inflated by an internal pressure. The Timoshenko beam model combined with the finite rotation kinematics enables one to correctly account for the shear effect and all the non-linear terms in the governing equations. The linearization is carried out around a pre-stressed reference configuration which has to be defined as opposed to the so-called natural state. Two examples are then investigated: the bending and the buckling of a cantilever beam. Their analytical solutions show that the inflation has the effect of increasing the material properties in the beam solution. This solution is compared with the three-dimensional finite element analysis, as well as the so-called wrinkling pressure for the bent beam and the crushing force for the buckled beam. New theoretical and numerical results on the buckling of inflatable beams are displayed.