Numerical buckling analysis of an inflatable beam made of orthotropic technical textiles
Résumé
This paper is devoted to the linear eigen and nonlinear buckling analysis of an inflatable beam made of orthotropic technical textiles. The method of analysis is based on a 3D Timoshenko beam model with a homogeneous orthotropic woven fabric. The finite element model established here involves a three-noded Timoshenko beam element with C0-type continuity for the transverse displacement and quadratic shape functions for the bending rotation and the axial displacement. In the linear buckling analysis, a mesh convergence test on the beam critical load was carried out by solving the linearized eigenvalue problem. The stiffness matrix in this case is generally assumed not to be a function of displacements, while in the nonlinear buckling problem, the tangent stiffness matrix includes the effect of changing the geometry as well as the effect of the stress stiffening. The nonlinear finite element solutions were investigated by using the straightforward Newton iteration with the adaptive load stepping for tracing the load–deflection response of the beam. To assess the effect of geometric nonlinearities and the inflation pressure on the stability behavior of inflatable beam: a simply supported beam was studied. The influence of the beam aspect ratios on the buckling load coefficient was also pointed out. To check the validity and the soundness of the results, a 3D thin-shell finite element model was used for comparison. For a further validation, the results were also compared with those from experiments at low inflation pressures.