Analytical buckling analysis of an inflatable beam made of orthotropic technical textiles

An analytical approach was considered to study the buckling and the behavior of an inflatable orthotropic beam subjected to uniform compression loads under different boundary conditions. In order to assess the stability of inflatable structures, it is necessary to evaluate the critical load of the inflatable components in their pressurized configurations. First, a 3D inflatable orthotropic beam model based on the Timoshenko's kinematics was briefly introduced: the nonlinearities (finite rotation, follower forces) were included in this model. The nonlinear equilibrium equations were derived from the total Lagrangian form of the virtual work principle: the linearized equations were then obtained. By solving these linearized equations, an analytical expression of the critical buckling load was obtained. This critical buckling load was investigated through several load cases with several boundary conditions. The discrepancy due to the orthotropic character between the present model and the isotropic models found in the literature was evaluated, as well as the influence of the inflation pressure and the fabric mechanical properties on the value of critical load. The buckling mode shapes were also determined. To check the limit of validity of the results, the wrinkling load was also presented in every case. ► We consider the buckling behavior of an inflatable orthotropic beam. ► Critical load of an inflatable beam was evaluated through several load cases. ► Discrepancy due to orthotropic character was pointed out by comparing with previous studies. ► Critical load value is governed by mechanical properties and inflation pressure. ► Fabric orthotropic level causes discrepancy between orthotropic and isotropic models.