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

Abstract

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.

An analytical solution for an inflated orthotropic membrane tube with an arbitrarily oriented orthotropy basis

“…Relation (14) shows that the components of the Green strain tensor E in the reference basis do not depend on Z. By virtue of Relations (9) and (12), the components of the second Piola Kirchhoff stress tensor R are independent of Z, whereas those of Cauchy stress ten sor r are independent of z.…”

“…Recently, Apedo et al [11] went further using a 3D Timo shenko's kinematics and derived their solutions for an orthotropic fabric in finite displacements and small rotations. This work was next extended to the buckling of an orthotropic beam by Nguyen et al [12]. Refinements of the previous formulations en abled Nguyen et al [13] to derive the governing nonlinear equa tions for inflatable orthotropic beams and simple formulae for the deflection and rotation.…”

Numerical and experimental study of buckling behavior of delaminated plate in glass woven fabric composite laminates

“…For this reason, the geometry of fabrics has received a great deal of attention by researchers. 21,[26][27][28][29][30] Alif et al 26 concentrated on the effect of weave pattern on mode I of delamination. They defined an index, named weave index, n g , which indicates the interlacing counts between the warp and weft yarns and found that the delamination resistance increased with the increase in weave index.…”

Inflation and bending of an orthotropic inflatable beam

“…Davids and Zhang [11] confirmed Fichter's results by considering the pressure work during the volume change in isotropic Timoshenko beams. On the basis of [10], Apedo et al [12], Nguyen et al [13] went further by developing a theory for pressurized membrane tube made of an orthotropic material. They first used a 3D kinematics and then linearized their formulation.…”