Theoretical analysis of inflatable beams made from orthotropic fabric

Apedo, Kl; Ronel, S.; Jacquelin, Éric; Massenzio, Michel; Bennani, A.

doi:10.1016/j.tws.2009.06.003

Cited by 29 publications

(36 citation statements)

References 12 publications

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“…Equations (45) slightly differ from those given in [12]. With our notations, the modulus [12] is replaced here by E ℓ and the term 1 2…”

Section: Application To the Bending Problem Of A Cantilever Pres-surimentioning

confidence: 99%

“…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.…”

Section: Introductionmentioning

confidence: 99%

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Inflation and bending of an orthotropic inflatable beam

Nguyen

Thomas

van

2015

Thin-Walled Structures

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An inflatable beam is an airtight structure made of a soft technical fabric and subjected to an internal pressure which gives it a final cylindrical shape, a pre-stress in the membrane and a bearing capacity. Against all appearances, it is not a standard beam and it requires a specific formulation in order to take account of the internal pressure which plays a key role in its mechanical response.This work deals with inflatable beams made of orthotropic materials. The first part of the paper is concerned with the inflation of the membrane tube, an important stage which is often neglected so far in the literature. As preliminaries of the bending problem studied in the next part of the paper, the constitutive law related to the inflated state of the tube -not the natural state -is investigated. It will be shown that the constitutive law related to the inflated pre-stressed state is not the same as the constitutive law related to the natural state. Expressions of the material coefficients involved in the former constitutive law will be established from the material coefficients defined on the natural reference configuration which are the only ones supposed to be known.The second part of the paper deals with the bending of the inflatable beam. The Timoshenko beam kinematics will be chosen because of the significant shear effect in the tube wall and the problem will be formulated in finite deformations in order to accounts for all the nonlinear effects, in particular the action due to the internal pressure which is a follower load. The nonlinear system of equations obtained will then be linearized around the pre-stressed configuration and will result in a more tractable linear system.Preprint submitted to Thin-Walled Structures November 20, 2014 The proposed formulation allows a comprehensive study of the influence of the internal pressure on the geometry and material properties of orthotropic inflatable beams The analytical results will be compared with numerical results obtained from a nonlinear membrane finite element code.

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“…Equations (45) slightly differ from those given in [12]. With our notations, the modulus [12] is replaced here by E ℓ and the term 1 2…”

Section: Application To the Bending Problem Of A Cantilever Pres-surimentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Inflation and bending of an orthotropic inflatable beam

Nguyen

Thomas

van

2015

Thin-Walled Structures

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“…where the reference dimensions l o , R o and t o depend on the inflation pressure and the mechanical properties of the fabric [7]:…”

Section: Theoretical Backgroundmentioning

confidence: 99%

“…Also, the fabric was often supposed to be hyperelastic isotropic and the Saint Venant-Kirchhoff hypothesis was always used as for the traditional beams. More recently, Apedo et al [7] performed a theoretical analysis of inflatable beams in which a homogeneous orthotropic fabric was considered. A 3D Timoshenko beam model has been developed, and, by using the total Lagrangian form of the virtual work principle, the nonlinear equations have been obtained: as an example, the bending problem has been investigated [7,8].…”

Section: Introductionmentioning

confidence: 99%

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

Nguyen¹,

Ronel²,

Massenzio³

et al. 2012

Thin-Walled Structures

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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.

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