Bending and buckling of inflatable beams: Some new theoretical results

van, Anh Le; Wielgosz, Christian

doi:10.1016/j.tws.2005.03.005

Cited by 88 publications

(49 citation statements)

References 6 publications

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“…an additional energy term in the virtual work approach. But, as also shown in the literature, [3] the beam model is at least applicable for small deflections. …”

Section: Numerical Examplesmentioning

confidence: 60%

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Validation and Limits of Finite Inflatable Beam Elements

Haßler¹,

Schweizerhof²

2008

Proc Appl Math and Mech

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Although nowadays inflatable tubular beams are often used in the field of civil engineering, by now there are only few publications dealing with finite deformation inflatable beam elements, see e.g. [1], [2] and [3]. All formulations of inflatable beams have several assumptions in common, as constant cross sections throughout the deformation, a constant internal gas pressure and the negligence of circumferential stresses. These assumptions have to be validated either by experiments or numerical analysis. In the current contribution beam–like structures are investigated using a finite element shell or membrane formulation and featuring a volume dependent gas loading, see e.g. [5] and [4]. In general the formulation substitutes the internal gas pressure by an energetically equivalent volume dependent loading and thus enables to check for potential gas pressure changes during the deformation process of the inflated beam as a consequence of volume changes. Further local deformations as occurring in the vicinity of supports or almost single loads can be considered. In this paper the focus will be only on the initial assumption of the beam theory that the biaxial stress state is neglected. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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“…an additional energy term in the virtual work approach. But, as also shown in the literature, [3] the beam model is at least applicable for small deflections. …”

Section: Numerical Examplesmentioning

confidence: 60%

“…A more detailed description can be found in the literature, e.g. [3]. A virtual work approach is chosen for the description of a state of equilibrium using δE el as the virtual elastic potential, δW g as the virtual work of the internal gas pressure and δW ext as the virtual work of the external forces.…”

Section: Mechanics Of Inflatable Beamsmentioning

confidence: 99%

Validation and Limits of Finite Inflatable Beam Elements

Haßler¹,

Schweizerhof²

2008

Proc Appl Math and Mech

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“…Let us now pass on to the study of the in-plane bending of the membrane tube inflated at a given pressure p. To do this, we shall extend the approach in [10] to the orthotropic case and formulate the problem in some detail since the transition from the isotropic to the orthotropic case is not so straightforward. From this point on, the reference configuration will be the pressurized pre-stressed one Ω 0 , the final configuration will be the pressurized-and-then-bent configuration Ω.…”

Section: Equilibrium Equations For the Bending Of An Inflatable Beammentioning

confidence: 99%

“…They considered the internal pressure as a follower force which represents the strengthening effect on the bending and shear stiffnesses. Le van and Wielgosz [10] improved Fichter's theory [6] by using the virtual power principle in the context of the total Lagrangian formulation.…”

Section: Introductionmentioning

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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Some remarks on load modeling in nonlinear structural analysis–Statics with large deformations–Consistent treatment of follower load effects and load control

Schweizerhof,

Konyukhov

2024

Numerical Meth Engineering

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Load modeling in nonlinear statics, particularly incorporating large deformations differs significantly from the treatment in linear analysis. As in structural dynamics masses in a gravity field generate the loading, their location, and their modifications within the deformation process must be considered in a nonlinear simulation. A specific view besides loading by masses is on gas and fluid interaction with structures. In addition, load control using specifically designed algorithms is evaluated with respect to realistic applications. Within the load modeling an unavoidable, however side aspect, is the general discussion about the so‐called follower forces and non‐conservative loading. As an example of real‐world applications, the specifics of inflated rubber dams are presented.

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Bending and buckling of inflatable beams: Some new theoretical results

Cited by 88 publications

References 6 publications

Validation and Limits of Finite Inflatable Beam Elements

Validation and Limits of Finite Inflatable Beam Elements

Inflation and bending of an orthotropic inflatable beam

Some remarks on load modeling in nonlinear structural analysis–Statics with large deformations–Consistent treatment of follower load effects and load control

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