Buckling and wrinkling of prestressed membranes

Diaby, Adama; van, Anh Le; Wielgosz, Christian

doi:10.1016/j.finel.2006.03.003

Cited by 35 publications

(17 citation statements)

References 24 publications

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“…The buckling problem of the inflated torus, studied by Diaby et al [45], involves both limit and bifurcation points. Therefore, it is possible to testify whether the proposed computational procedure is capable of dealing with this complicated case or not.…”

Section: Buckling Of An Inflated Torusmentioning

confidence: 99%

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Nonlinear static and dynamic analysis of hyper-elastic thin shells via the absolute nodal coordinate formulation

et al. 2016

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A new hyper-elastic thin shell finite element of absolute nodal coordinate formulation (ANCF) is proposed based on the Kirchhoff-Love theory. Under the condition of plane stress, a two-dimensional compressible neo-Hookean constitutive model and a twodimensional incompressible Mooney-Rivlin constitutive model for the thin shell element of ANCF are derived. Based on the continuum mechanics, the efficient analytical formulations of the internal forces and their Jacobians of the shell element are also deduced. Then, a computation methodology for performing the nonlinear static analysis including buckling analysis of hyper-elastic thin shells is proposed. To accurately track the load-displacement equilibrium path in the analysis, the arc-length method is used to solve the nonlinear algebraic equations. The dynamics of the thin shells made of different hyper-elastic materials is also comparatively studied by using the generalized-alpha algorithm. Finally, six case studies are given to validate the proposed hyper-elastic thin shell element and computation methodology. The influence of different constitutive models on the static and dynamic responses of thin shells is revealed.

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Section: Buckling Of An Inflated Torusmentioning

confidence: 99%

“…13. According to the study [45], given the symmetry, only one-fourth of the torus is considered. For the compressible neo-Hookean model, the Lamé's second parameter μ = 1.34228 MPa is adopted, and the value of Poisson's ratio ν is set to be 0.49.…”

Section: Buckling Of An Inflated Torusmentioning

confidence: 99%

Nonlinear static and dynamic analysis of hyper-elastic thin shells via the absolute nodal coordinate formulation

et al. 2016

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“…6 Diaby et al used another method, bifurcation analysis, to analyze the buckling and wrinkling phenomena of pre-stressed membranes. 11 The bifurcation theorem was introduced to track the bifurcation path, which requires considerable computational effort. Therefore, a simpler and more accurate analytical model is desired.…”

Section: Introductionmentioning

confidence: 99%

Analysis of wrinkled membrane structures based on a wrinkle-wave model

2017

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As research on the applications of high-precision membrane structures develops, wrinkling has become a popular topic. Here, we present a new wrinkle-wave model to describe wrinkles more accurately. First, the characteristics of wrinkle-waves that result from radial tension stress applied at the vertex of a triangular structure were analyzed. However, for polygonal structures under more than two tensions, the influence of the other vertexes should also be considered. Therefore, by introducing a load ratio, we constructed a wrinkle-wave model of a square membrane structure subjected to corner forces. This model is applicable to various loading cases and polygonal membrane structures. Comparison among the results of the finite element analysis, and the experimental and analytical results showed that the proposed model more accurately described the wrinkling details and solved the problem of convergence that is encountered during finite element analysis.

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“…The internal pressure p is assumed to remain constant, which simplifies the analysis and is consistent with the experimental observations and the prior studies on inflated fabric beams and arches [1][2][3][4][5][6][9][10][11][12][13]. The initial pressurization takes place prior to the application of concentrated and distributed external loads, and is not included in the structural analysis per se.…”

Section: Theoretical Backgroundmentioning

confidence: 96%

“…When a negative (compressive) stress is about to appear the membrane will wrinkle and the negative stress should vanish. Concerning the inflatable cylindrical beams, many studies have dealt with the wrinkling phenomenon [1][2][3]5,7,9,13,22,23]. The theoretical model developed in this paper supposes that no wrinkle occurs.…”

Section: Wrinkling Load For An Inflatable Beam Under a Compressive Comentioning

confidence: 99%

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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Buckling and wrinkling of prestressed membranes

Cited by 35 publications

References 24 publications

Nonlinear static and dynamic analysis of hyper-elastic thin shells via the absolute nodal coordinate formulation

Nonlinear static and dynamic analysis of hyper-elastic thin shells via the absolute nodal coordinate formulation

Analysis of wrinkled membrane structures based on a wrinkle-wave model

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

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