Buckling

Riks, E.

doi:10.1002/0470091355.ecm027

Cited by 6 publications

(5 citation statements)

References 37 publications

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“…In this paper, particular emphasis is given to free vibration and linearized buckling problems. As far as linearized buckling is concerned, the tangent stiffness matrix can be obtained from the linearization of the virtual variation of the nonlinear internal strain energy δ (δ L int ), see [17,18]. To a first-order approximation, δ (δ L int ) can be expressed as the sum of the contributions given by the linear stiffness as in the previous section and the virtual variation of the work of the initial stresses (or pre-stresses), σ σ σ 0 .…”

Section: Fundamental Nucleus Of the Geometrical Stiffness Matrixmentioning

confidence: 99%

Component-Wise Models for the Accurate Dynamic and Buckling Analysis of Composite Wing Structures

Carrera

Pagani

Cabral

et al. 2016

Volume 1: Advances in Aerospace Technology

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In the present work, a higher-order beam model able to characterize correctly the three-dimensional strain and stress fields with minimum computational efforts is proposed. One-dimensional models are formulated by employing the Carrera Unified Formulation (CUF), according to which the generic 3D displacement field is expressed as the expansion of the primary mechanical variables. In such a way, by employing a recursive index notation, the governing equations and the related finite element arrays of arbitrarily refined beam models can be written in a very compact and unified manner. A Component-Wise (CW) approach is developed in this work by using Lagrange polynomials as expanding cross-sectional functions. By using the principle of virtual work and CUF, free vibration and linearized buckling analyses of composite aerospace structures are investigated. The capabilities of the proposed methodology and the advantages over the classical methods and state-of-the-art tools are widely demonstrated by numerical results.

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Section: Fundamental Nucleus Of the Geometrical Stiffness Matrixmentioning

confidence: 99%

Component-Wise Models for the Accurate Dynamic and Buckling Analysis of Composite Wing Structures

Carrera

Pagani

Cabral

et al. 2016

Volume 1: Advances in Aerospace Technology

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“…These eight atoms are constrained to move solely in radial direction so that the global buckling mode is prevented. Within this force‐driven simulation, the first buckling mode is analysed, and the non‐linear load‐deformation path is calculated with the help of a modified Riks algorithm . Three different calculations are performed, where the first simulation is carried out without modelling non‐bonded interactions at all.…”

Section: Numerical Examples On Buckling Of Carbon Nanotubesmentioning

confidence: 99%

Buckling analysis of carbon nanotubes – a molecular statics investigation into the influence of non‐bonded interactions

Hollerer

2012

Numerical Meth Engineering

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SUMMARY This paper analyses the buckling behaviour of single‐walled and double‐walled carbon nanotubes. The total potential of the atomic structure consists of the bonded energy and the non‐bonded energy, both resulting from interatomic potentials, as well as the energy of external contributions. In particular, the influence of the in‐layer and inter‐layer non‐bonded interactions is investigated. These non‐bonded interactions are important to avoid the nanotubes from self‐intersection or penetration and govern the morphology of the buckled tubes. The simulation model is based on a molecular statics approach embedded in the finite element framework. The search for equilibrium configurations of the structure leads to a non‐linear system of equations, which is linearised and solved iteratively. Therefore, the model relies on the fully non‐linear description of the interatomic potential and the atomic kinematics. Stability points of the loaded carbon nanotubes are detected by an accompanying eigenvalue analysis in combination with a bisection algorithm. By means of branch switching, the continuation of the non‐linear load‐deformation path in the postbuckling regime is enabled. With this framework, the buckling characteristics of carbon nanotubes in consequence of different loading conditions is studied. Results of numerical simulations are given for carbon nanotubes under torsion, axial compression and bending. Copyright © 2012 John Wiley & Sons, Ltd.

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“…Nowadays, several approaches can be used to solve these three main problems. Incremental-iterative strategies with arc-length control are the most popular, see (Crisfield 1997, Riks 2004. Alternative methods such as the asymptotic numerical method have also been proposed, see (Damil et al 1990).…”

Section: Buckling and Post-buckling Analysismentioning

confidence: 99%

“…This mechanical analysis is carried out with an arc-length continuation method (Crisfield 1997, Riks 2004. The singular points are detected and analyzed to identify the presence of a bifurcation.…”

Section: Introductionmentioning

confidence: 99%

Model reduction method: an application to the buckling analysis of laminated rubber bearings

Lejeunes

Boukamel

Cochelin

2006

European Journal of Computational Mechanics

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In this paper, we apply a model reduction method to find the equilibrium state at finite strain of geometrically complex structures which have periodic properties in one direction and exhibit a non-linear material behavior. This method, based on a finite-element approach, consists in projecting the unknowns fields onto a polynomial basis in order to reduce the size of the problem. This method was combined with a continuation resolution scheme to find the instabilities of a laminated rubber bearing subjected to compression loading. Comparisons with standard finite-element models show the reliability of the present method.On présente, dans ce papier, une application d'une technique de réduction de modèles pour résoudre les problèmes d'équilibre de structures géométriquement complexes possédant des propriétés de périodicité selon une direction et dont le comportement présente des non-linéarités géométriques et matérielles. Basée sur une formulation en éléments finis, cette méthode consiste à projeter sur une base polynômiale, bien choisie vis-à-vis des propriétés d'invariance, les champs inconnus. Elle permet ainsi de réduire la dimension du problème à résoudre. Le couplage d'une telle méthode avec une méthode de continuation, nous permet d'analyser les instabilités d'un lamifié élastomère-métal en compression. Des comparaisons avec des modèles éléments-finis standard sont présentées

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Buckling

Cited by 6 publications

References 37 publications

Component-Wise Models for the Accurate Dynamic and Buckling Analysis of Composite Wing Structures

Component-Wise Models for the Accurate Dynamic and Buckling Analysis of Composite Wing Structures

Buckling analysis of carbon nanotubes – a molecular statics investigation into the influence of non‐bonded interactions

Model reduction method: an application to the buckling analysis of laminated rubber bearings

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