A three-dimensional finite-strain rod model. part II: Computational aspects

Simo, J. C.; Vu‐Quoc, L.

doi:10.1016/0045-7825(86)90079-4

Cited by 1,037 publications

(907 citation statements)

References 26 publications

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“…With a tip load of 300 N, the solution converges with 5 iterations on average. Table 3 shows the tip displacement of the uncoupled beam compared to results by Simo & Vu-Quoc [16]. And the coupled beam compared to results obtained with the element proposed by Kim et al which was implemented in the co-rotational formulation used in the present study.…”

Section: Pre-bend Cantilevermentioning

confidence: 98%

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Timoshenko Beam Element With Anisotropic Cross-Sectional Properties

Stäblein¹,

Hansen²

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Abstract. Beam models are used for the aeroelastic time and frequency domain analysis of wind turbines due to their computational efficiency. Many current aeroelastic tools for the analysis of wind turbines rely on Timoshenko beam elements with classical crosssectional properties (EA, EI, etc.). Those cross-sectional properties do not reflect the various couplings arising from the anisotropic behaviour of the blade material. A twonoded, three-dimensional Timoshenko beam element was therefore extended to allow for

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Section: Pre-bend Cantilevermentioning

confidence: 98%

“…The beam is 2.54 m long, has a height of 16 The cantilever was discretised with 16 elements. In Table 1 the results of the present model are compared with beam models by Hodges et al [9] and Armanios and Badir [11] as well as a finite element shell model by Kim et al [5].…”

Section: Eigenfrequencies Of a Coupled Cantilevermentioning

confidence: 99%

Timoshenko Beam Element With Anisotropic Cross-Sectional Properties

Stäblein¹,

Hansen²

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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“…An L-shaped extensible and shearable rod is attached at both endpoints such that the tangents are able to move freely (moment free support). This example has previously been discussed in the articles [24,32] and all data are taken from there. The length of each leg is 1 2 L = 120 and the stiffness parameters are GA = 16.62 · 10 6 , EA = 43.2 · 10 6 , EI = 14.4 · 10 6 and GJ = 11.08 · 10 6 .…”

Section: Two-dimensional Hinged Framementioning

confidence: 99%

A discrete mechanics approach to the Cosserat rod theory—Part 1: static equilibria

Jung

Leyendecker

Linn

et al. 2010

Numerical Meth Engineering

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A theory of discrete Cosserat rods is formulated in the language of discrete Lagrangian mechanics. By exploiting Kirchhoff's kinetic analogy, the potential energy density of a rod is a function on the tangent bundle of the configuration manifold and thus formally corresponds to the Lagrangian function of a dynamical system. The equilibrium equations are derived from a variational principle using a formulation that involves null‐space matrices. In this formulation, no Lagrange multipliers are necessary to enforce orthonormality of the directors. Noether's theorem relates first integrals of the equilibrium equations to Lie group actions on the configuration bundle, so‐called symmetries. The symmetries relevant for rod mechanics are frame‐indifference, isotropy, and uniformity. We show that a completely analogous and self‐contained theory of discrete rods can be formulated in which the arc‐length is a discrete variable ab initio. In this formulation, the potential energy density is defined directly on pairs of points along the arc‐length of the rod, in analogy to Veselov's discrete reformulation of Lagrangian mechanics. A discrete version of Noether's theorem then identifies exact first integrals of the discrete equilibrium equations. These exact conservation properties confer the discrete solutions accuracy and robustness, as demonstrated by selected examples of application. Copyright © 2010 John Wiley & Sons, Ltd.

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“…Simo and Vu-Quoc [23,24] generalised the approach to the fully three-dimensional dynamic case by introducing quaternions to describe the rotational DoF. The equations are solved using finite elements with displacement and finite rotation coordinates as the independent variables.…”

Section: Introductionmentioning

confidence: 99%

“…The application in mind is for the nonlinear flight dynamics of flexible aircraft [29] and the methodology has been integrated into the framework for Simulation of High-Aspect Ratio Planes (SHARP) [30]. Our starting point will be a geometrically-exact formulation of the beam dynamics, using a displacement-based approach [24,28]. Local beam rotations are parametrised using the CRV with respect to a body-attached reference frame.…”

Section: Introductionmentioning

confidence: 99%

Consistent structural linearisation in flexible-body dynamics with large rigid-body motion

Hesse

Palacios

2012

Computers & Structures

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A consistent linearisation, using perturbation methods, is obtained for the structural degrees of freedom of flexible slender bodies with large rigid-body motions. The resulting system preserves all couplings between rigid and elastic motions and can be projected onto a few vibration modes of a reference configuration. This gives equations of motion with cubic terms in the rigid-body degrees of freedom and constant coefficients which can be pre-computed prior to the time-marching simulation. Numerical results are presented to illustrate the approach and to show its advantages with respect to mean-axes approximations.

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A three-dimensional finite-strain rod model. part II: Computational aspects

Cited by 1,037 publications

References 26 publications

Timoshenko Beam Element With Anisotropic Cross-Sectional Properties

Timoshenko Beam Element With Anisotropic Cross-Sectional Properties

A discrete mechanics approach to the Cosserat rod theory—Part 1: static equilibria

Consistent structural linearisation in flexible-body dynamics with large rigid-body motion

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