A continuum mechanics based derivation of Reissner’s large-displacement finite-strain beam theory: the case of plane deformations of originally straight Bernoulli–Euler beams

Irschik, Hans; Gerstmayr, Johannes

doi:10.1007/s00707-008-0085-8

Cited by 93 publications

(99 citation statements)

References 16 publications

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“…Whereas the physical interpretation of S is often not obvious, the one ofS is clear: our derivations show that it is associated with the generalized forces on the current configuration of the beam. The interested reader can also refer to [35,36] for more details about those issues.…”

Section: Comparison With Other Workmentioning

confidence: 99%

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Hardening/softening behavior and reduced order modeling of nonlinear vibrations of rotating cantilever beams

2016

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This work addresses the large amplitude nonlinear vibratory behavior of a rotating cantilever beam, with applications to turbomachinery and turbopropeller blades. The aim of this work is twofold. Firstly, we investigate the effect of rotation speed on the beam nonlinear vibrations and especially on the hardening/softening behavior of its resonances and the appearance of jump phenomena at large amplitude. Secondly, we compare three models to simulate the vibrations. The first two are based on analytical models of the beam, one of them being original. Those two models are discretized on appropriate mode basis and solve by a numerical following path method. The last one is based on a finite-element discretization and integrated in time. The accuracy and the validity range of each model are exhibited and analyzed.

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Section: Comparison With Other Workmentioning

confidence: 99%

“…(35). To take into account higher-order geometrical nonlinearities, an extension to the rotating case of the elastica model of [17,54] is proposed here.…”

Section: Inextensible Modelmentioning

confidence: 99%

Hardening/softening behavior and reduced order modeling of nonlinear vibrations of rotating cantilever beams

2016

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“…In general the tensorÛ has to be constructed via the spectral decomposition ofĈ, which in 3-D cannot be expressed easily 17 in closed form. For special simplified problems, like the plane deformation of an extensible Kirchhoff rod as discussed by Irschik and Gerstmayr (2009) and Humer and Irschik (2011), it is possible to derive simple, kinematically exact closed form expressions 18 forÛ andR pd by inspection of the deformation gradient. Also in the more general case ofĈ given by Eq.…”

Section: A1 the Biot Strain And Its Approximationmentioning

confidence: 99%

Geometrically exact Cosserat rods with Kelvin–Voigt type viscous damping

2013

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Abstract. We present the derivation of a simple viscous damping model of Kelvin-Voigt type for geometrically exact Cosserat rods from three-dimensional continuum theory. Assuming moderate curvature of the rod in its reference configuration, strains remaining small in its deformed configurations, strain rates that vary slowly compared to internal relaxation processes, and a homogeneous and isotropic material, we obtain explicit formulas for the damping parameters of the model in terms of the well known stiffness parameters of the rod and the retardation time constants defined as the ratios of bulk and shear viscosities to the respective elastic moduli. We briefly discuss the range of validity of the Kelvin-Voigt model and illustrate its behaviour for large bending deformations with a numerical example.

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“…The present work covers a formulation of the elastic forces based on Reissner's nonlinear rod theory, as well as a continuum mechanics approach based on a St. Venant-Kirchhoff material law. For a continuum mechanics based derivation of Reissner's finite-strain beam theory, see [5]. Note that it is possible to transform any suitable continuum mechanics based constitutive law from the continuum level to the beam level; for details, refer to Irschik and Gerstmayr [6].…”

Section: Introductionmentioning

confidence: 99%

A new locking-free formulation for planar, shear deformable, linear and quadratic beam finite elements based on the absolute nodal coordinate formulation

et al. 2011

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Many widely used beam finite element formulations are based either on Reissner's classical nonlinear rod theory or the absolute nodal coordinate formulation (ANCF). Advantages of the second method have been pointed out by several authors; among the benefits are the constant mass matrix of ANCF elements, the isoparametric approach and the existence of a consistent displacement field along the whole cross section. Consistency of the displacement field allows simpler, alternative formulations for contact problems or inelastic materials. Despite conceptional differences of the two formulations, the two models are unified in the present paper.In many applications, a nonlinear large deformation beam element with bending, axial and shear deformation properties is needed. In the present paper, linear and quadratic ANCF shear deformable beam finite elements are presented. A new locking-free continuum mechanics based formulation is compared to the classical Simo and Vu-Quoc formulation based on Reissner's virtual work of internal forces. Additionally, the introduced linear and quadratic ANCF elements are compared to a fully parameterized ANCF element from the literature. The performance of the respective elements is evaluated through analysis of conventional static and dynamic example problems. The investigation shows that the obtained linear and quadratic ANCF elements are advantageous compared to the original fully parameterized ANCF element.

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A continuum mechanics based derivation of Reissner’s large-displacement finite-strain beam theory: the case of plane deformations of originally straight Bernoulli–Euler beams

Cited by 93 publications

References 16 publications

Hardening/softening behavior and reduced order modeling of nonlinear vibrations of rotating cantilever beams

Hardening/softening behavior and reduced order modeling of nonlinear vibrations of rotating cantilever beams

Geometrically exact Cosserat rods with Kelvin–Voigt type viscous damping

A new locking-free formulation for planar, shear deformable, linear and quadratic beam finite elements based on the absolute nodal coordinate formulation

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