On the Dynamics of Flexible Beams Under Large Overall Motions—The Plane Case: Part II

Simo, J. C.; Vu‐Quoc, L.

doi:10.1115/1.3171871

Cited by 207 publications

(184 citation statements)

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“…(24), with rigid-body velocities, β, we write the modal system matrices in terms of constant tensors, c and k, as shown in Eq. (25).…”

Section: Structural Linearisation In the Flexible-body Dynamics Of Thmentioning

confidence: 99%

“…The problem at hand was first introduced by Simo and Vu-Quoc for the planar case [25], later expanded to 3-D in Ref. [26], and has been used subsequently to validate various geometrically-nonlinear flexible-body dynamics formulations [40][41][42][43].…”

Section: Flying Flexible Beam (Ffb)mentioning

confidence: 99%

“…The beam is discretised using 10 2-noded elements, following Refs. [25,26]. In the 3-D case, the FFB is subjected to an additional dead moment M 2 (t) acting along the z axis, indicated in Fig.…”

Section: Flying Flexible Beam (Ffb)mentioning

confidence: 99%

“…M 2 (t)=M 1 (t)/2 EA = GA s = 10 4 EI = GJ = 500 ρA = 1 ρJ = diag (20,10,10) Geometry and material properties: Figure 2: FFB geometry, material properties and load histories [25,26].…”

Section: Flying Flexible Beam (Ffb)mentioning

confidence: 99%

“…Vu-Quoc extended the theory to rods undergoing large unconstrained motions in space including rotations [25,26]. They used a global body-fixed reference frame attached to the reference configuration to include the rigid-body motion of the beam.…”

Section: Introductionmentioning

confidence: 99%

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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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“…(24), with rigid-body velocities, β, we write the modal system matrices in terms of constant tensors, c and k, as shown in Eq. (25).…”

Section: Structural Linearisation In the Flexible-body Dynamics Of Thmentioning

confidence: 99%

Section: Flying Flexible Beam (Ffb)mentioning

confidence: 99%

Section: Flying Flexible Beam (Ffb)mentioning

confidence: 99%

“…M 2 (t)=M 1 (t)/2 EA = GA s = 10 4 EI = GJ = 500 ρA = 1 ρJ = diag (20,10,10) Geometry and material properties: Figure 2: FFB geometry, material properties and load histories [25,26].…”

Section: Flying Flexible Beam (Ffb)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Hesse

Palacios

2012

Computers & Structures

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Sliding beams, Part II: time integration

Behdinan¹,

Stylianou²,

Tabarrok³

1998

Int. J. Numer. Meth. Engng.

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In this paper we obtain solutions for the discretized incremental system equations, as obtained in Part I, under certain initial and boundary conditions and/or specified applied loads, using the variable domain beam element. As a check on the validity of implementation, we first limit ourselves to linear analysis and obtain results for the axially inextensible sliding beams which we compare with the results reported in the literature. Second we set the axial velocity to zero and solve some special cases when the length of the beam is constant. In this case, we check the formulation and its implementation for non‐linearities in the system due to large displacements. Finally, we solve the sliding beam problem for small amplitude oscillations, with a non‐linear solver and compare the results with those obtained by the linear solver used for inextensible sliding beams. With these preliminary tests completed, we obtain the transient response of the free and forced large amplitude vibrations of the flexible sliding beam and demonstrate the need for using a non‐linear analysis for this complex system. Finally, we consider the stability of the motion of periodically time varying flexible sliding beams and show that in the case of parametric resonance, the unstable regions obtained in the linear analysis, which imply unbounded amplitudes, are indeed stable and bounded when non‐linear terms are taken into account. © 1998 John Wiley & Sons, Ltd.

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Models and Finite Elements for Thin‐Walled Structures

Bischoff

Bletzinger

Wall

et al. 2004

Encyclopedia of Computational Mechanics

145

143

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The present study provides an overview of modeling and discretization aspects in finite element analysis of thin‐walled structures. Shell formulations based upon derivation from three‐dimensional continuum mechanics, the direct approach, and the degenerated solid concept are compared, highlighting conditions for their equivalence. Rather than individually describing the innumerable contributions to theories and finite element formulations for plates and shells, the essential decisions in modeling and discretization, along with their consequences, are discussed. It is hoped that this approach comprises a good amount of the existing literature by including most concepts in a generic format. The contribution focuses on nonlinear finite element formulations for large displacements and rotations in the context of elastostatics. Although application to dynamics and problems involving material nonlinearities is straightforward, these subjects are not taken into account explicitly.

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On the Dynamics of Flexible Beams Under Large Overall Motions—The Plane Case: Part II

Cited by 207 publications

References 0 publications

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

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

Sliding beams, Part II: time integration

Models and Finite Elements for Thin‐Walled Structures

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