A consistent co-rotational finite element formulation for geometrically nonlinear dynamic analysis of 3-D beams

Hsiao, Kuo Mo; Lin, Jer Yan; Lin, Wen Yi

doi:10.1016/s0045-7825(98)00152-2

Cited by 72 publications

(58 citation statements)

References 22 publications

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“…Instead, for the given material properties in Fig. 2 very good comparison was found with the solution by Hsiao et al [42] who also reported differences to Ref. [26].…”

Section: Flying Flexible Beam (Ffb)supporting

confidence: 74%

“…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%

“…Ref. [42] used a co-rotational finite-element formulation with 10 beam elements. The comparison is shown in Fig.…”

Section: Flying Flexible Beam (Ffb)mentioning

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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“…Instead, for the given material properties in Fig. 2 very good comparison was found with the solution by Hsiao et al [42] who also reported differences to Ref. [26].…”

Section: Flying Flexible Beam (Ffb)supporting

confidence: 74%

Section: Flying Flexible Beam (Ffb)mentioning

confidence: 99%

See 1 more Smart Citation

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

Hesse

Palacios

2012

Computers & Structures

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“…Some authors [8,18] proposed to keep only the mass matrix M, and to eliminate the gyroscopic C k and centrifugal K k dynamic matrices. However, in [30], extensive numerical studies have shown that it is advantageous to retain also the gyroscopic matrix as it enhances the computational efficiency.…”

Section: Inertia Force Vector and Tangent Dynamic Matrixmentioning

confidence: 99%

A New 3d Co-Rotational Beam Element for Nonlinear Dynamic Analysis

Le¹,

Battini²,

Hjiaj³

2015

Proceedings of the 5th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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Abstract. The paper investigates the contribution of the warping deformations and the shear center location on the dynamic response of 3D thin-walled beams obtained with an original consistent co-rotational formulation developed by the authors. Consistency of the formulation is ensured by employing the same kinematic assumptions to derive both the static and dynamic terms. Hence, the element has seven degrees of freedom at each node and cubic shape functions are used to interpolate local transversal displacements and axial rotations. Accounting for warping deformations and the position of the shear center produces additional terms in the expressions of the inertia force vector and the tangent dynamic matrix. The performance of the present formulation is assessed by comparing its predictions against 3D-solid FE solutions.

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“…Indeed, this framework has been adopted by several authors to develop efficient beam and shell elements for the nonlinear static and dynamic analysis of flexible structures. [1,5,7,10,11,12,14,15,18,19,22,29,31,33,38]. The main idea of the method is to decompose the motion of the element into rigid body and pure deformational parts.…”

Section: Introductionmentioning

confidence: 99%

A New Corotational Element for Nonlinear Dynamic Analysis of 3d Beams

Le¹,

Battini²

2014

Proceedings of the 4th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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Abstract. The purpose of the paper is to present a corotational beam element for the nonlinear dynamic analysis of 3D flexible frames. The novelty of the formulation lies in the use of the corotational framework (i.e. the decomposition into rigid body motion and pure deformation) to derive not only the internal force vector and the tangent stiffness matrix but also the inertia force vector and the tangent dynamic matrix. As a consequence, cubic interpolations are adopted to formulate both inertia and internal local terms. In the derivation of the dynamic terms, an approximation for the local rotations is introduced and a concise expression for the global inertia force vector is obtained. To enhance the efficiency of the iterative procedure, an approximate expression of the tangent dynamic matrix is adopted. Several numerical examples are considered to assess the performance of the new formulation against the one suggested by . It was observed that the proposed formulation proves to combine accuracy with efficiency. In particular, the present approach achieves the same level of accuracy as the formulation of Simo and Vu-Quoc but with a significantly smaller number of elements.

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A consistent co-rotational finite element formulation for geometrically nonlinear dynamic analysis of 3-D beams

Cited by 72 publications

References 22 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

A New 3d Co-Rotational Beam Element for Nonlinear Dynamic Analysis

A New Corotational Element for Nonlinear Dynamic Analysis of 3d Beams

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