Dynamics of 3D beam elements in a corotational context: A comparative study of established and new formulations

Le, Thanh-Nam; Battini, Jean‐Marc; Hjiaj, Mohammed

doi:10.1016/j.finel.2012.06.007

Cited by 47 publications

(29 citation statements)

References 26 publications

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“…In the present work, at the beginning of each time step, the predictor proposed by Crisfield [12] for the particular case of linear inertia force vector and further developed for the general case by the authors [30], is adopted. The idea of this predictor is to use the tangent operator at the time instant t n to predict the values at the time instant t n+1 .…”

Section: Numerical Examplementioning

confidence: 99%

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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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Section: Numerical Examplementioning

confidence: 99%

“…However, in [30], extensive numerical studies have shown that it is advantageous to retain also the gyroscopic matrix as it enhances the computational efficiency. The same approach is used here.…”

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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“…However, in [27], extensive numerical studies have shown that it is better to keep also the gyroscopic matrix in order to enhance the computational efficiency. The same approach is used here.…”

Section: Inertia Force Vector and Tangent Dynamic Matrixmentioning

confidence: 99%

“…Several predictors are available in the literature and a comparative study of the performances of these predictors can be found in [27]. As shown in [27], the quality of the predictor has a significant influence on the convergence of the iterative procedure.…”

Section: Numerical Examplesmentioning

confidence: 99%

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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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An energy‐momentum method for in‐plane geometrically exact Euler–Bernoulli beam dynamics

Sansour

Nguyen

2015

Numerical Meth Engineering

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SummaryNonlinear geometrically exact rod dynamics is of great interest in many areas of engineering. In recent years, the research was focused towards Timoshenko‐type rod theories where shearing is of importance. However, in many general model of mechanisms and spatial deformations, it is desirable to have a displacement‐only formulation, which brings us back to the classical Bernoulli beam. While it is well known for linear analysis, the Bernoulli beam is not as common in geometrically exact models of dynamics, especially when we want to incorporate the rotational inertia into the model. This paper is about the development of an energy‐momentum integration scheme for the geometrically exact Bernoulli‐type rod. We will show that the task is achievable and devise a general framework to do so. Copyright © 2014 John Wiley & Sons, Ltd.

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Dynamics of 3D beam elements in a corotational context: A comparative study of established and new formulations

Cited by 47 publications

References 26 publications

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

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

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

An energy‐momentum method for in‐plane geometrically exact Euler–Bernoulli beam dynamics

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