A consistent 3D corotational beam element for nonlinear dynamic analysis of flexible structures

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

doi:10.1016/j.cma.2013.11.007

Cited by 85 publications

(77 citation statements)

References 48 publications

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“…The formulation is an extension of the one proposed by the authors in [31]. The same kinematic assumptions were used to derive the static and dynamic terms.…”

Section: Discussionmentioning

confidence: 99%

“…The purpose of the present paper is to further develop the dynamic formulation proposed in [31] so that beams with arbitrary thin-walled open cross-sections can be studied. For that, two main ideas are used.…”

Section: Introductionmentioning

confidence: 99%

“…Regarding the dynamic terms, i.e. the inertia force vector and tangent dynamic matrix, the formulation proposed in [31] is extended and several additional terms are introduced. The contribution of these terms in the performance of the formulation is then investigated in the numerical examples.…”

Section: Introductionmentioning

confidence: 99%

“…Firstly, a seventh degree of freedom is added at each node to describe the warping of the cross-section. Consequently, the linear interpolation for the local axial rotation used in [31] is replaced by a cubic interpolation. Secondly, the main difficulty in the nonlinear analysis of beams with arbitrary cross-sections is that, due to the eccentricity of the shear center, the cross-section rotations are usually not defined at the same point.…”

Section: Introductionmentioning

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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“…The formulation is an extension of the one proposed by the authors in [31]. The same kinematic assumptions were used to derive the static and dynamic terms.…”

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Self Cite

View full text Add to dashboard Cite

show abstract

“…The reduced equations are obtained via a classical Galerkin projection, i.e., the residual obtained by introducing (32) in (16) is projected onto the same reduced basis used for the approximation of the displacements. As discussed in the previous section, it is possible to precompute the nonlinear terms to directly obtain modal terms rather than performing the full evaluation and projection.…”

Section: Reduced Equationsmentioning

confidence: 99%

Nonlinear model order reduction for flexible multibody dynamics: a modal derivatives approach

Tiso

2015

Multibody Syst Dyn

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An effective reduction technique is presented for flexible multibody systems, for which the elastic deflection could not be considered small. We consider here the planar beam systems undergoing large elastic rotations, in the floating frame description. The proposed method enriches the classical linear reduction basis with modal derivatives stemming from the derivative of the eigenvalue problem. Furthermore, the Craig-Bampton method is applied to couple the different reduced components. Based on the linear projection, the configuration-dependent internal force can be expressed as cubic polynomials in the reduced coordinates. Coefficients of these polynomials can be precomputed for efficient runtime evaluation. The numerical results show that the modal derivatives are essential for the correct approximation of the nonlinear elastic deflection with respect to the body reference. The proposed reduction method constitutes a natural and effective extension of the classical linear modal reduction in the floating frame.

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Geometrically nonlinear quadratic solid/solid‐shell element based on consistent corotational approach for structural analysis under prescribed motion

Cho

Yoh

2017

Numerical Meth Engineering

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Summary This study proposed geometrically nonlinear quadratic solid/solid‐shell elements applicable for moving structures. Coordinates in the corotational (CR) formulation were established for a solid element. The proposed CR formulation was consistent with other hexahedral or tetrahedral solid type finite elements. The study involved an explicit description of relevant quantities induced during the derivation. Centrifugal and inertial terms were derived to analyze the behavior of moving structures. The formulation derived in the study was applicable for various solid type elements. Thus, an assumed‐strain 18‐node solid‐shell element was developed based on the Hellinger–Reissner principle to avoid locking in the local element. In addition, quadratic solid elements (i.e., a 10‐node tetrahedron and a 20‐node hexahedron) were developed in the CR solid formulation. Finally, the results were compared with those derived by previous researches involving typical static benchmark problems and commercial software. The findings indicated a good agreement between the comparisons and validated the proposed finite elements. Copyright © 2017 John Wiley & Sons, Ltd.

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A consistent 3D corotational beam element for nonlinear dynamic analysis of flexible structures

Cited by 85 publications

References 48 publications

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

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

Nonlinear model order reduction for flexible multibody dynamics: a modal derivatives approach

Geometrically nonlinear quadratic solid/solid‐shell element based on consistent corotational approach for structural analysis under prescribed motion

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