Corotational formulation for nonlinear dynamics of beams with arbitrary thin-walled open cross-sections

Le, Thanh-Nam; Battini, Jean‐Marc

doi:10.1016/j.compstruc.2013.11.005

Cited by 30 publications

(30 citation statements)

References 36 publications

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“…Besides, the numerical results also showed that the warping deformations have a negligible influence in the dynamic terms and could be omitted. As shown in [32] However, the additional dynamic terms due to the shear center eccentricity cannot always be neglected.…”

Section: Discussionmentioning

confidence: 99%

“…It appears that for slender beams (Examples 7.1), these terms do not affect the results and can be therefore neglected. But as it has bee shown in [32], they may have a significant contribution for short beams.…”

Section: Inertia Force Vector and Tangent Dynamic Matrixmentioning

confidence: 91%

“…In Example which consists of a slender beams, the same results have been obtained with y c = z c = 0. However, for the short beam (see [32], different results are obtained with and without account for the eccentricity of the shear center.…”

Section: Numerical Examplementioning

confidence: 99%

“…However, to incorporate the bending shear deformations, the Hermitian shape functions for the transverse displacements are slightly modified as suggested in the Interdependent Interpolation Element (IIE) [39]. The Maple codes for f w l and K w l are given [32]. A low order of geometrical nonlinearity is introduced through a shallow arch strain description and the Wagner term.…”

Section: Inertia Force Vector and Tangent Dynamic Matrixmentioning

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: Discussionmentioning

confidence: 99%

Section: Inertia Force Vector and Tangent Dynamic Matrixmentioning

confidence: 91%

Section: Numerical Examplementioning

confidence: 99%

Section: Inertia Force Vector and Tangent Dynamic Matrixmentioning

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

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“…The co-rotational method is a very attractive approach to derive highly nonlinear beam elements [1,4,3,2,5,6,7,8,9,10,11,12]. The fundamental idea is to decompose the motion of the element into rigid body and pure deformational parts through the use of a local system which continuously rotates and translates with the element.…”

Section: Introductionmentioning

confidence: 99%

An Energy-Momentum Formulation for Nonlinear Dynamics of Planar Co-Rotating Beams

Chhang¹,

Battini²,

Sansour³

2017

Proceedings of the 6th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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Abstract. This article presents an energy-momentum integration scheme for the nonlinear dynamic analysis of planar Bernoulli/Timoshenko beams. The co-rotational approach is adopted to describe the kinematics of the beam and Hermitian functions are used to interpolate the local transverse displacements. In this paper, the same kinematic description is used to derive both the elastic and the inertia terms. The classical midpoint rule is used to integrate the dynamic equations. The central idea, to ensure energy and momenta conservation, is to apply the classical midpoint rule to both the kinematic and the strain quantities. This idea, developed by one of the authors in previous work, is applied here in the context of the co-rotational formulation to the first time. By doing so, we circumvent the nonlinear geometric equations relating the displacement to the strain which is the origin of many numerical difficulties. It can be rigorously shown that the proposed method conserves the total energy of the system and, in absence of external loads, the linear and angular momenta remain constant. The accuracy and stability of the proposed algorithm, especially in long term dynamics with a very large number of time steps, is assessed through two numerical examples.

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Combined co-rotational beam/shell elements for fluid–structure interaction analysis of insect-like flapping wing

et al. 2019

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Flapping wing micro-air vehicles are biologically inspired by nature flyers, specifically insects and birds. Specifically, insect wings generally consist of veins and membrane components. In this study, a structural analysis considering the vein/membrane components of an insect-like flapping wing is presented. Co-rotational (CR) finite elements are adopted in order to consider the complex wing configuration including both vein and membrane. The CR beam ele-H. Cho BK21 Plus Transformative Training Program for Creative Mechanical and Aerospace Engineers, Institute of Advanced Machines and Design, ments with warping degrees of freedom are employed for veins and CR shell elements for the wing membrane. The present structural analysis is verified against the analytical results obtained by an existing software, and it is validated by comparison to existing results from the literature. A fluid-structure interaction analysis is then performed. In the procedure, an aerodynamic analysis based on three-dimensional preconditioned Navier-Stokes equations is employed. Finally, a comparative study with respect to the structural characteristics is conducted. As a result, an efficiency of the present structural analysis is confirmed by comparing with the existing software. It is found that the present FSI results are in good agreement with the existing experimental and numerical results. Moreover, the passive wing twist may have a significant influence on the hover performance.Keywords Co-rotational beam and shell analysis · Fluid-structure interaction · Insect-like flapping wing

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Corotational formulation for nonlinear dynamics of beams with arbitrary thin-walled open cross-sections

Cited by 30 publications

References 36 publications

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

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

An Energy-Momentum Formulation for Nonlinear Dynamics of Planar Co-Rotating Beams

Combined co-rotational beam/shell elements for fluid–structure interaction analysis of insect-like flapping wing

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