Dynamic analysis of planar flexible beams with finite rotations by using inertial and rotating frames

Iura, Masashi; Atluri, Satya N.

doi:10.1016/0045-7949(95)98871-m

Cited by 53 publications

(24 citation statements)

References 24 publications

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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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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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“…Iura and Atluri [22] suggested to simply switch to a Timoshenko beam model where the mass matrix is constant and therefore the inertial terms are simple to evaluate. Behdinan et al [7] proposed a 2D corotational dynamic formulation where cubic interpolations have been used to describe the global displacements, which is not consistent with the idea of the corotational method as originally introduced by Nour-Omid and Rankin [30].…”

Section: Introductionmentioning

confidence: 99%

“…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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“…Regarding corotational dynamic formulations, constant Timoshenko mass matrices [1,2,5] are often used to express the dynamic terms. However, such an approach assumes that the inplane local displacements are zero, which is not accurate.…”

Section: Introductionmentioning

confidence: 99%

“…The corotational method is an attractive approach to derive non-linear finite beam elements [1,2,3,4,5,6,7,8] . The idea is to decompose the large 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%

Energy-Momentum Method for Nonlinear Dynamic of 2d Corotational Beams

Chhang¹,

Battini²,

Sansour³

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Abstract. This paper presents an energy-momentum method for nonlinear dynamics of 2D Bernoulli corotational beams. It is shown that the time stepping algorithm conserves energy, linear momentum and angular momentum. To be consistent in the corotational approach, cubic interpolations of Bernoulli element are employed to derive both inertia and elastic terms. The shallow arch strain definition is used to get an element which produce accurate results for less number of elements. To avoid membrane locking, we use a constant and average value of the axial strains. In addition, the energy-momentum method is used to preserve the conserving properties, which is able to maintain the stability and accuracy in a non-dissipative system for a long period. The midpoint velocities of kinematic fields and strains are used to tackle any non-linear form of strain displacement relations. Finally, two examples including large overall displacement are presented to illustrate the stability and efficiency of the proposed algorithms.5496

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Dynamic analysis of planar flexible beams with finite rotations by using inertial and rotating frames

Cited by 53 publications

References 24 publications

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

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

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

Energy-Momentum Method for Nonlinear Dynamic of 2d Corotational Beams

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