An Energy-Conserving Co-Rotational Procedure for the Dynamics of Planar Beam Structures

Galvanetto, Ugo; Crisfield, M. A.

doi:10.1002/(sici)1097-0207(19960715)39:13<2265::aid-nme954>3.0.co;2-o

Cited by 61 publications

(37 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Recently, Urthaler and Reddy [13] developed three locking-free co-rotational planar beam element formulations by adopting respectively the Euler-Bernoulli, Timoshenko, and simplified Reddy theories in modelling of the element kinematic behaviour. Galvaneito and Crisfield [14] proposed an energy-conserving procedure for the implicit non-linear dynamic analysis of planar beam structures by using a form of co-rotational technique. Iura et al [15] investigated the accuracy of the co-rotational formulation for 3-D Timoshenko beam undergoing finite strains and finite rotations.…”

Section: Introductionmentioning

confidence: 99%

A Mixed Co-Rotational 3d Beam Element Formulation for Arbitrarily Large Rotations

Vu‐Quoc²

2010

Volume 6 Number 2

View full text Add to dashboard Cite

A new 3-node co-rotational element formulation for 3D beam is presented. The present formulation differs from existing co-rotational formulations as follows: 1) vectorial rotational variables are used to replace traditional angular rotational variables, thus all nodal variables are additive in incremental solution procedure; 2) the Hellinger-Reissner functional is introduced to eliminate membrane and shear locking phenomena, with assumed membrane strains and shear strains employed to replace part of conforming strains; 3) all nodal variables are commutative in differentiating Hellinger-Reissner functional with respect to these variables, resulting in a symmetric element tangent stiffness matrix; 4) the total values of nodal variables are used to update the element tangent stiffness matrix, making it advantageous in solving dynamic problems. Several examples of elastic beams with large displacements and large rotations are analysed to verify the computational efficiency and reliability of the present beam element formulation.

show abstract

Section: Introductionmentioning

confidence: 99%

A Mixed Co-Rotational 3d Beam Element Formulation for Arbitrarily Large Rotations

Vu‐Quoc²

2010

Volume 6 Number 2

View full text Add to dashboard Cite

show abstract

“…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%

“…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 Newmark family of algorithms [10] is one of the most commonly employed. However, these methods present instabilities in non-linear analyses [4,5]. To avoid these instabilities, Geradin and Cardona [11] introduced numerical dissipations (Alpha method [12]) in order to damp the high frequencies.…”

Section: Introductionmentioning

confidence: 99%

“…In the corotational context, Crisfield and Shi [4] used a mid-point configuration combined to average strains in order to conserve the energy. Galvanetto and Crisfield [5] developed an energyconserving time-integration procedure for implicit non-linear dynamic analysis of planar beam structures. They used the constant Timoshenko mass matrix for the inertia term.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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)

View full text Add to dashboard Cite

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

show abstract

On non-linear dynamics of shells: implementation of energy-momentum conserving algorithm for a finite rotation shell model

Brank

Briseghella

Tonello

et al. 1998

Int. J. Numer. Meth. Engng.

View full text Add to dashboard Cite

Continuum and numerical formulations for non-linear dynamics of thin shells are presented in this work. An elastodynamic shell model is developed from the three-dimensional continuum by employing standard assumptions of the ÿrst-order shear-deformation theories. Motion of the shell-director is described by a singularityfree formulation based on the rotation vector. Temporal discretization is performed by an implicit, one-step, second-order accurate, time-integration scheme. In this work, an energy and momentum conserving algorithm, which exactly preserves the fundamental constants of the shell motion and guaranties unconditional algorithmic stability, is used. It may be regarded as a modiÿcation of the standard mid-point rule. Spatial discretization is based on the four-noded isoparametric element. Particular attention is devoted to the consistent linearization of the weak form of the initial boundary value problem discretized in time and space, in order to achieve a quadratic rate of asymptotic convergence typical for the Newton-Raphson based solution procedures. An unconditionally stable time ÿnite element formulation suitable for the long-term dynamic computations of exible shell-like structures, which may be undergoing large displacements, large rotations and large motions is therefore obtained. A set of numerical examples is presented to illustrate the present approach and the performance of the isoparametric four-noded shell ÿnite element in conjunction with the implicit energy and momentum conserving time-integration algorithm. ? 1998 John Wiley & Sons, Ltd.

show abstract

An Energy-Conserving Co-Rotational Procedure for the Dynamics of Planar Beam Structures

Abstract: SUMMARY

Cited by 61 publications

References 15 publications

A Mixed Co-Rotational 3d Beam Element Formulation for Arbitrarily Large Rotations

A Mixed Co-Rotational 3d Beam Element Formulation for Arbitrarily Large Rotations

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

On non-linear dynamics of shells: implementation of energy-momentum conserving algorithm for a finite rotation shell model

Contact Info

Product

Resources

About