A Cosserat Rod Model of Multi-Symplectic Structure and its Numerical Treatment

Article Preview

Abstract:

In this paper, a Hamiltonian formulation of the Cosserat rod model is proposed. The model, based on the Cossert rod theory incorporates shear, elongation, flexure and twist deformation, is of multi-symplectic structure. A multi-symplectic algorithm is employed to discretize the equation and a numerical example is giving.

You might also be interested in these eBooks

Info:

Periodical:

Advanced Materials Research (Volumes 712-715)

Pages:

1395-1400

Citation:

Online since:

June 2013

Export:

Price:

Permissions CCC:

Permissions PLS:

Сopyright:

© 2013 Trans Tech Publications Ltd. All Rights Reserved

Share:

Citation:

[1] Kirchhoff G.Uber das Gleichgewicht und die bewegung eines unendlich dunnen elastischen Stabes.J.Rein Angew.Math.,1859,56:285-313

DOI: 10.1515/9783112368688-027

Google Scholar

[2] Love.A treatise on mathematical theory of elasticity.4th ed.New York:Dover,(1927)

Google Scholar

[3] Antman S.S. Nonlinear Problems of Elasticity.(Spring-Verlag,New York,1994)

Google Scholar

[4] Svetlitsky V.A., Dynamics of Rods, Springer, Berlin, Heidelberg, New York, (2004)

Google Scholar

[5] Benham C J. An elastic model of the large-scale structure of duples DNA. Biopolymers, 1979,18: 609~623

DOI: 10.1002/bip.1979.360180310

Google Scholar

[6] Le Bret M. Catastophic variation of twist and writhing of circular DNAs with contraint, Biopolymers, 1979, 18 : 1709~1725

DOI: 10.1002/bip.1979.360180710

Google Scholar

[7] J.C. Simo, J.E. Marsden, P.S. Krishnaprasad, The Hamiltonian structure of nonlinear elasticity: the material and convective representations of solids,rods, and plates, Arch. Ration. Mech. Anal. 104 (2) (1988) 125–183

DOI: 10.1007/bf00251673

Google Scholar

[8] J.C. Simo, N. Tarnow, M. Doblaré, Non-linear dynamics of three-dimensional rods: exact energy and momentum conserving algorithms, Int. J. Numer. Meth.Engrg. 38 (9) (1995) 1431–1473

DOI: 10.1002/nme.1620380903

Google Scholar

[9] J.C. Simo, L. Vu-Quoc, A three-dimensional finite-strain rod model. Part II:Computational aspects, Comput. Meth. Appl. Mech. Engrg. 58 (1) (1986) 79–116

DOI: 10.1016/0045-7825(86)90079-4

Google Scholar

[10] J.C. Simo, L. Vu-Quoc, On the dynamics in space of rods undergoing large motions – A geometrically exact approach, Comput. Meth. Appl. Mech. Engrg.66 (2) (1988) 125–161.

DOI: 10.1016/0045-7825(88)90073-4

Google Scholar

[11] D.J. Dichmann,Yiwei Li,J.H. Maddocks,Hamiltonian formulations and symmetries in rod mechanics, Mathematics and its Applications 82 (1996) Springer Verlag, 71-113

DOI: 10.1007/978-1-4612-4066-2_6

Google Scholar

[12] E. Celledoni , N. S. A Hamiltonian and multi-Hamiltonian formulation of a rod model using quaternions, Comput. Methods Appl. Mech. Engrg. 199 (2010) 2813–2819

DOI: 10.1016/j.cma.2010.04.017

Google Scholar

[13] Yanzhu Liu, in China, non-linear mechanics of elastic rods–the theoric basis of DNA mechanic model, Tsinghua University Press&Springer, (2006)

Google Scholar

[14] Mourad Chamekh S.M.A,M.M., Modeling and numerical treatment of elastic rods with frictionless self-contact Comput. Methods Appl. Mech. Engrg.198(2009)3751-3764

DOI: 10.1016/j.cma.2009.08.005

Google Scholar

[15] Dichmann D.J. Hamiltonian Dynamics an elastica and stability of solitary waves.PH.D.thesis university of maryland

Google Scholar