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Finite Element Formulation for 3-Dimensional Large Rotation Analysis of A Beam

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Computational Mechanics ’95

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Abstract

Finite element analysis of 3-dimensional large rotation problem has been possible with nonlinear beam element by J.C.Simo,L.Vu-Quoc[1,2]. Their beam model is described by a configulation manifold which involves special orthogonal group SO(3). But the special orthogonal group is noncomutative, so the tangent stiffness matrix becomes non-symmetric away from equilibrium.

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References

  1. J.C. Simo,“A finite strain beam formulation. The three dimensional dynamic problem. Part”,Comput.Meths.Appl.Mech.Engrg.49(1985)55–70

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  2. J.C. Simo and L. Vu-Quoc,“A three-dimensional finite-strain rod model, part II. Computational aspects”,Comp.Meths.Appl.Mech.Engrg.58(1986)79–116

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  3. J. Argyris,“An excursion into large rotations”,Comput.Meths.Appl.Mech.Engrg.32 (1982)85–155

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  4. B. Nour-Omid and C.C. Rankin,“Finite rotation analysis and consistent linearization usingprojectors”,Comput.Meths.Appl.Mech.Engrg.93(1991)353–384

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  5. ABAQUS Theory Manual Version 5.2,Hibbit,Karlsson & Sorensen,Inc.

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  6. Y. Miyazaki,“Research of 3-dimensional erastica”,doctoral dissertation, 1993

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Author information

Authors and Affiliations

  1. Cray Research Japan LTD., Tokyo, Japan

    Masabumi Ishihara

Authors
  1. Masabumi Ishihara
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Editor information

Editors and Affiliations

  1. Computational Modeling Center, Georgia Institute of Technology, Atlanta, GA, 30332-0356, USA

    S. N. Atluri

  2. Department of Quantum Engineering & Systems Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113, Japan

    G. Yagawa

  3. Department of Mechanical Engineering, Vanderbilt University, P.O. Box 1592, Station B, Nashville, TN, 37235, USA

    Thomas Cruse

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© 1995 Springer-Verlag Berlin Heidelberg

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Ishihara, M. (1995). Finite Element Formulation for 3-Dimensional Large Rotation Analysis of A Beam. In: Atluri, S.N., Yagawa, G., Cruse, T. (eds) Computational Mechanics ’95. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-79654-8_405

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  • DOI: https://doi.org/10.1007/978-3-642-79654-8_405

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-79656-2

  • Online ISBN: 978-3-642-79654-8

  • eBook Packages: Springer Book Archive

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