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Some Considerations on Variational Principle for Elastic Rods with Finite Rotations in Space

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Computational Mechanics ’86

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Summary

An effort is made to derive a complementary energy principle for large deflection problems of nonplanar rods with finite rotations in space. As with the existing literature the subsidiary conditions are given in linear forms while the complementary energy functional is given in nonlinear forms with respect to the generalized stress resultants and moments.

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References

  1. Washizu, K., “Variational Methods in Elasticity and Plasticity” Pergamon Press, 3rd edition, 1982.

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  2. Washizu, K., “On the principle of Complementary Energy in Nonlinear Elasticity” Proc. of the 11th JSSC Matrix Symp., 1977.

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  3. Stumpf, H., “Die Extremalprinzipe der nichtlinearen Plattentheorie” ZAMM, 55(1975) 110–112.

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  4. Stumpf, H., “Die dualen Variationsprinzipien mit Extremal- eigenschaft in der nichtlinearen Theorie flacher Schalen” ZAMM 56 (1976) 53–155.

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  5. Fraeijs de Veubeke, B.,”A New Variational Principle for Finite Elastic Displacements” Int. J. Engng. Sci. 10(1972) 745–763.

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  6. Murakawa, H. and S.N. Atluri, “Finite Elasticity Solutions Using Hybrid Finite Elements Based on a Complementary Energy Principle” J. Appl. Mech., 45(1978) 539–547.

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  7. Iura, M. and M. Hirashima, “Geometrically Nonlinear Theory of Naturally Curved and Twisted Rods Undergoing Finite Rotations” J. of Structural Engineering, Vol.32A/1986.3.

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Author information

Authors and Affiliations

  1. Department of Civil and Structural Engineering, Tokyo Denki University, Hatoyama, Hiki-gun, Saitama, 350-03, Japan

    M. Iura

Authors
  1. M. Iura
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Editor information

Editors and Affiliations

  1. Department of Nuclear Engineering, The University of Tokyo, 3-1, Hongo 7-chome, Bunkyo-ku, Tokyo 113, Japan

    Genki Yagawa

  2. Center for the Advancement of Computational Mechanics, School of Civil Engineering, Georgia Institute of Technology, 225, North Avenue, Atlanta, GA, 30332, USA

    Satya N. Atluri

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© 1986 Springer Japan

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Iura, M. (1986). Some Considerations on Variational Principle for Elastic Rods with Finite Rotations in Space. In: Yagawa, G., Atluri, S.N. (eds) Computational Mechanics ’86. Springer, Tokyo. https://doi.org/10.1007/978-4-431-68042-0_67

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  • DOI: https://doi.org/10.1007/978-4-431-68042-0_67

  • Publisher Name: Springer, Tokyo

  • Print ISBN: 978-4-431-68044-4

  • Online ISBN: 978-4-431-68042-0

  • eBook Packages: Springer Book Archive

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