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Theories of elastic slender curved rods

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Abstract

The linear and nonlinear theories of elastic slender curved rods are formulated in a systematic manner. Equations of equilibrium for stress resultants and moments are derived. The generalized strains are defined based on the principle of virtual work. Constitutive equations corresponding to small strains are obtained. The field equations for finite deformations of curved rods can be simplified in the case of small axial strain and moderately small rotations. Further simplifications can be made for the case of slightly curved rods. Two examples are presented to illustrate applications of the developed theories.

Resumé

Les théories linéaires et nonlinéaires des barres minces courbées élastiques sont formulées d'une manière systématique. Les équations d'équilibre pour les résultantes des contraintes et des moments sont dérivées. Les déformations généralisées sont définies d'après le principe des travaux virtuels. Les équations constitutives correspondant à des petites déformations sont obtenues. Les equations du champ pour des déformations finies des barres courbées peuvent être simplifiées dans le cas où la déformation axiale et les rotations sont petites. Des simplifications supplémentaires peuvent être effectuées dans le cas des barres légèrement courbées. Deux exemples sont présentées pour illustrer des applications des théories développées.

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References

  1. A.E.H. Love,A Treatise on the Mathematical Theory of Elasticity, Dover Publ., New York, Chapter 18, 381–398.

  2. J.E. Ericksen andC. Truesdell,Exact Theory of Stress and Strain in Rods and Shells, Arch. Rat. Mech. Anal.1, 295–323 (1957–1958).

    Google Scholar 

  3. E. Reissner,Variational Considerations for Elastic Beams and Shells, J. Eng. Mech. Div., Proc. American Soc. Civil Eng.88, EM 1, 23–57 (1962).

    Google Scholar 

  4. K. Washizu,Some Considerations on a Naturally Curved and Twisted Slender Beam, J. Math. Phys.43, 111–116 (1964).

    Google Scholar 

  5. G.E. Hay,The Finite Displacement of Thin Rods, Trans. American Math. Soc.51, 65–102 (1942).

    Google Scholar 

  6. H. Cohen,A Nonlinear Theory of Elastic Directed Curves, Int. J. Eng. Sci.4, 511–524 (1966).

    Google Scholar 

  7. S.S. Antman andW.H. Warner,Dynamical Theory of Hyperelastic Rods, Arch. Rat. Mech. Anal.23, 135–162 (1966).

    Google Scholar 

  8. A.E. Green andN. Laws,A General Theory of Rods, Proc. Royal Soc. London, Ser. A,293, 145–155 (1966).

    Google Scholar 

  9. A.E. Green, N. Laws andP. M. Nagadi,Rods, Plates and Shells, Proc. Cambridge Phil. Soc.64, 895–913 (1968).

    Google Scholar 

  10. C.B. Kafader,On the Nonlinear Theory of Rods, Int. J. Eng. Sci.10, 369–391 (1972).

    Google Scholar 

  11. J.L. Sanders, Jr.,Nonlinear Theories for Thin Shells, Quart. Appl. Math.21, 21–36 (1963).

    Google Scholar 

  12. S. Timoshenko,Strength of Materials, Part II, D. Van Nostrand Co., Inc. New York 292–296 (1958).

    Google Scholar 

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Authors and Affiliations

  1. Dept. of Aerospace and Mechanical Eng., University of Notre Dame, Notre Dame, Indiana, USA

    Nai-Chien Huang

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  1. Nai-Chien Huang
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Additional information

This research was supported by the Department of Navy, Office of Naval Research, under Project Themis and Contract ONR-N00014-68-A-0152 with the University of Notre Dame. This paper was presented at the 13th International Congress of Theoretical and Applied Mechanics, Moscow, USSR, August 21–26, 1972.

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Huang, NC. Theories of elastic slender curved rods. Journal of Applied Mathematics and Physics (ZAMP) 24, 1–19 (1973). https://doi.org/10.1007/BF01593995

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  • DOI: https://doi.org/10.1007/BF01593995

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