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Direct approach to elastic deformations and stability of thin-walled rods of open profile

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Abstract

A new geometrically nonlinear theory of thin-walled rods of open profile accounting for warping and bi-moment is developed. The direct approach we employ is based on the principles of Lagrangean mechanics. Linear equations for small deformations in the vicinity of a pre-stressed state are derived. These equations can be used in particular for stability analysis. Stability of a beam subjected to axial or transversal loading is considered as an example. Solutions with coupled bending and twisting mode of buckling are compared with the classical Euler’s solution, existing results for thin-walled rods and numerical solutions for a shell model.

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References

  1. Antman, S.S.: The theory of rods. In: Flügge, S., Truesdell, C. (eds.) Handbuch der Physik, Bd.VIa/2. Springer, Berlin (1972)

    Google Scholar 

  2. Eliseev, V.V.: Mechanics of Elastic Bodies [in Russian]. SPbSPU, St.Petersburg, p. 336 (2003)

  3. Yeliseyev V.V., Orlov S.G.: Asymptotic splitting in the three-dimensional problem of linear elasticity for elongated bodies with a structure. J. Appl. Math. Mech. 63, 85–92 (1999)

    Article  MathSciNet  Google Scholar 

  4. Vlasov V.Z.: Thin-Walled Elastic Beams, 2nd edn. Israel Program for Scientific Translations, Jerusalem (1961)

    Google Scholar 

  5. Timoshenko S., Gere J.M.: Theory of Elastic Stability, 2nd edn, Chap. 5. McGraw-Hill, New-York (1961)

    Google Scholar 

  6. Epstein M.: Thin-walled beams as directed curves. Acta Mech. 33, 229–242 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  7. Golubev O.B.: Generalization of the theory of thin rods [in Russian]. Trudy LPI (Leningrad Polytechnical Institute) 226, 83–92 (1963)

    MathSciNet  Google Scholar 

  8. Simo J.C., Vu-Quoc L.: A geometrically exact rod model incorporating shear and torsion-warping deformation. Int. J. Solids Struct. 27, 371–393 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  9. Kim M.Y., Chang S.P., Kim S.B.: Spatial stability analysis of thin-walled space frames. Int. J. Numer. Methods Eng. 39, 499–525 (1996)

    Article  MATH  Google Scholar 

  10. Yiu, F.: A geometrically exact thin-walled beam theory considering in-plane cross-section distortion. PhD thesis, Cornell University, Ithaca (2005)

  11. Vetyukov Yu.: Consistent approximation for the strain energy of a 3D elastic body adequate for the stress stiffening effect. Int. J. Struct. Stab. Dyn. 4, 279–292 (2004)

    Article  Google Scholar 

  12. Vetyukov, Yu.: Lagrangian mechanics and finite deformations of thin shells. ZAMM (submitted for publication)

  13. Nayfeh A.H.: Perturbation Methods. John Wiley, New York (1972)

    Google Scholar 

  14. Ziegler H.: Principles of Structural Stability. Blaisdell Pub. Co., London (1968)

    Google Scholar 

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Authors and Affiliations

  1. Department of Computer Technologies in Engineering, St. Petersburg State Polytechnical University, Polytechnicheskaya ul. 29, 195251, St. Petersburg, Russia

    Yury Vetyukov

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  1. Yury Vetyukov
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Correspondence to Yury Vetyukov.

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Vetyukov, Y. Direct approach to elastic deformations and stability of thin-walled rods of open profile. Acta Mech 200, 167–176 (2008). https://doi.org/10.1007/s00707-008-0026-6

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  • DOI: https://doi.org/10.1007/s00707-008-0026-6

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