Meccanica

, Volume 44, Issue 6, pp 733–739 | Cite as

Large deflections of nonlinearly elastic non-prismatic cantilever beams made from materials obeying the generalized Ludwick constitutive law

Article

Abstract

This paper studies large deflections of nonlinearly elastic cantilever beams made from materials obeying the generalized Ludwick constitutive law. An exact moment-curvature formula which can be applied to study arbitrarily loaded and supported beams of rectangular cross-sections is developed. Several advantages of the generalized Ludwick’s model are illustrated. Numerical examples considered in this materially and geometrically nonlinear analysis clearly indicate rich nonlinear behavior of the beams.

Keywords

Large deflections Generalized Ludwick constitutive law Non-prismatic beams Material and geometrical nonlinearities 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Lee BK, Wilson JF, Oh SJ (1993) Elastica of cantilevered beams with variable cross sections. Int J Non-Linear Mech 28(5):579–589 CrossRefGoogle Scholar
  2. 2.
    Baker G (1993) On the large deflections of non-prismatic cantilevers with a finite depth. Comput Struct 46(2):365–370 CrossRefGoogle Scholar
  3. 3.
    Scarpello GM, Ritelli D (2006) Elliptic integral solutions of spatial elastica of a thin straight rod bent under concentrated terminal forces. Meccanica 41(5):519–527 MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Levyakov SV (2001) States of equilibrium and secondary loss of stability of a straight rod loaded by an axial force. Prikl Mekh Tekh Fiz 42(2):153–160 MATHGoogle Scholar
  5. 5.
    Oden JT, Childs SB (1970) Finite deflections of a nonlinearly elastic bar. J Appl Mech 69:48–52 CrossRefGoogle Scholar
  6. 6.
    Prathap G, Varadan TK (1976) The inelastic large deformation of beams. J Appl Mech 43:689–690 Google Scholar
  7. 7.
    Lo CC, Das Gupta S (1978) Bending of a nonlinear rectangular beam in large deflection. J Appl Mech 45:213–215 Google Scholar
  8. 8.
    Lewis G, Monasa F (1981) Large deflections of cantilever beams of nonlinear materials. Comput Struct 14(5–6):357–360 CrossRefGoogle Scholar
  9. 9.
    Lewis G, Monasa F (1982) Large deflections of cantilever beams of non-linear materials of the Ludwick type subjected to an end moment. Int J Non-Linear Mech 17(1):1–6 MATHCrossRefGoogle Scholar
  10. 10.
    Wang CY (1996) Global buckling load of a nonlinearly elastic bar. Acta Mech 119:229–234 MATHCrossRefGoogle Scholar
  11. 11.
    Lee K (2002) Large deflections of cantilever beams of non-linear elastic material under a combined loading. Int J Non-Linear Mech 37(3):439–443 MATHCrossRefGoogle Scholar
  12. 12.
    Jung JH, Kang TJ (2005) Large deflection analysis of fibers with nonlinear elastic properties. J Textile Inst 75(10):715–723 Google Scholar
  13. 13.
    Baykara C, Güven U, Bayer I (2005) Large deflections of a cantilever beam of nonlinear bimodulus material subjected to an end moment. J Reinf Plast Comp 24(12):1321–1326 CrossRefGoogle Scholar
  14. 14.
    Anandjiwala RD, Gonsalves JW (2006) Nonlinear buckling of woven fabrics Part I: Elastic and nonelastic cases. Textile Res J 76(2):160–168 CrossRefGoogle Scholar
  15. 15.
    Baragetti S (2006) A theoretical study on nonlinear bending of wires. Meccanica 41(4):443–458 MATHCrossRefGoogle Scholar
  16. 16.
    Brojan M, Videnic T, Kosel F (2007) Non-prismatic non-linearly elastic cantilever beams subjected to an end moment. J Reinf Plast Comp 26(11):1071–1082 CrossRefGoogle Scholar
  17. 17.
    Brojan M, Puksic A, Kosel F (2007) Buckling and post-buckling of a nonlinearly elastic column. Z Angew Math Mech 87(7):518–527 MATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Shatnawi AS, Al-Sadder S (2007) Exact large deflection analysis of nonprismatic cantilever beams of nonlinear bimodulus material subjected to tip moment. J Reinf Plast Comp 26(12):1253–1268 CrossRefGoogle Scholar
  19. 19.
    Al-Sadder S, Shatarat N (2007) A proposed technique for large deflection analysis of cantilever beams composed of two nonlinear elastic materials subjected to an inclined tip concentrated force. Adv Struct Eng 10(3):319–335 CrossRefGoogle Scholar
  20. 20.
    Eren I (2008) Determining large deflections in rectangular combined loaded cantilever beams made of non-linear Ludwick type material by means of different arc length assumptions. Sadhana 33(1):45–55 MATHCrossRefGoogle Scholar
  21. 21.
    Solano-Carrillo E (2009) Semi-exact solutions for large deflections of cantilever beams of non-linear elastic behaviour. Int J Non-Linear Mech 44:253–256 CrossRefGoogle Scholar
  22. 22.
    Rivlin RS (1948) Large elastic deformations of isotropic materials—I. Fundamental concepts. Phil Trans R Soc Lond Ser A 240(822):459–490 MATHCrossRefMathSciNetADSGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Faculty of Mechanical EngineeringUniversity of LjubljanaLjubljanaSlovenia

Personalised recommendations