Advertisement

A holistic approach for local buckling of composite laminated beams under compressive load

  • Philip SchreiberEmail author
  • Christian Mittelstedt
Original
  • 28 Downloads

Abstract

The present paper deals with a new holistic closed-form analytical model for the local buckling load of thin-walled composite beams with I-, Z-, C-, L- and T-cross sections under axial compressive load. The beam is simply supported at both ends (Euler case II), and the plate behaviour of web and flanges is described by the Classical Laminated Plate Theory. Furthermore, symmetric and orthotropic laminates are considered. In previous investigations on composite beams under compression, the web and flange plates are considered as separate composite plates. The present analysis is performed using the Ritz method in which an approach for the entire cross section is realized. The individual webs and flanges of the beam are assembled by suitable continuity conditions into one system. In order to achieve that, new displacement shape functions for web and flange that fulfil all boundary conditions have been developed. The present closed-form analytical method enables the explicit representation of the buckling load for the entire composite beam under axial compression. The comparison between the present approach and comparative finite element simulations shows a very satisfactory agreement. The present method is ideal for pre-designing such structures, highly efficient in terms of computational effort and very suitable for practical engineering work.

Keywords

Composites Laminates Buckling Stability 

Notes

References

  1. 1.
    Allen, H.G., Bulson, P.S.: Background to Buckling. McGraw-Hill, London (1980)Google Scholar
  2. 2.
    Altenbach, H., Altenbach, J., Kissing, W.: Mechanics of Composite Structural Elements. Berlin, Heidelberg (2004)CrossRefGoogle Scholar
  3. 3.
    Barbero, E.J., Raftoyiannis, I.G.: Local buckling of frp beams and columns. J. Mater. Civ. Eng. 5(3), 339–355 (1993)CrossRefGoogle Scholar
  4. 4.
    Becker, W., Hansel, W., Oehm, M.: Buckling analysis of non-orthotropic laminates by means of b-spline functions. Technische Mechanik 21(1), 31–40 (2000)Google Scholar
  5. 5.
    Cardoso, D.C.T., Vieira, J.D.: Comprehensive local buckling equations for FRP I-sections in pure bending or compression. Compos. Struct. 182, 301–310 (2017)CrossRefGoogle Scholar
  6. 6.
    Cardoso, D.C.T., Harries, K.A., de Batista, E.M.: Closed-form equations for compressive local buckling of pultruded thin-walled sections. Thin-Walled Struct 79, 16–22 (2014)CrossRefGoogle Scholar
  7. 7.
    Chung, D.D.L.: Composite Materials: Science and Applications, 2nd edn. Engineering Materials and Processes. London (2010)CrossRefGoogle Scholar
  8. 8.
    Dassault Systems: Abaqus 6.14 documentation., Providence RI, USA (2014)Google Scholar
  9. 9.
    Herrmann, J., Küuhn, T., Müllenstedt, T., Mittelstedt, S., Mittelstedt, C.T.: Closed-form approximate solutions for the local buckling behavior of composite laminated beams based on third-order shear deformation theory. In: Altenbach, H., Jablonski, F., Müller, W., Naumenko, K., Schneider, P. (eds.) Advances in Mechanics of Materials and Structural Analysis. Advanced Structured Materials, vol. 80. Springer, Cham (2018)Google Scholar
  10. 10.
    Kirchhoff, G.: Über das Gleichgewicht und die Bewegung einer elastischen Scheibe. Journal für die reine und angewandte Mathematik 39, 51–88 (1850)CrossRefGoogle Scholar
  11. 11.
    Kollár, L.P.: Local buckling of fiber reinforced plastic composite structural members with open and closed cross sections. J. Struct. Eng. 129(11), 1503–1513 (2018)CrossRefGoogle Scholar
  12. 12.
    Kollár, L.P., Springer, G.S.: Mechanics of Composite Structures. Cambridge University Press, Cambridge (2003)CrossRefGoogle Scholar
  13. 13.
    Kroll, W.D., Fisher, G.P., Heimerl, G.J.: Charts for Calculation of the Critical Stress for Local Instability of Columns with I-, Z-, Channel and Rectangular-Tube Section. National Advisory Committee for Aeronautics (1943)Google Scholar
  14. 14.
    Kuehn, T., Pasternak, H., Mittelstedt, C.: Local buckling of sheardeformable laminated composite beams with arbitrary cross-sections using discrete plate analysis. Compos. Struct. 113, 236–248 (2014)CrossRefGoogle Scholar
  15. 15.
    Liu, Q., Qiao, P., Guo, X.: Buckling analysis of restrained orthotropic plates under combined in-plane shear and axial loads and its application to web local buckling. Compos. Struct. 111, 540552 (2014)Google Scholar
  16. 16.
    Lundquist, E.E.: Local Instability of Centrally Loaded Columns of Channel Section and Z-Section. National Advisory Committee for Aeronautics (1939)Google Scholar
  17. 17.
    Lundquist, E.E., Stowell, E.Z., Schuette, E.H.: Principles of Moment Distribution Applied to Stability of Structures Composed of Bars or Plates. National Advisory Committee for Aeronautics (1943)Google Scholar
  18. 18.
    Mittelstedt, C.: Closed-form analysis of the buckling loads of symmetrically laminated orthotropic plates considering elastic edge restraints. Compos. Struct. 81(4), 550–558 (2007a)CrossRefGoogle Scholar
  19. 19.
    Mittelstedt, C.: Local buckling of wide- ange thin-walled anisotropic composite beams. Arch. Appl. Mech. 77(7), 439–452 (2007b)CrossRefGoogle Scholar
  20. 20.
    Mittelstedt, C.: Stability behaviour of arbitrarily laminated composite plates with free and elastically restrained unloaded edges. Int. J. Mech. Sci. 49(7), 819–833 (2007c)CrossRefGoogle Scholar
  21. 21.
    Mittelstedt, C., Becker, W.: Strukturmechanik ebener Laminate. Studienbereich Mechanik, Darmstadt (2016)Google Scholar
  22. 22.
    Ni, Q.-Q., Xie, J., Iwamoto, M.: Buckling analysis of laminated composite plates with arbitrary edge supports. Compos. Struct. 69(2), 209–217 (2005)CrossRefGoogle Scholar
  23. 23.
    Qiao, P., Shan, L.: Explicit local buckling analysis and design of fiber reinforced plastic composite structural shapes. Compos. Struct. 70(4), 468–483 (2005)CrossRefGoogle Scholar
  24. 24.
    Qiao, P., Zou, G.: Local buckling of elastically restrained fiber-reinforced plastic plates and its application to box sections. J. Eng. Mech. 128(12), 1324–1330 (2002)CrossRefGoogle Scholar
  25. 25.
    Qiao, P., Davalos, J.F., Wang, J.: Local buckling of composite frp shapes by discrete plate analysis. J. Struct. Eng. 127(3), 245–255 (2001)CrossRefGoogle Scholar
  26. 26.
    Reddy, J.N.: Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, 2nd edn. CRC Press, Boca Raton (2004)CrossRefGoogle Scholar
  27. 27.
    Ritz, W.: Über eine neue Methode zur Lösung gewisser Variationsprobleme der mathematischen Physik. Journal für reine und angewandte Mathematik 135, 1–61 (1909)MathSciNetzbMATHGoogle Scholar
  28. 28.
    Schürmann, H.: Konstruieren mit Faser-Kunststoff-Verbunden. Springer, Berlin (2005)Google Scholar
  29. 29.
    Stowell, E.Z., Lundquist, E.E.: Local Instability of Columns with I-, Z-, Channel, and Rectangular-Tube Sections. National Advisory Committee for Aeronautics (1939)Google Scholar
  30. 30.
    Tarjáan, G., Kollár, L.P.: Local buckling of composite beams with edge-stiffened anges subjected to axial load. J. Reinf. Plast. Compos. 34(22), 1884–1901 (2015)CrossRefGoogle Scholar
  31. 31.
    Timosenko, S.P., Gere, J.M.: Theory of Elastic Stability, p. 9780486472072. Mineola, New York (2009)Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Fachgebiet Konstruktiver Leichtbau und BauweisenTechnische Universität DarmstadtDarmstadtGermany

Personalised recommendations