On Stability of Elastic Rectangular Sandwich Plate Subject to Biaxial Compression

  • Denis SheydakovEmail author
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 15)


In the present paper, in the framework of a general stability theory for three-dimensional bodies the buckling analysis has been carried out for a rectangular sandwich plate subject to biaxial compression. The sandwich plate consists of a porous core, covered by a hard and stiff shell. The behavior of a coating is investigated in the framework of a classic (non-polar) continuum model, while to describe the properties of a core the Cosserat continuum model is used. Using the linearization method in the vicinity of a basic state, the neutral equilibrium equations have been derived, which describe the perturbed state of a sandwich plate. The linearized boundary-value problems have been formulated both for a case of a general sandwich plate and for a sandwich plate with identical top and bottom coatings. By solving these problems numerically for some specific materials, the critical curves and corresponding buckling modes can be found, and the stability regions can be constructed in the plane of loading parameters (relative axial compressions).


Buckling analysis Sandwich plate Biaxial compression 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Cosserat, E., Cosserat, F.: Theorie des Corps Deformables. Hermann et Fils, Paris (1909)Google Scholar
  2. 2.
    Eremeyev, V.A., Zubov, L.M.: On stability of elastic bodies with couple-stresses. Mekhanika Tverdovo Tela (3):181–190, (1994) (in Russian)Google Scholar
  3. 3.
    Eringen, A.C.: Microcontinuum Field Theory I, Foundations and Solids. Springer, New York (1999)CrossRefGoogle Scholar
  4. 4.
    Kafadar, C.B., Eringen, A.C.: Micropolar media - I, The classical theory. Int. J. Eng. Sci. 9, 271–305 (1971)CrossRefGoogle Scholar
  5. 5.
    Lakes, R.: Experimental methods for study of Cosserat elastic solids and other generalized elastic continua. In: Muhlhaus, H., Wiley, J. (ed.) Continuum models for materials with micro-structure, pp. 1–22. New York (1995)Google Scholar
  6. 6.
    Lurie, A.I.: Non-linear Theory of Elasticity. North-Holland, Amsterdam (1990)Google Scholar
  7. 7.
    Maugin, G.A.: On the structure of the theory of polar elasticity. Philosophical Transactions of Royal Society London A 356, 1367–1395 (1998) Google Scholar
  8. 8.
    Nikitin, E., Zubov, L.M.: Conservation laws and conjugate solutions in the elasticity of simple materials and materials with couple stress. J. Elast. 51, 1–22 (1998)CrossRefGoogle Scholar
  9. 9.
    Pietraszkiewicz, W., Eremeyev, V.A.: On natural strain measures of the non-linear micropolar continuum. Int. J. Solids Struct. 46, 774–787 (2009)CrossRefGoogle Scholar
  10. 10.
    Sheydakov, D.N.: Stability of a rectangular plate under biaxial tension. J. Appl. Mech. Tech. Phys. 48(4), 547–555 (2007)CrossRefGoogle Scholar
  11. 11.
    Sheydakov, D.N.: Buckling of elastic composite rod of micropolar material subject to combined loads. In: Altenbach, H., Erofeev, V.I., Maugin, G.A.: (eds.) Mechanics of Generalized Continua – From Micromechanical Basics to Engineering Applications, pp. 255–271. Springer, Berlin, (2011)Google Scholar
  12. 12.
    Toupin, R.A.: Theories of elasticity with couple-stress. Arch. Ration. Mech. Anal. 17, 85–112 (1964)CrossRefGoogle Scholar
  13. 13.
    Zubov, L.M.: Nonlinear Theory of Dislocations and Disclinations in Elastic Bodies. Springer, Berlin (1964)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.South Scientific Center of Russian Academy of SciencesRostov-on-DonRussia

Personalised recommendations