Abstract
Buckling analysis of isotropic and orthotropic plates resting on two-parameter Pasternak’s foundations using the four-variable refined plate theory is presented in this paper. The theory takes account of transverse shear effects and parabolic distribution of the transverse shear strains through the thickness of the plate; hence, it is unnecessary to use shear correction factors. Governing equations are derived from the principle of virtual displacements. The nonlinear strain–displacement of Von Karman relations is also taken into consideration. The closed-form solution of a simply supported rectangular plate subjected to in-plane loading has been obtained by using the Navier method. Numerical results obtained by the present theory are compared with classical plate theory solutions, first-order shear deformable theory solutions, higher-order shear deformation theory and available exact solutions in the literature. The effects of the foundation parameters, side-to-thickness ratio and modulus ratio, the isotropic and orthotropic square plates are considered in this analysis. It can be concluded that the present theory, which does not require shear correction factor, is not only simple but also comparable to the first-order shear deformable theory.
We’re sorry, something doesn't seem to be working properly.
Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.
References
J. Seyvet, The French Composite Materials Industry (Louis Berreur, Bertrand de Maillard & Stanislas Nösperger, Paris, 2002)
D. Gay, Design and Applications, 3rd edn. (CRC Press, Boca Raton, 2014)
P. Ponte Castañeda, P. Suquet, Nonlinear composites. Adv. Appl. Mech. 34, 171–302 (1997)
G.W. Milton, The Theory of Composites (Cambridge University Press, Cambridge, 2002)
H. Moulinec, P. Suquet, A numerical method for computing the overall response of nonlinear composites with complex microstructure. Comput. Methods Appl. Mech. Eng. 157, 69–94 (1998)
Y. Das, Buckling of rectangular orthotropic plates. Appl. Sci Res. 11(1), 97–103 (1963)
S.P. Timoshenko, S. Woinowsky-Krieger, Theory of Plates and Shells (McGraw-Hill, New York, 1959)
S.P. Timoshenko, J.M. Gere, Theory of Elastic Stability (McGraw-Hill, New York, 1961)
L. Bank, J. Yin, Buckling of orthotropic plates with free and rotationally restrained unloaded edges. Thin Wall Struct. 24(1), 83–96 (1996)
J.H. Kang, A.W. Leissa, Exact solutions for the buckling of rectangular plates having linearly varying in-plane loading on two opposite simply supported edges. Int. J. Solids Struct. 42(14), 4220–4238 (2005)
M. Aydogdu, M.C. Ece, Buckling and vibration of non-ideal simply supported rectangular isotropic plates. Mech. Res. Commun. 33(4), 532–540 (2006)
I. Hwang, J.S. Lee, Buckling of orthotropic plates under various inplane loads. KSCE J. Civ. Eng. 10(5), 349–356 (2006)
E. Reissner, The effect of transverse shear deformation on the bending of elastic plates. J. Appl. Mech. 12(2), 69–77 (1945)
R.D. Mindlin, Influence of rotary inertia and shear on flexural motions of isotropic, elastic plates. J. Appl. Mech. 18(1), 31–38 (1951)
M. Levinson, An accurate simple theory of the statics and dynamics of elastic plates. Mech. Res. Commun. 7(6), 343–350 (1980)
J.N. Reddy, A simple higher-order theory for laminated composite plates. J. Appl. Mech. 51, 745–752 (1984)
R.P. Shimpi, H.G. Patel, A two variable refined plate theory for orthotropic plate analysis. Int. J. Solids Struct. 43(22–23), 6783–6799 (2006)
Y. Khalfi, M.S.A. Houari, A. Tounsi, A refined and simple shear deformation theory for thermal buckling of solar functionally graded plates on elastic foundation. Int. J. Comput. Method 11(5), 1350077 (2014)
H.H. Abdelaziz, H.A. Atmane, I. Mechab, L. Boumia, A. Tounsi, E.A. AddaBedia, Static analysis of functionally graded sandwich plates using an efficient and simple refined theory. Chin. J. Aeronaut. 24, 434–448 (2011)
M.A. Aiello, L. Ombres, Buckling and vibrations of unsymmetric laminates resting on elastic foundations under in-plane and shear forces. Compos. Struct. 44, 31–41 (1999)
K. Draiche, A. Tounsi, Y. Khalfi, A trigonometric four variable plate theory for free vibration of rectangular composite plates with patch mass. Steel Compos. Struct. Int. J 17(1), 69–81 (2014)
S.-E. Kim, H.-T. Thai, J. Lee, Buckling analysis of plates using the two variable refined plate theory. Thin-Walled Struct. 47, 455–462 (2009)
I. Harik, R. Ekambaram, Elastic stability of orthotropic plates. Thin-Wall Struct. 6(5), 405–416 (1988)
G. Bao, W. Jiang, J.C. Roberts, Analytic and finite element solutions for bending and buckling of orthotropic rectangular plates. Int. J. Solids Struct. 34(14), 1797–1822 (1997)
I. Hwang, J. Lee, Buckling of orthotropic plates under various inplane loads. KSCE J. Civ. Eng. 10(5), 349–356 (2006)
J.M. Whitney, N.J. Pagano, Shear deformation in heterogeneous anisotropic plates. J. Appl. Mech. 37, 1031–1036 (1970)
J.N. Reddy, A refined nonlinear theory of plates with transverse shear deformation. Int. J. Solids Struct. 20(9), 881–896 (1984)
J.N. Reddy, Mechanics of Laminated Composite Plate: Theory and Analysis (CRC Press, New York, 1997)
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Khalfi, Y., Sofiane, G., Bouchikhi, A.S. et al. A Novel Refined Shear Deformation Theory for the Buckling Analysis of Thick Isotropic and Orthotropic Plates on Two-Parameter Pasternak’s Foundations. J Fail. Anal. and Preven. 20, 75–84 (2020). https://doi.org/10.1007/s11668-019-00713-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11668-019-00713-y