Issue 48

Y. Khalfi et alii, Frattura ed Integrità Strutturale, 48 (2019) 208-221; DOI: 10.3221/IGF-ESIS.48.22 220 Figure 6: The effect of modulus ratio on the critical buckling load of square plate with or without elastic foundations subjected to biaxial compression: (a)a =10h and (b)a =20h. C ONCLUSION refined and simple shear deformation theory is presented for mechanical buckling of rectangular composite plates in contact with two-parameter elastic foundation. Unlike the conventional shear deformation theories, the proposed refined shear deformation theory contains only four unknowns and has strong similarities with the CPT in many aspects, accounts for a quadratic variation of the transverse shear strains across the thickness, and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. To clarify the effect of shear deformation on the critical buckling, the results obtained by the present theory as well as HSDT, S and FSDT are compared with those obtained by CPT. It is shown through the numerical examples that the results of the shear deformation plate theories are lower than those of the CPT, indicating the shear deformation effect. All comparison studies show that the critical buckling mechanical obtained by the proposed theory with four unknowns are almost identical with those predicted by other shear deformation theories containing five unknowns. It can be concluded that the proposed theory is accurate and efficient in predicting the mechanical buckling responses of rectangular composite plates resting on two parameter (Pasternak’s model) elastic foundations. Due to the interesting features of the present theory, the present findings will be a useful benchmark for evaluating the reliable of other future plate theories. R EFERENCES [1] Seyvet, J. (2002). The French composite materials industry (Louis Berreur, Bertrand de Maillard & Stanislas Nösperger., Paris). [2] Gay, D. (2014). Design and Applications (Composite Materials third edition, CRC Press) . [3] Ponte Castañeda, P and Suquet, P. (1997). Nonlinear composites, Adv. Appl. Mech., 34, pp. 171–302. [4] Milton, G. W. (2002). The Theory of Composites Cambridge University Press. [5] Moulinec, H. and Suquet, P. (1998). A numerical method for computing the overall response of nonlinear composites with complex microstructure, Comput. Meth-ods Appl. Mech. Eng. 157, pp. 69–94. [6] Jones, R. M. (1998). Mechanics of Composite Materials, CRC Press. [7] Timoshenko, S.P., Woinowsky-Krieger S. (1959), Theory of plates and shells, New York: McGraw-Hill. [8] Timoshenko, S. P., Gere, J. M. (1961). Theory of elastic stability, New York, McGraw-Hill. [9] Bank, L., Yin, J. (1996). Buckling of orthotropic plates with free and rotationally restrained unloaded edges, Thin Wall Struct. 24(1), pp. 83–96. [10] Kang, J. H., Leissa, A. W. (2005). 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), pp. 4220–38. A