Issue 48

Y. Khalfi et alii, Frattura ed Integrità Strutturale, 48 (2019) 208-221; DOI: 10.3221/IGF-ESIS.48.22 216 Clearly, when the effect of transverse shear deformation is neglected, the Eq.(29) yields the result obtained using the classical plate theory [22]. It indicates that transverse shear deformation has the effect of reducing the buckling load. For each choice of m and n , there is a corresponsive unique value of N 0 . The critical buckling load is the smallest value of N 0 ( m, n ). R ESULTS AND DISCUSSION o illustrate the proposed theory, a simply supported rectangular plate subjected to the different types of loading (or even Figure.2), is considered to verify the accuracy of the current theory in the prediction of the critical loads of the mechanical buckling of rectangular composite plates. Comparisons are made with different plate theories available in the literature The description of the different displacement models is given in Table 1. In order to study the effects of the parameters of the foundation, side-to-thickness ratio ( a/h ) and the modulus ratios ( E 1 / E 2 ), isotropic square plates and orthotropes are considered. The shear correction factor (k=5/6) and also used for the first order shear deformation theory (FSDT) and a comparison with the current theory is established. Figure 3: The loading conditions of square plate for (a) uniaxial compression, (b) biaxial compression. Model Theory Unknown functions CPT FSDT HSDT Present Classical plate theory First-order shear deformation theory [23] Higer order shear deformation theory [24] Present refined plate theory 3 5 5 4 Table 1 : Displacement models. It is assumed that the thickness and properties of materials for all laminates are the same. The following engineer constants are used [25]:  for isotropic rectangular plates: E 1 = E 2 = E , G 12 = G 13 = G 23 = G = E /2(1+ ν ), ν 12 = ν 13 = ν 23 = ν = 0.3 (30)  For orthotropic rectangular plates: E 1 = E 2 varied, G 12 / E 2 = G 13 / E 2 = 0.5, G 23 / E 2 = 0.2, ν 12 = 0.25, ν 21 :=( ν 12 E 2 )/ E 1 (31) For convenience, the following nondimensional buckling load is used: T