Comment on "Buckling of Composite Plates with a Free Edge in Edgewise Bending and Compression"

Abstract

T ABLE 2 of Ref. 1 presented buckling loads for a laminated rectangular plate with two loaded edges simply supported, one side free and the opposite side either simply supported or clamped, for linearly varying edge loads. Since the analysis of Ref. 1 is based on classical plate theory, it is of interest to compare those results with buckling loads that include the effect of transverse shear deformations. Such buckling loads have been presented for plates with uniformly loaded edges. These were calculated using the shell-of-revolution program FASOR by considering the plate as part of a cylinder of very large radius. The circumferential direction of the cylindrical model corresponds to the longitudinal (loaded) direction of the plate, and the axial length of the cylinder equals the plate width b. The plate buckling load is obtained by minimizing the model buckling load with respect to the circumferential wave number N subject to the condition N=nirR/a, where n is the number of longitudinal half-waves of the plate buckle, R is the radius of the cylindrical model, and a is the length of the plate. This procedure is also applicable to plates with linearly varying edge loading. The dimensions of the laminated plate analyzed in Ref. 1 are 0 = 254 mm (10 in.) and 6 = 50.8 mm (2 in.). It is made of 0.127-mm (0.005-in.)-thick tape with the following insurface elastic properties: EX/E2 = 10.05, G12/E2 = Q.349, Hi =0.34, and E2 = 13.03 GPa (1.89x 10 psi), where 1 and 2 signify directions parallel and transverse, respectively, to the fibers and /*, is the major Poisson's ratio. The laminate definition is [±453/03]5 (erroneously reported as [±453 / 03/903]5in Ref. 1), thus giving a laminate thickness /z = 2.286 mm (0.090 in.) Neglecting the small anisotropic effect, this laminate has the bending stiffness matrix given by Eq. (25) of Ref. 1. Since the values of the transverse shear moduli G13 and G23 are unavailable, it is assumed that G13 = G23 = G12. (For typical unidirectional laminae, G23<G12 .) Again neglecting the small anisotropic effect, FASOR gives the transverse shear stiffness matrix [K] =8.951 x 10 N/m (5.112xl0 Ib/in.) [/], where [/] is the 2 x 2 unit matrix. Table 1 compares the classical plate theory results of Ref. 1 with the transverse shear deformation theory results Simply supported