Question 10.S.P.6: A structure is being designed that will involve a [(02/90)2]...
A structure is being designed that will involve a [(0_{2}/90)_{2}]_{s} graphite–epoxy laminate with a width (in the y direction) of 150 mm. The length of the panel (in the x direction) has not yet been established, and could be anywhere from 150 to 750 mm. During service, the panel will be subjected to a compressive load N_{xx} (only), and simple supports of type S4 along all four edges. Buckling is therefore of concern. Predict the buckling load and mode for the panel, for any panel length ranging from 150 to 750 mm.
A [(0_{2}/90)_{2}]_{s} graphite–epoxy laminate was also considered in Sample Problem 1, and numerical values for the [ABD] matrix are listed there. As before, the 12-ply laminate has a total thickness t = 1.5 mm. Buckling loads and modes will be predicted using Eq. (39). According to the problem statement, b = 0.15 m, and 0.15 m < a< 0.75 m. The plate aspect ratio therefore varies over 1 ≤ R ≤ 5. Because transverse loading is zero (N_{yy} = 0), n = 1 and Eq. (39) becomes:
N_{xx} = \frac{-π^{2}}{(ma)^{2}} [D_{11} m^{4} + 2 (D_{12} + 2D_{66} (mnR)^{2} + D_{22} (nR)^{4}+ N_{yy} \left(\frac{naR}{\pi } \right) ^{2}] (39)
N_{xx} = \frac{-π^{2}}{(ma)^{2}} [40.1 m^{4} + 16.34 (mR)^{2} + 10.8 R^{4}]
A plot of the predicted critical buckling load over the specified range in aspect ratio is presented in Fig. 11. The buckling mode is predicted to increase as the aspect ratio increases: mode [1,1] is predicted over the range 1 < R < 1.96, mode [2,1] is predicted over the range 1.96 < R < 3.40, mode [3,1] is predicted for 3.40 < R < 4.81, and mode [4,1] is predicted for 4.81 < R < 5.00. Still higher buckling modes would occur at higher aspect ratios.
The predicted buckling load generally decreases with aspect ratio, although a local maximum in the buckling load occurs at each aspect ratio corresponding to a change in mode shape. At an aspect ratio R = 1 (i.e., for a square plate), buckling is predicted to occur at N_{xx}^{c} = 29.5 kN/m.
