Question 11.6: A structure is being designed that will involve a [(02/90)2]...

A [(0_2/90)2]_s graphite–epoxy laminate was also considered in Example Problem 11.1, 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 Equation 11.39.

N_{xx}=\frac{-\pi ^2}{(ma)^2}\left[D_{11}m^4+2(D_{12}+2D_{66})(mnR)^2+D_{22}(nR)^4+N_{yy}\left\lgroup\frac{naR}{\pi } \right\rgroup ^2\right]   (11.39)

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. Since transverse loading is zero (N_{yy} = 0), n = 1 and Equation 11.39

A plot of the predicted critical buckling load over the specified range in aspect ratio is presented in Figure 11.11. 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.