The optimum stacking sequence of lamination of graphite-epoxy cylindrical shells is analytically studied under the condition to get the highest compressive buckling load. The shells are composed of three types of layers of whichfiber directions are 0° (axial layer), 90° (circumferential layer) and ±α° (helical layer)with respect to the generatrix of the cylinder. The buckling load is evaluated with the coefficient f=σ
cr·(R/t). For the optimum constitution of the orthotropic cylinder corresponding to the case where the laminates are composed of many numbers of layers and regarded as homogeneous in the thickness direction, it is disclosed that the maximum value of f, i.e. f
0max, is 34. 1GPa for V
f=65%, at first. The values of f of the 2-, 3-, 4-, 6- and 8-layer cylinders are calculated for all combinations of the stacking sequences of each number of layers in the use of an energy method. In the case of 2-layer one the value of f for the optimum lamination is only about 47% of f
0max. However, the maximum value of f of the 6-layer one is very close to f
0max.
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