Design a cylindrical thin$-$wall composite fuselage for storing compressed natural gas at a maximum operating

pressure of $20$ MPa $.$ The pressure vessel is to be made by filament winding with fibres at $+-45$ degrees and required

to sustain three times the operating pressure without failure. The radius of the cylindrical pressure vessel is required

to be $0\mathrm{.}25$ meters, and the length is $2$ meters. The maximum strengths of the composite ply are equal to $2000$ MPa

in the fibre direction and zero perpendicular to the fibre direction. Determine the minimum number of composite

plies required to meet the design requirements.

Hoop stress and longitudinal stress of the cylinder are ${}_h=\frac{pr}{t}{}_a=\frac{pr}{2t}.$