The cylindrical vessels are used for storing fluids at high pressure. If the magnitude of the internal/external pressure is closer to the yield strength of the material used, then no thickness of the material will prevent the failure of the vessel. Hence shrink-fitted compound cylinders are used, which can store the fluids at higher pressure closer to the yield stress of the material. Optimally designed compound cylinder has equal maximum hoop stress in both — the inner and outer cylinders. The value of this hoop stress is closer to the value of yield stress of the material used. Such compound cylindrical vessels can be used in future automobile and space vehicles for storing gaseous fuels. In such case, the compound cylinder will be subjected to repeated loading — the internal pressure varying from zero to maximum value. In this paper, an effort is made to analyze the compound cylinder under fatigue loading by using ANSYS DesignSpace FEA software. The analysis is interesting because the inner cylinder is subjected to fluctuating hoop stress varying in magnitude and direction; and the outer cylinder is subjected to hoop stress varying in magnitude only. Finally an effort is made to find out the optimum thickness of both the cylinders under fatigue loading.

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