APPLICATION OF LAPLACE TRANSFORM TO THE STATIC ANALYSIS OF THIN CIRCULAR CYLINDRICAL SHELL UNDER INTERNAL HYDROSTATIC PRESSURE AND RING FORCE.
Abstract
The analysis of a circular cylindrical shell under internal hydrostatic pressure and ring force is carried out in this paper. The governing fourth order differential equation, similar to that of a beam on elastic foundation was adopted from the bending theory of shells. Laplace transform was successfully used to solve the differential equation for the displacements and stresses. The results accurately agreed with those obtained using the classical and initial value methods as well as the method proposed by the Indian Standard IS 3370. The Laplace transform, less tedious and more time saving than its counterparts, proved to be well conditioned for handling the local line force induced by the ring. The introduction of the ring reduced considerably the displacements and stresses in the cylinder. Specifically reduction of 43.75%, 38.85%, 25.10%, 1.65% and 43.75% on the maximum deflection, rotation, bending moment, shear force, and hoop tension respectively was achieved as a result of the introduction of the ring. The optimum location of the ring along the height of the cylindrical shell was also established to be 0.69 times height, measured from the top of cylinder.
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KEYWORDS Â Â Laplace transform, cylindrical shell, hydrostatic pressure, ring force.
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