A fourier series solution for a cylindrical shell subject to a radial loading acting over a circular patch

摘要

The case of a cylindrical vessel or pipe subject to a radial load, uniformly distributed, acting over a circular area is addressed utilising the Sanders' linear shell equations. Using these equations to describe the behaviour of the shell underload, derivations are made for thc vessel displacements and stress resultants. The loading, together with the displacements and stress resultants are represented by double Fourier series expressions. By examining thc boundary conditions which representthe circular loaded area, an expression is found which when integrated, adequately describes the loading on the shell. Applying this to the Sanders equations allows the displacements and stress resultants to be formulated in a suitable form forprogramming into a microcomputer. Illustrative examples are given and comparisons are made with the approach used by the Pressure Vessel Standard BS5500, where the circular patch of radius R{sub}0 is considered by analysing a square patch of length equalto 1.7 R{sub}0, and with the ASME VIII patch, where the square patch is a length of 1.75R{sub}0.