A simplified solution for stresses in thick-wall cylinders for various loading conditions

Abstract

The determination of stresses in thick-wall cylinders, under non-uniform external pressure, may be performed by means of Airy's stress function approach. In this work a simplified closed-form solution has been obtained for hollow cylinders subjected to loads symmetrically distributed about an axis of the cross-section, acting in the radial direction over part of the circumference. The cylinder is considered to be long, elastic and with a constant wall-thickness. The problem may be treated as a two-dimensional elasticity problem of plane-strain, since the loads are uniformly distributed along the length. The distribution of pressure is represented by the Fourier series, whose coefficients are calculated for some simple cases through elementary functions or, in general, by numerical integration. The oscillations of the expanded functions in the Fourier series are dampened by introducing Lanczos's σ factors in the corresponding Fourier coefficients. Additionally, the finite Fourier series is evaluated by proper three-term recurrence relations. Bessel functions, when they appear, are computed by their polynomial approximations or series representation with nested-form formulas. The results obtained using these computational tools are accurate enough for practical purposes.