Shell Theory Solution for Asymmetric Balanced Radial Loads on Long Cylinders

Abstract

The elastic behavior of a long cylinder subjected to equilibrated radial loads is considered. The problem is formulated by the use of shell theory equations. Although numerical results are available for simply supported cylinders, these results do not apply to long cylinders. The simply supported results were calculated, by Bijlaard, on the basis of equations formulated by Timoshenko and the use of a double Fourier series. The Bijlaard work uses some assumptions which limit the length of the cylinder. In the current work, the more complete equations derived by Flu¨gge and by Biezeno and Grammel are used as transformed by Kempner with the added simplification that the square of the thickness to mean radius ratio is negligible as compared to unity. Solutions for equal and opposite balanced uniformly distributed radial line loads of an any angle are obtained. The solution is carried out by means of a Fourier integral, Fourier series product. All the results are given by a single expression with tabulated coefficients. The infinite cylinder stress and deflection results are presented in graphical form for the parameters of axial position, circumferential position, angle of loading, and mean radius to thickness ratio of the cylinder. The results were checked with axisymmetric thin shell theory.