Cienkościenna Powłoka Toroidalna Obciążona Równomiernym Ciśnieniem

In this paper is presented an approximate computation method of stress and strain components in a thin-walled toroidal elastic shell of circular cross-section limited by two parallels, a 01; and a = dg, and loaded with a uniform a pressure (Fig. 1). The problemes reduced to the determination of a complex function X satisfying the differential equation (3.22) (with suitable boundary conditions), derived by means of the «complex stress» method of V. V. Novozhilov. The solution of this differential equation is, in all the works known to the author, given in the form of power or trigonometric series. It is true that in Refs. [14] and [15] the homogeneous problem is solved by E. F. Zenowa and V. V. Nvozhilov in a closed form (by means of Bessel functions), the particular solution of the nonhomogeneous problem, however, is represented in those papers in the form of a series. This draw-back of the solution of E. F. Zenova and V. V. Novozhilov is avoided in this paper, the particular solution of the nonhomogeneous problem being also expressed in a closed form by means of Bessel
functions.
The particular solution is based on the paper [1] by R. Clark and E. Reissner and the method evolved can be called the method of Novozhilov-Reissner. As a result, full solution is obtained in a closed form, convenient for use [Eqs. (6.27)], where the values of Bessel functions can be read from the graphs (Figs. 9, 10 and 12) or calculated by means of simple asymptotic formulae [Eqs. (5.18), and (6.24)]. The exactness of the Novozhilov -Reissner method increases with decreasing wall thickness. If. the wall thickness 8 tends to zero the computation formulae (4.3) are reduced to Eqs. (2.11) of the membrans theory, provided that the considered cross-sections are sufficiently distant from the singular lines of the torus. The application of the method is illustrated by numerical examples.