Pressurized oval cylinders with closely spaced rings.

Abstract

An analysis is presented for the classical, linear, elastic behavior of a ring-reinforced oval cylinder subjected to a uniform hydrostatic pressure. Use is made of the theorem of the minimum of the total potential energy as well as an appropriate combination of the results of two previously published analyses. One of these deals with oval cylindrical shells alone, whereas the other deals with isolated oval rings. The combined analysis presented herein is employed to obtain numerical results for a limited parametric study that covers major-to- minor axis ratios in the range from 1.0 (circular cylinders) to 1.5. In addition to the antici- pated result that the severity of the stresses and deformations generally increases as the major- to-minor axis ratio increases, it is shown that a change from inside rings to outside rings, or vice versa (all other parameters being held constant) generally results in radical changes in the stress distribution throughout the entire oval cylinder. ING-REINFORCED circular cylindrical shells subjected to either an internal or external pressure have found wide application in structures designed for either flight, land- based, or undersea operation. The elastic behavior of such structures, even including the so-called beam-column effect, is well understood and has been widely reported upon in the literature.1 At times, the designer is confronted with the problem of having to analyze ring-reinforced cylinders of oval cross section. Such shapes are sometimes deliberately intro- duced to satisfy space confinements or other design require- ments, but often they are the result of measurable imper- fections in supposedly circular cylinders. In order to gain insight into the relatively unexplored behavior of ring-rein- forced cylinders deliberately designed with oval cross sec- tions, the David Taylor Model Basin (DTMB) has con- ducted and published the results of initial tests on such a cylinder.2 This report presents a theoretical analysis of the classical, linear, elastic behavior, under a uniform hydrostatic pressure, of a typical bay (located at some distance from the ends) in an oval cylindrical shell that is reinforced by many oval rings equally spaced along the cylinder axis (Figs. 1 and 2). The rings are assumed to be closely spaced, so that there results a large number of short bays having lengths that are less than the average radius. Each ring is taken to include the con- tacted region of shell. The analysis is based upon the principle of the minimum of the total potential energy and incorporates the theoretical work of Refs. 3 and 4, the major results of which are applicable to short oval shells under arbitrary edge loads, and to arbi- trarily loaded oval reinforcing rings, respectively. In fact, the analysis of Ref. 3 has been applied to simply supported short oval shells under a uniform lateral load5 and has been shown to result in good agreement with a more exact double Fourier series solution.6 In a preliminary application7 (in which results are presented without the accompanying