Stresses in Short Noncircular Cylindrical Shells Under Lateral Pressure

Abstract

This paper presents an analysis of the deflections of and stresses in a short noncircular cylindrical shell of uniform wall thickness whose median-surface cross section is described analytically by a simple expression corresponding to a family of doubly symmetric ovals. The cylinder is under a uniform lateral load and is simply supported at its edges. The small deflection analysis considered is based upon a series solution of appropriate differential equations of shell theory which leads ultimately to infinite sets of algebraic equations, truncated forms of which are considered. Numerical values of the significant stresses and displacements for points of the oval cylinder, which are 5 percent of the axial length and 2.5 percent of the circumferential length a part, have been calculated for an oval cross section with a major-minor axis ratio of 1.10.

Free vibrations of simply supported cylindrical shells of oval crosssection

“…Thus, for any value of m greater than zero, the following set of three ordinary linear differential equations with variable coefficients is obtained for the functions U m (s), V m (s), and W m (s), P m =0, Q m =0, R m =0 for m = l,2,3... (13) For w = 0, referring to Eqs. (9), it can be seen that the motion is purely longitudinal (w^O, i> = w = 0).…”

Stress analysis of composite cylindrical shells with an elliptical cutout

“…As derived by [Romano and Kempner 1958], the coordinates y and x in Equation (1) can be related to the radius of curvature of an oval-cross-section cylindrical shell R(s 2 , ξ ) by…”

“…The nonuniform shell curvature associated with a noncircular cross section is represented by using trigonometric series for the coordinates of an oval cross-section shell reference surface (1958). The aspect ratio, or out-of-roundness, of the cross section is represented in the analysis using an eccentricity parameter introduced by [Romano and Kempner 1962] and later used by [Culberson and Boyd 1971;Chen and Kempner 1976]. This parameter is defined in the subsequent section, and the aspect ratio, related to the eccentricity parameter, represents the ratio of the minor axis to the major axis.…”

“…Following [Romano and Kempner 1958], the noncircular cross section of the cylindrical shell is defined as an oval with the coordinates y and z expressed as…”

Structural design of elliptical hollow sections: a review

“…The aspect ratio of an ellipse is defined as a/b, while the maximum and minimum radii of curvature may be shown to be: rmax = a . Romano and Kempner (1958) derived a relationship between the eccentricity  of an oval and the aspect ratio a/b of an ellipse and concluded that the two shapes, defined by equations (1) and (2), were comparable provided 0 ≤  ≤ 1. It is worth noting that for  = 0, equation (1) exactly represents a circle (i.e.…”