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Buckling and initial postbuckling of an oval cylindrical shell under pure bending and under combined uniform axial compression and bending is investigated. The first-and second-order stability equations are developed from the Donnelltype equations that are shown to be appropriate. The solution of these two sets of equations determines, respectively, the buckling characteristics and a "sensitivity parameter." The buckling loads are found to be in good agreement with b e engineering approximation based on the assumption that buckling occurs when the local axial stress equals that corresponding to the classical buckling stress of a locally equivalent circular cylindrical shell under uniform axial compression.Results also show that an oval cylinder can be stronger or weaker than the equivalent circular cylinder, depending on the orientation of the couples. However, in any case the oval shell is always found to be sensitive to imperfections: the greater the load-carrying capacity, the greater the sensitivity.Furthermore, in contrast to the behavior of the circular and weak oval cylinders, buckling of the strong oval cylinder need not initiate at the position of maximum compressive stress.INTRODUCTION During the last ten years the present authors have been involved with a program concerned with the investigation of the behavior of noncircular (oval) cylindrical shells. One phase of their research, first reported in 1962, has been directed toward the understanding of the buckling and postbuckling processes of such &ells under uniform axially compressive end loads.1-6 Other investigations include that of Hutchinson7 and of Tennyson and colleagues.8Having gained insight into such problems, we have extended some of this work to the closely related problems of the buckling of oval cylinders under the action of pure bending couples, as well as under the combined action of uniform axial compression and bending couples. In this connection, the earliest work that has mme to the authors' attention actually was published only quite recently. The study was carried out by liozarov.9 who attempted to analyze the problem of thermal buckling of oval cylinders in which the temperature-dependent axial compressive load call vary along the circumference. Since the load is synthesized in the form of a Fourier series i n the circumferential direction, obviously, the zeroth and *Accorded the I. B. Laskewitz

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Presented in this work is a method of construction of approximate functions in connection with the energy formulation of certain eigenvalue problems of web-stiffened sandwich structures. The construction is based upon the method of Young together with a group of fundamental functions deduced from Timoshenko’s flexural equations for elastic beams. The analysis is exemplified and numerically tested by the eigenvalue problems of free vibrations and buckling of one-dimensional sandwich structures. Results indicate that the present method possesses advantages over similar constructions oriented from the classical flexural normal modes of Bernoulli-Euler.

An analysis of the free vibrations of simply supported and clamped, web-stiffened, circular, cylindrical sandwich shells is presented. The mathematical model formulated includes the effect of translatory and rotatory inertia in each layer of the sandwich, and treats the two face layers as thin shells in which the classical (Donnell) theory of shells applies. However, shear deformations are permitted in the core, which is treated as a layer of inhomogeneous, orthotropic material. In the analysis, the discrete nature of the webs is maintained, except for the inclusion of an average secondary shear modulus induced by the bending of the webs and faces. The effect of smearing-out, or averaging, a given web-stiffened core is also investigated. A Galerkin procedure is employed to determine the natural frequencies from a variational functional generated by means of Hamilton's principle.