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The two simultaneous nonlinear first-order differential equations characterizing the problems that were derived by the senior author in a paper in 1956 and were at that time solved for a few cases by numerical integration are solved here analytically with the aid of a few simplifying assumptions. The very simple formula derived in this manner is used to compute the critical times of a series of shells tested in the laboratory. It is found that the formula predicts somewhat larger values for the critical time than the experimental results. (Author).
Twenty-nine circular cylindrical shells manufactured of 5052-0 aluminum alloy were tested in pure bending at a temperature of 500F. Ten of these were unreinforced, nine had longitudinal, and ten longitudinal and circumferential reinforcing elements. All the specimens failed in creep buckling. The results of the experiments are presented in tables and diagrams. A few theoretical considerations are given in three appendices. (Author).
The stability of circular cylindrical shells under pure bending is investigated by means of Batdorf's modified Donnell's equation and the Galerkin method. The results have shown that contrary to the commonly accepted value, the maximum critical bending stress is for all practical purposes equal to the critical compressive stress. (Author).
The problem of creep induced instability in structures is discussed. A linearization procedure proposed by Onat and Wang (Creep in Structures, Springer-Verlag, 1962, p. 125) and generalized by Carlson (Recent Progress in Applied Mechanics - The Folke Odgvist Volume, Almqvist and Wiksell, Gebers, Stockholm, 1966) is applied to the problem of the creep buckling of circular cylindrical shells under uniform, axial compression. Solutions for axisymmetric creep buckling of semi-infinite and infinite cylinders are obtained and a comparison with experimental data is made. In accordance with expectations based on the criterion for instability, the theoretically predicted critical times are smaller than the experimentally observed critical times.
The present theoretical investigation studies the effect of small multilobed initial deviations from the exact shape upon the deformations and the critical time of a thin-walled circular cylindrical shell which was manufactured with initial axisymmetric deformations. To facilitate the analytical work, the actual solid wall of the shell is imagined to be replaced by an equivalent sandwich wall. The general equilibrium equations derived for shallow shells are expressed in terms of the stresses and deviations corresponding to the equivalent sandwich model. The radial displacement as well as the meridional, circumferential and membrane shear stresses are expressed by finite Fourier series for each face of the sandwich model. A closed form solution is found for the multilobed deformation rates and for the critical time as well. A numerical integration of the deformation rates shows, for a given cylinder, that the multilobed creep buckling deformations grow much faster than the axisymmetric. (Modified author abstract).
The purpose of the investigation described in this paper is the study of the effect of very small nonaxisymmetric initial deviations from the exact shape upon the deformations and the critical time of a thin-walled circular cylindrical shell which was manufactured with larger initial deviations of an axisymmetric type. The calculations are carried out in a manner similar to that of a recent paper by the senior author. It is assumed that all the deformations are due to nonlinear steady creep governed by Odqvist's law. In consequence of the nonlinearity of the constitutive equation and the use of three terms in the expressions for the deformations and the stresses the trigonometric calculations become so complicated that they must be carried out by means of the high-speed digital computer. For this purpose use is made of the 'REDUCE' program. It is found that in a particular case the critical time of the shell is reduced to about one-half the original value when one adds to the small axially symmetric component of the initial deviations a nonaxisymmetric component which is ten orders of magnitude smaller. The reduction in critical time is represented by a factor of about 1/15 when the amplitudes of the axisymmetric and nonaxisymmetric initial deviations are equal. (Author).
Experimental results obtained with 31 nickel circular cylindrical shell specimens are evaluated in the light of the theory. The test results have already been reported in SUDAAR No. 415. The experimental creep buckling times obtained in axial compression at a temperature of 650F were found to be in reasonable agreement with the theoretical formulas. (Author).