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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).
Forty-three cylinders of 40-inch length and 16-inch diameter, made of 5052-0 aluminum-alloy sheets of 0.032-, 0.040-, 0.051-, and 0.064-inch thickness, were subjected to bending moments constant along the cylinder and in time in an oven which maintained a constant temperature of 500 degrees F during the test. All the cylinders failed by buckling. The time that elapsed between load application and collapse was measured.
A review is presented of the fundamental considerations that enter into the calculation of the buckling of plates and shells whose material deforms in consequence of nonlinear creep. Results are given of analyses that have been carried out for flat plates subjected to edge-wise compression and for circular cylindrical shells subjected to uniform axial compression, to a uniform external pressure and to a constant bending moment. The character of the behavior of these structural elements after buckling is also discussed. (Author).
Test equipment suitable for the study of the creep buckling of axially compressed circular cylindrical shells was developed and built. With the aid of this equipment, thirty-one electroformed nickel cylinders of radius-to-thickness ratios ranging from 30.6 to 96.4 were tested at a temperature of 650F. The loading of each specimen was interrupted usually once, and in some cases twice, to permit an exact measurement of the creep deformations produced by the axial compression. Diagrams showing the deformed shapes of eight generators of each specimen are presented at two or three stages of the creep buckling process. Inspection of the figures reveals that specimens of this kind either buckle axisymmetrically, or begin the creep buckling process in a axisymmetric manner but change over to a multilobed pattern in later stages of the deformations. (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 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).
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).