The Preferred Mode Shape in the Linear Buckling of Circular Cylindrical Shells Under Axial Compression

[+] Author and Article Information
P. Mann-Nachbar

Lockheed Missiles and Space Company, Palo Alto, Calif.

W. Nachbar

Aeronautics and Astronautics, Stanford University, Stanford, Calif.

J. Appl. Mech 32(4), 793-802 (Dec 01, 1965) (10 pages) doi:10.1115/1.3627318 History: Received July 02, 1964; Revised April 21, 1965; Online September 15, 2011


The chessboard buckle pattern in the solution of the linearized Donnell equations for buckling of a thin, cylindrical shell under axial compression is so sensitive to uncertainties in shell dimensions that the number of circumferential waves and the aspect ratio of the buckles is indeterminate. This problem is treated statistically. Shell dimensions are treated as random variables with probability distributions dependent on nominal values and manufacturing tolerances. Distributions for aspect ratio and number of circumferential waves are found by a Monte-Carlo technique. It is found that the linear theory does contain a mechanism for distinguishing among buckle modes. There is always a preferred buckle mode. For thin shells and attainable manufacturing tolerances, the aspect ratio of the preferred mode is closer to one than that of any other possible mode, and the corresponding number of buckles is large.

Copyright © 1965 by ASME
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