Affiliation:
1. Graduate School, New York University, New York, N. Y.
2. College of Engineering, New York University, New York, N. Y.
Abstract
Abstract
In this paper a complete mathematical solution of the problem of the buckling with large deflections of a thin circular plate under uniform radial pressure is given, assuming radial symmetry. Buckling takes place as soon as the prescribed thrust pe at the edge reaches a certain critical value pE. Thin plates do not, however, fail if the thrust pe is increased beyond pE. It is of importance, then, to determine the stresses when the ratio Λ = pe/pE becomes greater than unity. This problem, which is a nonlinear one, is solved by two methods for finite values of Λ; also an asymptotic solution is given for the limit state when Λ tends to infinity. The most notable single result is that the membrane stresses for large values of Λ become tensions in the interior of the plate and change abruptly to compressions in a narrow “boundary layer” at the edge of the plate. Curves showing the behavior of the deflection and the stresses are given for a series of values of Λ. Such curves show clearly, in particular, that the limit state is approached quite closely for relatively small values of Λ, i.e., Λ > 5. In closing, the authors discuss the relation between their results and von Kármán’s theory of effective width for the buckling of rectangular plates.
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics
Cited by
41 articles.
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