The Linearization of the Prebuckling State and Its Effect on the Determined Instability Loads

[+] Author and Article Information
A. D. Kerr

Department of Aeronautics and Astronautics, New York University, New York, N. Y.

M. T. Soifer

Technik Inc., Jericho, N. Y.

J. Appl. Mech 36(4), 775-783 (Dec 01, 1969) (9 pages) doi:10.1115/1.3564770 History: Received November 26, 1968; Online September 14, 2011


The effect of the linearization of the prebuckled state upon the determined buckling loads is studied first on an elastic system of two degrees of freedom and then on a shallow arch subjected to a uniform lateral load; structures that exhibit a nontrivial state of stress, an upper buckling load, a lower buckling load, and a bifurcation load. For each case the exact solution of the nonlinear formulation is discussed first. Then, using the perturbation analysis, the instability loads are determined again using the exact and the linearized prebuckled state, respectively. The paper concludes with a comparison of the obtained buckling loads and a discussion of relevant problems. It was found that the usual “adjacent equilibrium” argument presented in the literature, according to which only the displacements are perturbed, is not applicable for the determination of the bifurcation pressures of the shallow arch. A proper argument is presented and then used to determine the bifurcation and limit points.

Copyright © 1969 by ASME
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