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.
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December 1969
Research Papers
The Linearization of the Prebuckling State and Its Effect on the Determined Instability Loads
A. D. Kerr,
A. D. Kerr
Department of Aeronautics and Astronautics, New York University, New York, N. Y.
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M. T. Soifer
M. T. Soifer
Technik Inc., Jericho, N. Y.
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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. Dec 1969, 36(4): 775-783 (9 pages)
Published Online: December 1, 1969
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Received:
November 26, 1968
Online:
September 14, 2011
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Discussion: “The Linearization of the Prebuckling State and Its Effect on the Determined Instability Loads” (Kerr, A. D., and Soifer, M. T., 1969, ASME J. Appl. Mech., 36, pp. 775–783)
Citation
Kerr, A. D., and Soifer, M. T. (December 1, 1969). "The Linearization of the Prebuckling State and Its Effect on the Determined Instability Loads." ASME. J. Appl. Mech. December 1969; 36(4): 775–783. https://doi.org/10.1115/1.3564770
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