Eigenvalue branching configurations and the Rayleigh-Ritz procedure

Thompson, J. M. T.

doi:10.1090/qam/99952

Author: J. M. T. Thompson
Journal: Quart. Appl. Math. 22 (1964), 244-251
DOI: https://doi.org/10.1090/qam/99952
MathSciNet review: QAM99952
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Abstract | References | Additional Information

Abstract: A general theory of elastic post-buckling, applicable to a wide class of structural eigenvalue problems, is developed in generalized coordinates. Attention is restricted to the initial post-buckling path of the structural system on a plot of the load against the critical principal coordinate, and exact first-order solutions for the path are presented. These solutions are compared with the predictions of the non-linear Rayleigh-Ritz analysis in which the linear buckling mode is employed as the assumed form, and theorems concerning the results of this analysis are established.

Y. C. Fung and E. E. Sechler, Instability of thin elastic shells, Structural mechanics, Pergamon Press, New York, 1960, pp. 115–168. MR 0136149

W. T. Koiter, On the stability of elastic equilibrium, Dissertation, Delft, 1945

W. T. Koiter, Elastic stability and post-buckling behavior, Nonlinear Problems (Proc. Sympos., Madison, Wis., 1962) Univ. of Wisconsin Press, Madison, Wis., 1962, pp. 257–275. MR 0148292
J. M. T. Thompson, Basic principles in the general theory of elastic stability, J. Mech. Phys. Solids 11 (1963), 13–20. MR 157533, DOI https://doi.org/10.1016/0022-5096%2863%2990003-6
H. S. Tsien, Buckling of a column with non-linear lateral supports, J. Aeronaut. Sci. 9 (1942), 119–132. MR 6927

S. Britvec, Ph.D. dissertation, Department of Engineering, Cambridge University, 1960

W. T. Koiter, Buckling and post-buckling behaviour of a cylindrical panel under axial compression, Trans. Natl. Aeron. Research Institute, Amsterdam, Report S476, 1955