Eigenvalue branching configurations and the Rayleigh-Ritz procedure
Author:
J. M. T. Thompson
Journal:
Quart. Appl. Math. 22 (1964), 244-251
DOI:
https://doi.org/10.1090/qam/99952
MathSciNet review:
QAM99952
Full-text PDF Free Access
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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.
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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
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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
Y. C. Fung and E. E. Sechler, Instability of thin elastic shells, Proc. First Symposium on Naval Structural Mechanics, Pergamon Press, 1960
W. T. Koiter, On the stability of elastic equilibrium, Dissertation, Delft, 1945
W. T. Koiter, Elastic stability and post-buckling behaviour, Nonlinear Problems, University of Wisconsin Press, 1963
J. M. T. Thompson, Basic principles in the general theory of elastic stability, J. Mech. Phys. Solids 11, (1963) 13
H. S. Tsien, Buckling of a column with non-linear lateral supports, J. Aeron. Sci., 9, (1942) 119
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
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Article copyright:
© Copyright 1964
American Mathematical Society