Secondary buckling of an elastic column with spring-supports at clamped ends |
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Authors: | B Wu |
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Institution: | (1) Department of Mathematics, Jilin University, Changchun 130023, P. R. China, CN |
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Abstract: | Summary The postbuckling behavior of an elastic column with spring supports of equal stiffness of extensional type at both clamped
ends is studied. Attention is focused on those of spring stiffnesses near the critical value at which, under axial load, the
column becomes critical with respect to two buckling modes simultaneously. By using the Liapunov-Schmidt-Koiter approach,
we show that there are precisely two secondary bifurcation points on each primary postbuckling state for the spring stiffness
greater than the critical value. The bifurcation takes place at one of the two least buckling loads. The corresponding secondary
postbuckling states connect all the secondary bifurcation points in a loop. For the spring stiffness less than the critical
value, no secondary bifurcation occurs. Asymptotic expansions of the primary and secondary postbuckling states are constructed.
The stability analysis indicates that the primary postbuckling state for the spring stiffness greater than the critical value
is bifurcating from the first buckling load and becomes unstable from a stable state via the secondary bifurcation, i.e.,
secondary buckling occurs.
Received 22 April 1997; accepted for publication 22 December 1997 |
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Keywords: | column spring support axial compression mode interaction bifurcations secondary buckling |
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