Electronic Resource
Springer
Archive for rational mechanics and analysis
85 (1984), S. 311-354
ISSN:
1432-0673
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Physics
Notes:
Abstract This paper describes previously unknown stabilities and instabilities of planar equilibrium configurations of a nonlinearly elastic rod that is buckled under the action of a dead-load. The governing equations are derived from variational principles, including ones of isoperimetric type. Properties of stability are accordingly determined by study of the second variation. Stabilities to deformations both in the plane and out of the plane are considered. Among the newly discovered properties are: secondary bifurcation from the first buckled mode, marked differences between stability to two-dimensional and to three-dimensional variations, and the stabilizing influence of resistance to twist. In the isoperimetric examples, the analysis makes crucial use of a novel device to account for the dependence of the second variation on constraints.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00275737
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