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Stability of nonlinearly elastic rods. (English) Zbl 0545.73039
The author studies in a quasistatic theory buckling of nonlinearly elastic rods that can deform in space under endloading. The governing rod equations are formulated in Euler angles using director theory and are derived from variational principles. Nonlinearity follows as well as from geometry and the constitutive relations. From the formulation as variational principle the stability and instability of planar equilibrium positions can be determined from the corresponding second variation. However, due to isoperimetric constrains the standard tests concerning the second variation are not applicable and a novel devise is used.
A wealth of interesting, previously unknown, results which are physically well interpreted, are presented which makes the paper very worthwhile to study also for the physicist and engineer.
Reviewer: H.Troger

MSC:
74G60 Bifurcation and buckling
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74B20 Nonlinear elasticity
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