Bifurcation analysis of a rod subjected to terminal couple and thrust. (English) Zbl 0790.73030

Buzano, Ernesto

Ann. Mat. Pura Appl., IV. Ser. 164, 195-227 (1993).

It is well known that a rod under thrust alone buckles supercritically and under a couple alone buckles subcritically. In the present paper, the buckling of a rod under combined conservative terminal thrust and couple is studied. The paper presents a very careful formulation of the problem first concerning the physical model where Kirchhoff’s rod theory for an isotropic linear material is stipulated and second concerning the bifurcation analysis. The latter is done studying a nonlinear variational problem. The reduction to a finite dimensional problem is archieved by means of the application of the splitting lemma in a weak form. To anybody interested in rod buckling this is a very recommendable paper.

Reviewer: H.Troger (Wien)

MSC:

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

Keywords:

Kirchhoff’s rod theory; nonlinear variational problem; finite dimensional problem; splitting lemma

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