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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
1/1997

Multiplicity results for free and constrained nonlinear elastic rods based on nonsmooth critical point theory

Marco Degiovanni and Friedemann Schuricht

Abstract

The main goal of this paper is to demonstrate that nonsmooth methods, generalizing the ideas of Ljusternik-Schnirelman theory to merely lower-semicontiuous functionals, can be applied to buckling problems in nonlinear elasticity. Based on some general nonsmooth critical point theory developped by Corvellec, Degiovanni, and Marzocchi we verify nontrivial buckling states of an axially compressed nonlinearly elastic rod. Here we work with the geometrically exact Cosserat theory describing planar deformations of elastic rods that can suffer flexure, extension, and shear and which involves a general nonlinear constitutive relation. In particular we can handle the presence of rigid obstacles and materials with nonsmooth constitutive functions. In that sense we generalize all previous buckling results. In contrast to the usual study of obstacle problems by means of variational inequalities we derive the Euler-Lagrange equations and show that our abstract critical points have physical relevance.

Received:
26.02.97
Published:
26.02.97

Related publications

inJournal
1998 Repository Open Access
Marco Degiovanni and Friedemann Schuricht

Buckling of nonlinearly elastic rods in the presence of obstacles treated by nonsmooth critical point theory

In: Mathematische Annalen, 311 (1998) 4, pp. 675-728