Search

MiS Preprint Repository

Delve into the future of research at MiS with our preprint repository. Our scientists are making groundbreaking discoveries and sharing their latest findings before they are published. Explore repository to stay up-to-date on the newest developments and breakthroughs.

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:
Feb 26, 1997
Published:
Feb 26, 1997

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