Search

MiS Preprint Repository

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
14/1998

Straight configurations of shearable nonlinearly elastic rods

Friedemann Schuricht

Abstract

In contact problems for elastic rods sometimes we have to look for a solution with some prescribed shape, in particular where some material curve has to be straight. While this question is a triviality for the Euler rod (or simplifications of it), the problem becomes much more subtle within the Cosserat theory which describes planar deformations of nonlinearly elastic rods that can bend, strech, and shear. For some selected material curve of the rod we assume that it is enforced to be straight by suitable external forces orthogonal to that straight axis. It is shown that such configurations satisfy a second order system of ordinary differential equations. In the case where this system is homogeneous a very rich structure can be observed by phase plane analysis. Finally some applications for rods which are in contact with a straight obstacle are discussed, and interesting new effects can be derived.

Received:
Mar 21, 1998
Published:
Mar 21, 1998

Related publications

inJournal
2000 Repository Open Access
Friedemann Schuricht

Straight configurations of shearable nonlinearly elastic rods

In: SIAM journal on applied mathematics, 60 (2000) 3, 1017-1036 (electronic)