Clamped elastic-ideally plastic beams and Prandtl-Ishlinskii hysteresis operators

Pavel Krejčí; Jürgen Sprekels

doi:10.3934/dcdss.2008.1.283

Article Contents

2008, Volume 1, Issue 2: 283-292. Doi: 10.3934/dcdss.2008.1.283

This issue Previous Article Invariant regions and global existence for a phase field model Next Article Computing long-lifetime science orbits around natural satellites

Clamped elastic-ideally plastic beams and Prandtl-Ishlinskii hysteresis operators

Pavel Krejčí^1, and
Jürgen Sprekels^1,

1.
Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, D–10117 Berlin

Received: October 2006

Revised: August 2007

Published: June 2008

Abstract / Introduction Related Papers Cited by

Abstract

We consider a model for one-dimensional transversal oscillations of an elastic-ideally plastic beam. It is based on the von Mises model of plasticity and leads after a dimensional reduction to a fourth-order partial differential equation with a hysteresis operator of Prandtl-Ishlinskii type whose weight function is given explicitly. In this paper, we study the case of clamped beams involving a kinematic hardening in the stress-strain relation. As main result, we prove the existence and uniqueness of a weak solution. The method of proof, based on spatially semidiscrete approximations, strongly relies on energy dissipation properties of one-dimensional hysteresis operators.

Keywords:

Mathematics Subject Classification: Primary: 35Q72; Secondary: 74C05; 74K10; 74N30; 34C55; 47J40.

Citation:

Article Metrics

HTML views() PDF downloads(77) Cited by(0)

Clamped elastic-ideally plastic beams and Prandtl-Ishlinskii hysteresis operators

Abstract

Access History

Article Metrics

Access History

Other Articles By Authors

Catalog

Clamped elastic-ideally plastic beams and Prandtl-Ishlinskii hysteresis operators

Abstract

Access History

SHARE

Article Metrics

Access History

Other Articles By Authors

Catalog

Export File

Citation

Format

Content