June  2008, 1(2): 283-292. doi: 10.3934/dcdss.2008.1.283

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

1. 

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

Received  October 2006 Revised  August 2007 Published  March 2008

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.
Citation: Pavel Krejčí, Jürgen Sprekels. Clamped elastic-ideally plastic beams and Prandtl-Ishlinskii hysteresis operators. Discrete & Continuous Dynamical Systems - S, 2008, 1 (2) : 283-292. doi: 10.3934/dcdss.2008.1.283
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