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Elastic-ideally plastic beams and Prandtl-Ishlinskii hysteresis operators

Please always quote using this URN:urn:nbn:de:0296-matheon-3556
  • In this paper, the one-dimensional equation for the transversal vibrations of an elastoplastic beam is derived from a general three-dimensional system. The plastic behavior is modeled using the classical three-dimensional von Mises plasticity model. It turns out that this single-yield model leads after a dimensional reduction to a multi-yield one-dimensional hysteresis model, given by a hysteresis operator of Prandtl-Ishlinskii type whose density function can be determined explicitly. This result indicates that the use of Prandtl-Ishlinskii hysteresis operators in the modeling of elastoplasticity is not just a questionable phenomenological approach, but in fact quite natural. In addition to the derivation of the model, it is shown that the resulting partial differential equation with hysteresis can be transformed into an equivalent system for which the existence and uniqueness of a strong solution is proved. The proof employs techniques from the mathematical theory of hysteresis operators.

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Metadaten
Author:Pavel Krejci, Jürgen Sprekels
URN:urn:nbn:de:0296-matheon-3556
Referee:Fredi Tröltzsch
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2006/08/09
Release Date:2006/08/09
Tag:
Institute:Freie Universität Berlin
Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS)
MSC-Classification:34-XX ORDINARY DIFFERENTIAL EQUATIONS / 34Cxx Qualitative theory [See also 37-XX] / 34C55 Hysteresis
47-XX OPERATOR THEORY / 47Jxx Equations and inequalities involving nonlinear operators [See also 46Txx] (For global and geometric aspects, see 58-XX) / 47J40 Equations with hysteresis operators [See also 34C55, 74N30]
74-XX MECHANICS OF DEFORMABLE SOLIDS / 74Cxx Plastic materials, materials of stress-rate and internal-variable type / 74C05 Small-strain, rate-independent theories (including rigid-plastic and elasto-plastic materials)
74-XX MECHANICS OF DEFORMABLE SOLIDS / 74Nxx Phase transformations in solids [See also 74A50, 80Axx, 82B26, 82C26] / 74N30 Problems involving hysteresis
Preprint Number:348
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