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Elastic–ideally plastic beams and Prandtl–Ishlinskii hysteresis operators
Author(s) -
Krejčí Pavel,
Sprekels Jürgen
Publication year - 2007
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.892
Subject(s) - mathematics , uniqueness , prandtl number , hysteresis , mathematical analysis , transversal (combinatorics) , partial differential equation , plasticity , vibration , scalar (mathematics) , von mises yield criterion , physics , finite element method , mechanics , geometry , heat transfer , thermodynamics , quantum mechanics
The one‐dimensional equation for transversal vibrations of an elastoplastic beam is derived from a general three‐dimensional system with a single‐yield tensorial von Mises plasticity model. It leads after dimensional reduction to a multiyield scalar Prandtl–Ishlinskii hysteresis model whose weight function is explicitly given. The use of Prandtl–Ishlinskii operators in elastoplasticity is thus not just a questionable phenomenological approach, but in fact quite natural. The resulting partial differential equation with hysteresis is 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. Copyright © 2007 John Wiley & Sons, Ltd.

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