TY - GEN A1 - Krejci, Pavel A1 - Sprekels, Jürgen T1 - Elastic-ideally plastic beams and Prandtl-Ishlinskii hysteresis operators N2 - 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. KW - Elastoplasticity KW - beam equation KW - hysteresis operators KW - Prandtl-Ishlinskii model KW - von Mises model Y1 - 2006 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/355 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-3556 ER -