WIAS Preprint No. 1430, (2009)

Elastoplastic Timoshenko beams



Authors

  • Krejčí, Pavel
  • Sprekels, Jürgen
  • Wu, Hao

2010 Mathematics Subject Classification

  • 34C55 35Q72 47J40 74C05 74K10 74N30

Keywords

  • elastoplasticity, Timoshenko beam, anisotropic hysteresis operators, Prandtl--Ishlinskii model, von Mises model

Abstract

A Timoshenko type elastoplastic beam equation is derived by dimensional reduction from a general 3D system with von Mises plasticity law. It consists of two second-order hyperbolic equations with an anisotropic vectorial Prandtl--Ishlinskii hysteresis operator. Existence and uniqueness of a strong solution for an initial-boundary value problem is proven via standard energy and monotonicity methods.

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