WIAS Preprint No. 1246, (2007)

Small strain oscillations of an elastoplastic Kirchhoff plate


  • Guenther, Ronald B.
  • Krejčí, Pavel
    ORCID: 0000-0002-7579-6002
  • Sprekels, Jürgen
    ORCID: 0009-0000-0618-8604

2010 Mathematics Subject Classification

  • 74C05 35Q72 47J40


  • elastoplastic plate, hysteresis operators, vector Prandtl-Ishlinskii model, von Mises model




The two dimensional equation for transversal vibrations of an elastoplastic plate is derived from a general three dimensional system with a single yield tensorial von Mises plasticity model in the five dimensional deviatoric space. It leads after dimensional reduction to a multiyield three dimensional Prandtl-Ishlinskii hysteresis model whose weight function is explicitly given. The resulting partial differential equation with hysteresis is solved by means of viscous approximations and a monotonicity argument.

Appeared in

  • ZAMM Z. Angew. Math. Mech., 88 (2008) pp. 199--217.

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