Small strain oscillations of an elastoplastic Kirchhoff plate
- Guenther, Ronald B.
- Krejčí, Pavel
- Sprekels, Jürgen
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.
- ZAMM Z. Angew. Math. Mech., 88 (2008) pp. 199--217.