WIAS Preprint No. 1246, (2007)
Small strain oscillations of an elastoplastic Kirchhoff plate
Authors
- Guenther, Ronald B.
- Krejčí, Pavel
ORCID: 0000-0002-7579-6002 - Sprekels, Jürgen
ORCID: 0009-0000-0618-8604
2010 Mathematics Subject Classification
- 74C05 35Q72 47J40
Keywords
- elastoplastic plate, hysteresis operators, vector Prandtl-Ishlinskii model, von Mises model
DOI
Abstract
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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