Elastoplastic Timoshenko beams
- Krejčí, Pavel
- Sprekels, Jürgen
- Wu, Hao
2010 Mathematics Subject Classification
- 34C55 35Q72 47J40 74C05 74K10 74N30
- elastoplasticity, Timoshenko beam, anisotropic hysteresis operators, Prandtl--Ishlinskii model, von Mises model
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.