Abstract: We study the dynamics of oscillating
thin elastoplastic beams and plates. Using 
dimensional reduction and the three-dimensional
von Mises flow rule of plasticity, we arrive at
systems of fourth-order PDEs in which multidemsional
hysteresis operators occur. Unique existence
is shown by exploiting special techniques from
the theory of hysteresis operators. The results are
joint work with P. Krejci (WIAS Berlin) and, in 
parts, with R.B. Guenther (Oregon State University).