  We present and analyze a method for thin plates based on cut
Bogner-Fox-Schmit elements, which are $C^1$ elements obtained by taking tensor
products of Hermite splines. The formulation is based on Nitsche's method for
weak enforcement of essential boundary conditions together with addition of
certain stabilization terms that enable us to establish coercivity and
stability of the resulting system of linear equations. We also take geometric
approximation of the boundary into account and we focus our presentation on the
simply supported boundary conditions which is the most sensitive case for
geometric approximation of the boundary.
