  For Kichhoff-Love shell problems a new mixed formulation solely based on
standard $H^1$ spaces is presented. This allows for flexibility in the
construction of discretization spaces, e.g., standard $C^0$-coupling of
multi-patch isogeometric spaces is sufficient. In terms of solution strategies,
for iterative solvers efficient methods for standard second-order problems like
multigrid can be used as building blocks of a preconditioner. Furthermore, a
combination of the proposed mixed formulation of the bending part with a
popular mixed formulation of the membrane part in order to avoid membrane
locking is considered. The performance of both mixed formulations is
demonstrated by numerical benchmark studies.
