A new mixed approach to Kirchhoff–Love shells

Abstract For Kirchhoff–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, efficient methods for standard second-order problems like multigrid methods can be used as building blocks of preconditioners for iterative solvers. 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.