A new mixed isogeometric approach to Kirchhoff-Love shells
For researchers in computational mechanics and isogeometric analysis, this work provides a more flexible and solver-friendly formulation for Kirchhoff-Love shells, though it is an incremental improvement over existing mixed methods.
The paper presents a new mixed formulation for Kirchhoff-Love shell problems that uses only standard H^1 spaces, enabling C^0 coupling of multi-patch isogeometric spaces and allowing the use of efficient iterative solvers designed for second-order problems. Numerical benchmarks demonstrate the performance of the method, including a combination with a mixed formulation to avoid membrane locking.
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.