A new mixed isogeometric approach to Kirchhoff-Love shells

TL;DR

This paper introduces a novel mixed isogeometric formulation for Kirchhoff-Love shells that simplifies discretization and improves solver efficiency, effectively addressing membrane locking through combined formulations.

Contribution

It presents a new mixed formulation based on standard $H^1$ spaces for Kirchhoff-Love shells, enabling flexible discretization and efficient solution strategies.

Findings

Effective $C^0$-coupling of multi-patch spaces demonstrated

Multigrid methods serve as efficient preconditioners

Combined formulation reduces membrane locking issues

Abstract

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.