ABSTRACT This paper presents a novel mixed‐hybrid finite element formulation for Kirchhoff–Love shells, designed to enable the use of standard ‐continuous higher‐order Lagrange elements. This is possible by introducing the components of the moment tensor as a primary unknown alongside the displacement vector, circumventing the need for ‐continuous shape functions. Following hybridization and static condensation of the moment tensor reduces the additional degrees of freedom. The method is derived using tangential differential calculus (TDC), allowing a coordinate‐free description of the shell geometry and mechanics. Numerical results on a smooth shell geometry demonstrate the method's optimal convergence rates in residual and stored energy norms, showcasing its effectiveness for higher‐order structural analysis. This approach facilitates robust modeling of shells using conventional finite element technology and opens pathways for extensions to isogeometric analysis and fictitious domain methods.
Neumeyer et al. (Sun,) studied this question.