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Stable and accurate modeling of thin shells requires proper enforcement ofall types of boundary conditions. Unfortunately, for Kirchhoff-Love shells,strong enforcement of Dirichlet boundary conditions is difficult because bothfunctional and derivative boundary conditions must be applied. A popularalternative is to employ Nitsche's method to weakly enforce all boundaryconditions. However, while many Nitsche-based formulations have been proposedin the literature, they lack comprehensive error analyses and verifications. Infact, existing formulations are variationally inconsistent and yieldsub-optimal convergence rates when used with common boundary conditionspecifications. In this paper, we present a novel Nitsche-based formulation forthe linear Kirchhoff-Love shell that is provably stable and optimallyconvergent for general sets of admissible boundary conditions. To arrive at ourformulation, we first present a framework for constructing Nitsche's method forany abstract variational constrained minimization problem. We then apply thisframework to the linear Kirchhoff-Love shell and, for the particular case ofNURBS-based isogeometric analysis, we prove that the resulting formulationyields optimal convergence rates in both the shell energy norm and the standard$L^2$-norm. In the process, we derive the Euler-Lagrange equations for generalsets of admissible boundary conditions and show that the Euler-Lagrangeboundary conditions typically presented in the literature is incorrect. Weverify our formulation by manufacturing solutions for a new shell obstaclecourse that encompasses flat, parabolic, hyperbolic, and elliptic geometricconfigurations. These manufactured solutions allow us to robustly measure theerror across the entire shell in contrast with current best practices wheredisplacement and stress errors are only measured at specific locations.

Weak Boundary Condition Enforcement for Linear Kirchhoff-Love Shells: Formulation, Error Analysis, and Verification