  Stable and accurate modeling of thin shells requires proper enforcement of
all types of boundary conditions. Unfortunately, for Kirchhoff-Love shells,
strong enforcement of Dirichlet boundary conditions is difficult because both
functional and derivative boundary conditions must be applied. A popular
alternative is to employ Nitsche's method to weakly enforce all boundary
conditions. However, while many Nitsche-based formulations have been proposed
in the literature, they lack comprehensive error analyses and verifications. In
fact, existing formulations are variationally inconsistent and yield
sub-optimal convergence rates when used with common boundary condition
specifications. In this paper, we present a novel Nitsche-based formulation for
the linear Kirchhoff-Love shell that is provably stable and optimally
convergent for general sets of admissible boundary conditions. To arrive at our
formulation, we first present a framework for constructing Nitsche's method for
any abstract variational constrained minimization problem. We then apply this
framework to the linear Kirchhoff-Love shell and, for the particular case of
NURBS-based isogeometric analysis, we prove that the resulting formulation
yields 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 general
sets of admissible boundary conditions and show that the Euler-Lagrange
boundary conditions typically presented in the literature is incorrect. We
verify our formulation by manufacturing solutions for a new shell obstacle
course that encompasses flat, parabolic, hyperbolic, and elliptic geometric
configurations. These manufactured solutions allow us to robustly measure the
error across the entire shell in contrast with current best practices where
displacement and stress errors are only measured at specific locations.
