  Shell analysis is a well-established field, but achieving optimal
higher-order convergence rates for such simulations is a difficult challenge.
We present an isogeometric Kirchhoff-Love shell framework that treats every
numerical aspect in a consistent higher-order accurate way. In particular, a
single trimmed B-spline surface provides a sufficiently smooth geometry, and
the non-symmetric Nitsche method enforces the boundary conditions. A
higher-order accurate reparametrization of cut knot spans in the parameter
space provides a robust, higher-order accurate quadrature for (multiple)
trimming curves, and the extended B-spline concept controls the conditioning of
the resulting system of equations. Besides these components ensuring all
requirements for higher-order accuracy, the presented shell formulation is
based on tangential differential calculus, and level-set functions define the
trimming curves. Numerical experiments confirm that the approach yields
higher-order convergence rates, given that the solution is sufficiently smooth.
