  The Kirchhoff-Love shell theory is recasted in the frame of the tangential
differential calculus (TDC) where differential operators on surfaces are
formulated based on global, three-dimensional coordinates. As a consequence,
there is no need for a parametrization of the shell geometry implying
curvilinear surface coordinates as used in the classical shell theory.
Therefore, the proposed TDC-based formulation also applies to shell geometries
which are zero-isosurfaces as in the level-set method where no parametrization
is available in general. For the discretization, the TDC-based formulation may
be used based on surface meshes implying element-wise parametrizations. Then,
the results are equivalent to those obtained based on the classical theory.
However, it may also be used in recent finite element approaches as the
TraceFEM and CutFEM where shape functions are generated on a background mesh
without any need for a parametrization. Numerical results presented herein are
achieved with isogeometric analysis for classical and new benchmark tests.
Higher-order convergence rates in the residual errors are achieved when the
physical fields are sufficiently smooth.
