A generalized formulation of classical shell models based on tangential differential calculus

The Tangential Differential Calculus (TDC) enables the mathematical modeling of general physical phenomena on curved surfaces. Herein, it is applied to reformulate classical models for Kirchhoff-Love and Reissner-Mindlin shells. In contrast to the classical approach, the resulting models do not only apply to parametrized shell geometries but also to implicit ones. All mechanical quantities are defined in the 3D Euclidean coordinate system and no curvilinear coordinates are needed. In addition to classical shell analyses based on the standard FEM, the proposed formulation enables implicit shell analyses based
on recently proposed Cut FEM and Trace FEM, which attract a lot of attention lately