Finite element modeling of Kirchhoff‐Love shells as smooth material surfaces

We consider large deformations of curved thin shells in the framework of a classical Kirchhoff‐Love theory for material surfaces. The geometry of the element is approximated via the position vector and its derivatives with respect to the material coordinates at the four nodes, and C 1 continuity of the surface over the interfaces between the elements is guaranteed. Theoretical background provides certainty concerning the boundary conditions, the range of applicability of the model, extensions to multi‐field problems, etc. Robust convergence and accuracy of the resulting simple numerical scheme is demonstrated by the analysis of benchmark problems in comparison with other solutions.