Geometrically nonlinear formulation for thin shells without rotation degrees of freedom

A finite element formulation is presented for modelling geometrically nonlinear thin shells which exploits standard Lagrange finite element basis functions without introducing rotation degrees of freedom. The classical regularity requirements associated with thin bending problems are circumvented by introducing special integrals over inter-element edges. The use of Lagrange finite element basis functions and the absence of rotation degrees of freedom make the formulation relatively simple, and discontinuities in material properties and non-smooth shell geometry can be incorporated trivially. The variational problem can be exactly linearised, leading to an efficient Newton–Raphson solution process. The performance of the approach is demonstrated via a range of numerical benchmarks for both geometrically linear and nonlinear problems. It is shown that cubic elements perform particularly well.