Shear-flexible subdivision shells

We present a new shell model and an accompanying discretization scheme that is suitable for thin and thick shells. The deformed configuration of the shell is parameterised using the mid-surface position vector and an additional shear vector for describing the out-of-plane shear deformations. In the limit of vanishing thickness, the shear vector is identically zero and the Kirchhoff-Love model is recovered. Importantly, there are no compatibility constraints to be satisfied by the shape functions used for discretizing the mid-surface and the shear vector. The mid-surface has to be interpolated with smoothC1-continuous shape functions, whereas the shear vector can be interpolated with C0-continuous shape functions. In the present paper, the mid-surface as well as the shear vector are interpolated with smooth subdivision shape functions. The resulting finite elements are suitable for thin and thick shells and do not exhibit shear locking. The good performance of the proposed formulation is demonstrated with a number of linear and geometrically nonlinear plate and shell examples. KEY WORDS: shells, subdivision surfaces, isogeometric analysis 1