Generalization of the C1 TUBA plate finite elements to the geometrically exact Kirchhoff–Love shell model

The finite element implementation of a geometrically exact thin shell model is reported in the present paper. The shell kinematics is based on the Kirchhoff–Love assumption and is characterized by the deformation gradient, which yielded the generalized cross-section strain measures — stretches and curvatures, written in terms of first- and second-order derivatives of displacements. The energetically conjugate quantity, the first Piola–Kirchhoff stress tensor, is used to define the generalized stresses. The shell’s initial geometry is exactly represented using a mapping from a reference configuration. A neo-Hookean material functional, supplemented by the plane stress condition, is incorporated in the constitutive level of the model. Both configuration dependent and independent forces are considered for the domain and boundary loading. The consistent linearization of the rendered weak form is addressed.