On the boundary conditions of the geometrically nonlinear Kirchhoff–Love shell theory

• Geometrically exact Kirchhoff–Love 3 parameters shell model is derived.
• The initial geometry is exactly represented by means of a mapping procedure.
• Several kinematic quantities are proposed to describe the boundary rotation.
• Need of pointwise corner kinematic restraints is reasoned and numerically assessed.
• Hybrid weak form is suitable for interpolative and non-interpolative approximations.

The present paper addresses the problem of establishing the boundary conditions of a geometrically nonlinear thin shell model, especially the kinematic ones. Our model is consistently derived from general 3D continuum mechanics statements. Generalized cross-sectional strains and stresses are based on the deformation gradient and the first Piola–Kirchhoff stress tensor. Since only the bending deformation is included in this model, no special technique needs to be adopted in order to avoid shear-locking. The theory is derived in such a way that any material model can be considered as a constitutive relation, once the zero transverse normal stress assumption is properly taken into account.Special attention is given to the question of devising the appropriate shell boundary conditions. Several parameters are proposed to characterize the boundary rotation for an arbitrary spatial shell configuration. The appearance of corner concentrated forces, related to jumps of torsion moments, is captured and justified.A weak form of the equilibrium is presented, which is suitable for implementation by means of any numerical technique that provides C1C1 continuity approximation. It is prone to be used with both interpolative, like the Finite Element Method, and non-interpolative methods, like the Element-Free Galerkin Method. The latter is used to exemplify the proposed approach.