A Fully Nonlinear Thin Shell Model of Kirchhoff-Love Type

This work presents a fully nonlinear Kirchhoff-Love shell model. In contrast with shear flexible models, our approach is based on the Kirchhoff-Love theory for thin shells, so that transversal shear deformation is not accounted for.

We define energetically conjugated cross-sectional generalized stresses and strains. The fact that both the first Piola-Kirchhoff stress tensor and the deformation gradient appear as primary variables is also appealing. The weak form of the equilibrium equations and their boundary conditions of the model are consistently derived.

Elastic constitutive equations are obtained from fully three-dimensional finite strain constitutive models in a consistent way. A genuine plane-stress condition is enforced by the vanishing of the mid-surface normal nominal stress (first Piola-Kirchhoff stress), yet rendering a symmetric linearized weak form.

A plane reference configuration is assumed for the shell mid-surface, but, initially curved shells can be accomplished, if one regards the initial configuration as a stress-free deformed state from the plane position. As a consequence, the use of convective non-Cartesian coordinate systems is not necessary and only components on orthogonal frames aie employed.