Geometrically exact shear-rigid shell and rod models

This work presents geometrically exact shear-rigid rod and shell formulations. Displacements and rotations are finite. Linear elastic constitutive equations for small strains are considered in the numerical examples for the rods. A Neo-Hookean material is considered for the shell. Energetically conjugated cross-sectional stresses and strains are defined. A straight reference configuration is assumed for the rod, and a flat reference configuration the shell. Consequently, the use of convective non-Cartesian coordinate systems is not necessary, and only components on orthogonal frames are employed. The parameterization of the rotation field is done by the rotation tensor with the Rodrigues formula, which makes the updating of the rotational variables very simple. The usual Finite Element Method was used and C1 continuity is achieved within the element. This method is used to discretize the potentials on a computational domain in terms of the nodal degrees of freedom. A set of numerical benchmark examples illustrates the usefulness of the formulation and its numerical illustrates the usefulness of the formulation and its numerical implementation.