On the simultaneous use of simple geometrically exact shear-rigid rod and shell finite elements

Abstract

This work addresses simultaneous use of geometrically exact shear-rigid rod and shell finite elements and describes both models within the same framework. Parameterization of the rotation field is performed by Rodrigues rotation vector, which makes the incremental updating of the rotational variables remarkably simple. For the rod element, cubic Hermitian interpolation for the displacements together with quadratic Lagrange interpolation for the incremental torsion angle were employed, while, for the triangular shell element, a complete quadratic Lagrange interpolation was used. The internal incremental torsion angle resulting from the displacement field within the shell element is then made compatible with the boundary incremental torsion angle of the shell element by an internal Lagrange multiplier. The compatibility between contiguous shell elements as well rod elements is mastered in the standard way by simply connecting nodes. This technique is an important contribution of the work, whose performance is illustrated by several numerical examples.