Modeling of shell-beam transitions in the presence of finite rotations

Abstract

A finite element formulation for a transition element between shells and beam structures is described in this paper. The elements should allow changes between models in an 'optimal' way without or with little disturbances which decrease rapidly due to the principle of Saint-Venant. Thus, the constraints are formulated in such a way that a transverse contraction within the coupling range is possible. The implementation of the coupling conditions is done with the Penalty Method or the Augmented Lagrange Method. The element formulation is derived for finite rotations. Same rotational formulations are used in beam and shell elements. Rotational increments up to an angle of 2π are possible without singularities based on a multiplicative update procedure. It can be shown that the transition to rigid bodies can be derived with some modifications. Examples prove the reliability of the transition formulation. Here simple element tests and practical applications are shown.