On an objective, geometrically exact coupling element for a director-based multi-body finite element framework

Abstract

In multi-body systems, flexible components and couplings between them can be subject to large displacements and rotations. This contribution presents a general objective and geometrically exact node-to-node coupling element that pursues two innovations. Firstly, the coupling element represents a consistent extension to an existing nonlinear mechanical framework. The coupling element is intended to preserve its attributes of objectivity, path independence and adherence to the energy-conserving or energy-dissipative time integration method. Secondly, beside elasticity, inertia and damping properties are also considered. For this purpose, a director-based formulation is employed within a total Lagrangian description. The avoidance of an angle-based representation, along with the additive updating of state variables, results not only in path independence but also in the avoidance of cumulative errors during extended simulations. An objective deformation measure is chosen based on the Green–Lagrange strain tensor. The inertia forces are considered by an arbitrarily shaped continuum located at the centre of the coupled nodes. Damping is considered by using two different objective first-order dissipation functions, which further ensure energy conservation or dissipation. We successfully demonstrate the coupling element within the mechanical framework on using example applications. Firstly, the geometrically exact behaviour is shown compared to a linear deformation measure. Secondly, we numerically show the path independence of the formulation. The dynamic behaviour is demonstrated in a transient analysis of a damped structure. Finally, the modal analysis of a wind turbine shows the application of the coupling element to model the soil–structure interaction.