Implementation-Friendly Visco-Elastic Nodal-Based Floating Frame of Reference Formulation

The Floating Frame of Reference Formulation (FFRF) is a widely used and efficient method for analyzing small-deformation flexible multibody systems, commonly implemented in commercial software. The FFRF conventionally relies on finite element codes to supply the necessary data for calculating the invariants - reduced, constant matrices crucial for constructing the equations of motion. This workflow ensures independence from lower-level finite element capabilities. While many studies in flexible multibody dynamics focus on elastic components and kinematic constraints, the analysis of viscoelastic behavior has received limited attention, despite its significant impact on dynamic response. Existing research primarily addresses beams and shells using geometrically-exact or absolute nodal coordinate formulations, leaving a gap in the literature regarding 3D volume finite element components modeled with the FFRF. This study addresses this gap by introducing a modally-reduced, nodal-based viscoelastic FFRF that incorporates anelastic displacement fields. The necessary additional invariants are clearly defined, and the procedure for exporting them from commercial finite element codes is demonstrated, ensuring compatibility with conventional multibody simulation workflows. This approach integrates seamlessly into existing FFRF codes with minimal modifications, and has been successfully implemented in the open-source software Exudyn.