The nodal-based floating frame of reference formulation with modal reduction How to calculate the invariants without a lumped mass approximation

In a recent paper of the authors, a novel nodal-based floating frame of reference formulation (FFRF) for solid finite elements has been proposed. The nodal-based approach bypasses the unhandy inertia shape integrals ab initio, i.e. they neither arise in the derivation nor in the final equations of motion, leading to a surprisingly simple derivation and computer implementation without a lumped mass approximation, which is conventionally employed within commercial multibody codes. However, the nodal-based FFRF has so far been presented without modal reduction, which is usually required for efficient simulations. Hence, the aim of this follow-up paper is to bring the nodal-based FFRF into a suitable form, which allows the incorporation of modal reduction techniques to reduce the overall system size down to the number of modes included in the reduction basis, which further reduces the computational complexity significantly. Moreover, this exhibits a way to calculate the so-called FFRF invariants, which are constant ingredients required to set up the FFRF mass matrix and quadratic velocity vector, without integrals and without a lumped mass approximation.

Automated summary

The paper introduces a novel nodal-based FFRF formulation for solid finite elements, which simplifies the derivation and implementation by bypassing inertia shape integrals. The aim is to incorporate modal reduction techniques to reduce system size and computational complexity, while also calculating FFRF invariants without integrals and lumped mass approximation.