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.

在作者的最新论文中，已经提出了一种针对固体有限元的新颖的基于节点的参考配方浮动框架（FFRF）。基于节点的方法从头开始绕过了惯用的惯性形状积分，也就是说，它们既不会出现在推导中也不会出现在运动的最终方程中，从而导致出乎意料的简单推导和计算机实现，而没有集总质量逼近，这在商业上通常采用多实体代码。但是，到目前为止，基于节点的FFRF都没有模态缩减，这通常是有效仿真所必需的。因此，本后续文件的目的是将基于节点的FFRF转换为合适的形式，这允许并入模态约简技术，以将整个系统大小缩减到约简基础中包含的模数，从而进一步显着降低了计算复杂性。而且，这展示了一种计算所谓的FFRF不变量的方法，它们是建立FFRF质量矩阵和二次速度矢量所需的常数“成分”，没有积分，也没有集总质量近似。