This paper presents a novel model order reduction technique for 3D flexible multibody systems featuring nonlinear elastic behavior. We adopt the mean-axis floating frame approach in combination with an enhanced Rubin substructuring technique for the construction of the reduction basis. The standard Rubin reduction basis is augmented with the modal derivatives of both free-interface vibration modes and attachment modes to consider the bending–stretching coupling effects for each flexible body. The mean-axis frame generally yields relative displacements and rotations of smaller magnitude when compared to the one obtained by the nodal-fixed floating frame. This positively impacts the accuracy of the reduction basis. Also, when equipped with modal derivatives, the Rubin method better considers the geometric nonlinearities than the Craig–Bampton method, as it comprises vibration modes and modal derivatives featuring free motion of the interface. The nonlinear coupling between free-interface modes and attachment modes is also considered. Numerical tests confirm that the proposed method is more accurate than Craig–Bampton’s, a nodal fixed floating frame counterpart originally proposed in Wu and Tiso (Multibody Syst. Dyn. 36(4): 405–425, [2016]), and produces significant speed-ups. However, the offline cost is increased because the mean-axis formulation produces operators with decreased sparsity patterns.

中文翻译：

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几何非线性多体系统的一种模态导数增强鲁宾子构造方法。

本文针对具有非线性弹性行为的3D柔性多体系统提出了一种新颖的模型降阶技术。我们采用平均轴浮动框架方法与增强的Rubin子构造技术相结合来构造简化基础。自由鲁宾减少的标准基础增加了自由界面振动模式和附着模式的模态导数，以考虑每个柔体的弯曲-拉伸耦合效应。与通过节点固定的浮动框架获得的相对位移和旋转相比，平均轴框架通常产生较小的相对位移和旋转。这对减少基准的准确性产生积极影响。此外，当配备模态导数时，鲁宾方法比克雷格-邦普顿方法更好地考虑了几何非线性，因为它包括振动模式和以界面自由运动为特征的模态导数。还考虑了自由界面模式和附着模式之间的非线性耦合。数值测试证实，该方法比最初在Wu和Tiso中提出的节点固定浮动框架对应物Craig–Bampton方法更准确（Multibody Syst。Dyn。36（4）：405–425，[2016]），并且产生了显着效果加速。但是，由于平均轴公式使操作员的稀疏度降低，因此离线成本增加了。最初在Wu和Tiso中提出的节点固定浮动框架对应物（Multibody Syst。Dyn。36（4）：405-425，[2016]），并且产生了显着的提速。但是，由于平均轴公式使操作员的稀疏度降低，因此离线成本增加了。最初在Wu和Tiso中提出的节点固定浮动框架对应物（Multibody Syst。Dyn。36（4）：405-425，[2016]），并且产生了显着的提速。但是，由于平均轴公式使操作员的稀疏度降低，因此离线成本增加了。