We propose to combine the ideas of mass redistribution and component mode synthesis. More specifically, we employ the MacNeal method, which readily leads to a singular mass matrix, and an accordingly modified version of the Craig-Bampton method. Besides obtaining a massless boundary, we achieve a drastic reduction of the mathematical model order in this way compared to the parent finite element model. Contact is modeled using set-valued laws and time stepping is carried out with a semi-explit scheme. We assess the method’s computational performance by a series of benchmarks, including both frictionless and frictional contact. The results indicate that the proposed method achieves excellent energy conservation properties and superior convergence behavior. It reduces the spurious oscillations and decreases the computational effort by about 1–2 orders of magnitude compared to the current state of the art (mass-carrying component mode synthesis method). We believe that the computational performance and favorable energy conservation properties will be valuable for the prediction of vibro-impact processes and physical damping.

我们建议将质量再分配和组件模式合成的思想结合起来。更具体地说，我们采用了 MacNeal 方法，它很容易导致奇异质量矩阵，以及相应的 Craig-Bampton 方法的修改版本。除了获得无质量边界外，与母有限元模型相比，我们通过这种方式实现了数学模型阶数的大幅减少。接触是使用定值定律建模的，时间步进是使用半显式方案进行的。我们通过一系列基准评估该方法的计算性能，包括无摩擦和摩擦接触。结果表明，所提出的方法实现了优异的能量守恒特性和优异的收敛行为。与当前最先进的技术（载重分量模式合成方法）相比，它减少了寄生振荡并将计算工作量减少了大约 1-2 个数量级。我们相信计算性能和有利的能量守恒特性对于振动冲击过程和物理阻尼的预测是有价值的。