This paper proposes a systematic and novel component level co-rotational (CR) framework, for upgrading existing 3D continuum finite elements to flexible multibody analysis. Without using any model reduction techniques, the high efficiency is achieved through sophisticated operations in both modeling and numerical implementation phrases. In modeling phrase, as in conventional 3D nonlinear finite analysis, the nodal absolute coordinates are used as the system generalized coordinates, therefore simple formulations of the inertia force terms can be obtained. For the elastic force terms, inspired by existing floating frame of reference formulation (FFRF) and conventional element-level CR formulation, a component-level CR modeling strategy is developed. By in combination with Schur complement theory and fully exploring the nature of the component-level CR modeling method, an extremely efficient procedure is developed, which enables us to transform the linear equations raised from each Newton-Raphson iteration step into linear systems with constant coefficient matrix. The coefficient matrix thus can be pre-calculated and decomposed only once, and at all the subsequent time steps only back substitutions are needed, which avoids frequently updating the Jacobian matrix and avoids directly solving the large-scale linearized equation in each iteration. Multiple examples are presented to demonstrate the performance of the proposed framework.

翻译：本文提出了一种系统且新颖的组件级共旋（CR）框架，用于将现有三维连续体有限元方法升级至柔性多体分析。在不采用任何模型降阶技术的情况下，通过建模与数值实现阶段的精细化操作实现了高效率。在建模阶段，与传统三维非线性有限分析相同，采用节点绝对坐标作为系统广义坐标，从而可推导出惯性力项的简洁表达式。针对弹性力项，受现有浮动参考系公式（FFRF）和传统单元级CR公式的启发，发展了一种组件级CR建模策略。通过结合舒尔补理论并充分挖掘组件级CR建模方法的本质，开发了一种极其高效的求解流程：该方法可将每个牛顿-拉夫森迭代步产生的线性方程组转化为具有常系数矩阵的线性系统。该系数矩阵可仅预计算并分解一次，在后续所有时间步中仅需进行回代，从而避免了频繁更新雅可比矩阵，并省去了每个迭代步中直接求解大规模线性化方程的需求。多个算例验证了所提出框架的性能。