An interpolating spline-based approach is presented for modeling multi-flexible-body systems in the divide-and-conquer (DCA) scheme. This algorithm uses the floating frame of reference formulation and piecewise spline functions to construct and solve the non-linear equations of motion of the multi-flexible-body system undergoing large rotations and translations. The new approach is compared with the flexible DCA (FDCA) that uses the assumed modes method [1]. The FDCA, in many cases, must resort to sub-structuring to accurately model the deformation of the system. We demonstrate, through numerical examples, that the interpolating spline-based approach is comparable in accuracy and superior in efficiency to the FDCA. The present approach is appropriate for modeling flexible mechanisms with thin 1D bodies undergoing large rotations and translations, including those with irregular shapes. As such, the present approach extends the current capability of the DCA to model deformable systems. The algorithm retains the theoretical logarithmic complexity inherent in the DCA when implemented in parallel.

提出了一种基于插值样条的方法，用于在分而治之 (DCA) 方案中对多柔体系统进行建模。该算法使用浮动参考系公式和分段样条函数来构造和求解经历大旋转和平移的多柔体系统的非线性运动方程。新方法与使用假设模式方法的灵活 DCA (FDCA) 进行了比较 [1]。在许多情况下，FDCA 必须采用子结构化来准确地模拟系统的变形。我们通过数值例子证明了基于插值样条的方法在准确性和效率上与 FDCA 相当。本方法适用于对具有大旋转和平移的薄 1D 体的柔性机构进行建模，包括那些形状不规则的。因此，本方法将 DCA 的当前能力扩展到对可变形系统建模。该算法在并行实施时保留了 DCA 固有的理论对数复杂度。