Abstract Cell-based smoothed finite element method (CS-FEM) offers a new paradigm for FEM with the desirable softening effect and makes marginal modifications to existing FE codes. It is found that CS-FEM wins exceptional flexibility in integrating smoothed Galerkin weak form of field equations. This paper continues to explore the method for predicting vortex-induced vibration (VIV) of multiple rigid and flexible bodies. CS-FEM is applied to both the Navier–Stokes and multibody elastodynamic equations. A supplementary proof is presented to further interpret the irrelevance of CS-FEM to integration points. The cell-based gradient smoothing concept is also designed to accompany accurate evaluation of external fluid forces acting on multiple bluff bodies. Following an efficient mesh deformation strategy, a partitioned strong coupling algorithm is employed to couple all interacting fields under the arbitrary Lagrangian–Eulerian description. VIV of four circular cylinders and two elastic cantilevers behind obstacles is analyzed to demonstrate the enlarged applicability and good robustness of CS-FEM. A reasonable agreement is revealed between previous and present results. The main characteristics of complex flow-induced multibody oscillations are successfully captured as well.

中文翻译：

---

基于单元的平滑有限元方法模拟多钝体涡激振动

摘要 基于单元的平滑有限元方法 (CS-FEM) 为 FEM 提供了一种新范式，具有理想的软化效果，并对现有 FE 代码进行了边缘修改。结果表明，CS-FEM 在整合平滑伽辽金弱场方程方面具有非凡的灵活性。本文继续探索预测多刚柔体涡激振动（VIV）的方法。CS-FEM 适用于 Navier-Stokes 和多体弹性动力学方程。提供了补充证明以进一步解释 CS-FEM 与积分点的无关性。基于单元的梯度平滑概念还设计用于精确评估作用在多个钝体上的外部流体力。遵循有效的网格变形策略，采用分区强耦合算法来耦合任意拉格朗日-欧拉描述下的所有相互作用场。对障碍物后面的四个圆柱体和两个弹性悬臂的 VIV 进行了分析，以证明 CS-FEM 的扩大适用性和良好的鲁棒性。以前和现在的结果之间显示出合理的一致性。复杂的流动引起的多体振荡的主要特征也被成功捕获。