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 引用本文: 韩石磊 洪嘉振. 柔性多体碰撞问题的多变量方法[J]. 力学学报, 2011, 43(5): 886-893.
Shilei Han J.-Z. Hong. Multi-variable method for flexible multi-body systems with contact/impact[J]. Chinese Journal of Theoretical and Applied Mechanics, 2011, 43(5): 886-893.
 Citation: Shilei Han J.-Z. Hong. Multi-variable method for flexible multi-body systems with contact/impact[J]. Chinese Journal of Theoretical and Applied Mechanics, 2011, 43(5): 886-893.

## Multi-variable method for flexible multi-body systems with contact/impact

• 摘要: 针对柔性多体系统碰撞问题的特点, 提出了柔性多体系统碰撞问题的多变量方法. 在未碰撞阶段和分离后的阶段, 多变量方法考虑了物体大范围运动与变形的耦合.在碰撞阶段, 考虑非碰撞区域的变形, 对非碰撞区域用浮动参考系方法求解, 对发生碰撞的局部区域用非线性有限元方法求解. 非碰撞区域采用浮动基位形坐标和柔性体相对浮动基的变形模态坐标描述, 大大减缩了变量的维数,提高了计算效率. 碰撞局部区域采用非线性有限元节点坐标描述, 可以得到碰撞局部区域高精度的应力、应变响应, 而且可以反映碰撞局部区域的大变形、塑性等非线性响应. 该方法既能体现碰撞对系统大范围运动和长期动力学仿真的影响, 又能精确反映出碰撞发生的微小时间段内物体碰撞局部区域的应力、应变响应, 表现出碰撞过程中物体接触区域的演化历程.介绍了两杆正碰撞与铅垂面内双摆撞击自由圆盘的算例, 设计了两柔性杆正碰撞实验,多变量方法的数值仿真结果与实验测量结果很好地吻合.

Abstract: Multi-variable method is proposed to dealwith flexible multi-body systems with contact/impact. With this method, thefloating reference frame technique is combined with the nonlinear finiteelement technique to raise the solving efficiency of the whole system andthe computation accuracy in the local contact/impact region. The motion ofthe non-contact/impact region is described with the floating reference frametechnique and the modal reduction approach is used to raise thesolving efficiency. The nonlinear finite element technique is employed fordescribing the nonlinear and plastic deformation in the local contact/impactregion. Some numerical examples are presented with the proposed method. Inaddition, experimental investigations with a Laser-Doppler vibrometer arepresented. The numerical results agree well with the experimental ones.

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