Joints with clearances in flexible multibody systems have been investigated for many years. However, the previous work is mainly concerned with the lower pair joints with small clearances. The aim of this paper is to present a formulation for the sliding joint with clearance between a flexible beam and a rigid hole, with special focus on the frictional contact. We thoroughly discuss a contact detection method for a flexible beam with circular cross-section and a rigid hole with rectangular cross-section. We employ the layer-wise contact detection concept and propose an efficient and robust approach to address the two-dimensional ellipse–rectangle contact detection problem within the rigid hole cross-section. After the potential contact points on the beam surface and on the hole cross-section are determined, a beam–rigid hole frictional contact element is proposed. The measure of tangential interaction is defined in the current configuration, and the changes of both contact points are taken into consideration. The constitutive relationship for the tangential contact is modeled by the Coulomb friction law with a penalty regularization, and the real tangential force vector in the current step is determined via a trial step and a subsequent return-mapping scheme. In addition, the discontinuity problem across the beam element boundaries in the case of large sliding is circumvented by a simple and effective transformation. Finally, two numerical examples are presented to verify the proposed contact detection method and the beam–rigid hole frictional contact element, and to demonstrate the influence of the frictional contact on the dynamic performance of flexible multibody systems.

中文翻译：

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柔性多体系统中柔性梁与刚性孔之间具有间隙的滑动接头的摩擦接触分析

挠性多体系统中带有间隙的接头已进行了多年研究。但是，先前的工作主要涉及间隙较小的下对接头。本文的目的是提出一种用于滑动接头的配方，该配方在柔性梁和刚性孔之间留有间隙，特别着重于摩擦接触。我们彻底讨论了圆形截面柔性梁和矩形截面刚性孔的接触检测方法。我们采用逐层接触检测的概念，并提出了一种有效且鲁棒的方法来解决刚性孔横截面内的二维椭圆-矩形接触检测问题。确定光束表面和孔横截面上的潜在接触点后，提出了一种梁刚孔摩擦接触元件。在当前配置中定义了切向相互作用的量度，并且考虑了两个接触点的变化。切向接触的本构关系由库仑摩擦定律和惩罚正则化建模，当前步骤中的实际切向力矢量是通过试验步骤和随后的返回映射方案确定的。另外，通过简单而有效的变换避免了在大滑动情况下横梁单元边界的不连续性问题。最后，通过两个数值示例来验证所提出的接触检测方法和梁-刚性孔摩擦接触元件，