基于边界积分方程求解二维移动滚动接触问题

工程机械中，由于接触体之间的相对运动造成的损伤或疲劳一直是研究的重点。然而相对运动中，接触相对位置不断变化。为保证接触区应力精确模拟，需对所有可能接触区网格进行加密。为避免这一问题，采用网格更新法，保证仅当前时刻可能接触区网格需加密，并保证接触区节点一一对应。同时采用旋转坐标系法，推导出边界积分方程移动滚动前后时刻的等价性，避免积分重复计算。基于上述方法，提出二维移动滚动接触问题解方法并利用数值算例证明本文方法的有效性。

Solving 2D Sliding and Rolling Contact Problems by Boundary Integral Equation

In mechanical engineering, damage or fatigue due to relative motion between contacting bodies has always been the focus of research. However, in relative motion, the zone of the contact area is constantly changing. To accurately simulate the stress in the contact area, the mesh of all potential contact areas needs to be refined. To avoid this problem, a mesh updating method is adopted. Employing this method, only the mesh of the potential contact area at the current moment needs to be refined, and the matching meshes can be ensured. Besides, the rotating coordinate system method is used in this paper. By this method, the equivalence of boundary integral equations before and after sliding or rolling can be derived, avoiding repeated integral calculations. Based on the above methods, the solution method for 2D sliding or rolling contact problems is proposed, and the effectiveness of the proposed method is verified by numerical examples.