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摩擦接触问题的求解是将基于移动最小二乘插值的数值流形法(MLS-NMM)应用到裂纹扩展的必经之路。该文通过结合罚-线性互补方式的施加接触边界条件,并使用拉格朗日乘子法施加本质边界条件,得出一套基于MLS_NMM的摩擦接触问题的求解体系。该方法无需节点与边界重合,则可域外布点和均匀布点,来提高插值精度和降低布点难度,尤其是接触边界处。采用罚-线性互补的方式施加接触条件,使计算格式统一而简洁,利于编程实现。通过算例表明,该方法能准确地模拟接触面的张开、黏结和滑动状态,证明该方法对求解接触摩擦问题是可行的、有效的。
The solution to the problem of frictional contact is to apply the numerical manifold method (MLS-NMM) based on moving least square interpolation to the crack propagation path. In this paper, a set of solution to the friction contact problem based on MLS_NMM is obtained through the application of the boundary condition with penalty-linear complementary method and the application of the essential boundary conditions by Lagrange multiplier method. This method does not need node overlap with the boundary, it can be outside the distribution and uniform distribution, to improve the interpolation accuracy and reduce the difficulty of distribution, especially at the contact boundary. Adopt penalty-linear complementary ways to impose contact conditions so that the calculation format is uniform and concise, which is good for programming implementation. The results show that this method can accurately simulate the open, cohesive and sliding states of the contact surface. It is proved that this method is feasible and effective for solving the contact friction problem.