基于MLS-NMM的摩擦接触问题研究

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 RESEARCH OF FRICTIONAL CONTACT PROBLEM BASED ON MLS-NMM

The solution of frictional contact problems is vital to the simulation of crack propagation in the MLS-based numerical manifold method (MLS-NMM). Through the application of penalty-linear complementarity model for contact constraint conditions and Lagrange multiplier method for imposing essential boundary condition, this study presents the solving method of frictional contact problems using MLS-NMM. The method does not require the nodes on the boundaries, which means that the nodes may be outside of domain and uniformly distributed. Thus it can improve the interpolation precision and reduce the difficulty of the distribution for nodes, especially for those on contact boundaries. The use of penalty-linear complementarity model can make the calculation format unified and concise, which is favorable for programming. Numerical examples show that the proposed method can accurately simulate the contact state of opening, bonding and slipping. The method is a feasible and effective solution for frictional contact problem.