模拟摩擦接触问题的新型无网格数值方法

针对摩擦接触问题，给出一种新型的无网格数值方法。该方法基于单位分解思想，在标准无网格Galerkin法的位移模式中嵌入不连续函数和裂尖奇异函数，分别反映接触面的不连续性和接触面端点的奇异性；结合接触摩擦定律，继而构造出求解摩擦接触问题的无网格线性互补模型。在该方法中，接触面方程使用接触点对离散，全局离散系统方程则转化为标准的线性互补问题，可以很方便地使用Lemke算法求解。算例分析证明，本文方法的正确性和有效性。

A new meshless numerical method for simulating frictional contact problems

A new meshless numerical method for frictional contact problem is presented.In order to represent the discontinuous displacement field along contact surface and stress singularity around the contact surface tip,a discontinuous function and asymptotic crack tip displacement fields are added to the standard displacement formula based on the idea of partition of unity.Then,combined with frictional contact laws,a linear complementary model with the meshless method is formulated.In this approach,contact interface equations are discretized by contact point-discretization;and the global discretized system equation are transformed into a standard linear complementary problem that can be solved readily by using the Lemke method.Numerical examples show that the method is effective for solving the frictional contact problems.