A new meshless numerical method for simulating frictional contact problems

MA Wen-tao; SHI Jun-ping; LI Ning

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A new meshless numerical method for simulating frictional contact problems

更新时间：2026-06-25

- A new meshless numerical method for simulating frictional contact problems
- Vol. 33, Issue 10, (2012)
- 作者机构：
  
  1. 西安理工大学土木建筑工程学院,西安,710048
  2. 宁夏大学数学计算机学院,银川,750021
- 作者简介：
- 基金信息：
- DOI：
  CLC： TU443
- Online First：19 October 2012，
  
  Published：2012
- 稿件说明：
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MA Wen-tao, SHI Jun-ping, LI Ning. A new meshless numerical method for simulating frictional contact problems[J]. 2012, 33(10).
DOI：

MA Wen-tao, SHI Jun-ping, LI Ning. A new meshless numerical method for simulating frictional contact problems[J]. 2012, 33(10). DOI：

摘要

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。

Abstract

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.

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