三维接触问题新模型研究

RESEARCH ON NEW MODEL FOR ANALYZING THREE DIMENSIONAL CONTACT PROBLEMS

本文提出了一种用于分析三维非线性接触问题的新模型.该模型以结点位移和接触应力作为基本未知量,考虑了三种接触条件:固定、滑动和张开,能模拟具有初始裂缝和无初始裂缝的两物体间的摩擦滑动、张开和闭合.基于增量形式的有限元法,建立了接触摩擦问题的等效单元刚度-约束矩阵和等效结点荷载向量.计算中,可用标准的有限元集成规则将其分别叠加到总刚度矩阵和总荷载向量中,因而具有计算简单,程序设计容易的优点.文中还给出了两个算例.

A new model for analyzing three dimensional non-linear contact problems with irreversible friction is presented in this paper. Taking the displacements and contact stresses as nodal parameters and considering three contact conditions, i.e. fixed, slip and free, the new model can simulate frictional slippage, decoupling and rebonding of two bodies initially mating at a common interface or with any initial gaps. Based on the Finite Element method and load incremental theory, the equivalent element stiffness-constraint matrix and the equivalent nodal load vector are obtained, which can be assembled into global stiffness matrix and global load vector in computation. This method is shown to be simple in computation and easy in programming. Finally, two numerical examples are given at the end of the paper.