动接触问题及其数值模拟的研究进展

本文试图对近二十年来，动接触问题的理论及数值计算方法进行全面系统地总结。动接触问题是接触力学领域里的新课题。近年来出现了许多关于这个问题的数值计算方法，包括：（１）Ｌａｇｒａｎｇｅ乘子法，罚方法，振动Ｌａｇｒａｎｇｅ乘子法，增广Ｌａｇｒａｎｇｅ乘子法；（２）线性补偿方法；（３）接触单元法：（４）动接触力法：（５）冲量模型，动接触模型，初始位移法等。本文首先总结了动接触问题的基本控制方程和动接触条件，然后—一陈述了上述方法的基本思想，展示其数值计算结果，并进行评述。最后对进一步的研究工作和工程应用提出了几点建议。

THE ADVANCES OF STUDIES ON THE DYNAMIC CONTACTPROBLEM AND ITS NUMERICAL METHODS

This paper aims to review systematically the theory and numerical methods fordynamic contact problems over the recent twenty years. The dynamic contact problem is a newsubject in the contact mechanics. Many numerical methods have been developed up to now, suchas (1) the Lagrange multiplier method the penalty method the perturbed Lagrange method, theaugmented Lagrange method; (2) the linear complementary method, (3) the joint element method,(4) the dynamic contact force method,;(5) the impulse model, the dynamic contact model, the initialdisplacement model, ect. The foundamental control equations and the dynamic contact conditionsneeded in the dynamic contact analysis are summarized in the paper. Principles of the methods areaddressed and the numerical results based on these methods are presented and evaluated. Finally,some research directions and potential engineering applications are suggested.