接触力学中的变分原理

The Variational Principles in Contact Mechanics

接触问题是工程结构、加工工艺中经常面临的重要问题之一。石油工业中钻铤螺纹联接、钻柱与井壁的／接触、钻头与岩石的接触等；铁路工业中桥梁与混凝土基础的准静态接触，火车车轮与轨道的滚动接触等都是接触问题的典型例子。而接触问题中最难最关键的问题就是建立其变分泛函和求解的方法。介绍和总结了近年来关于接触力学中变分原理发表的有关文献和使用的理论和方法，并对这些理论和方法进行了分析和比较。为建立适合于石油钻铤螺纹联接的接触变分原理奠定了基础。

Contact problem is one of the most important problems frequently encountered in engineering structures and processing technology. Collar rotary shouldered connection, contact between drillstring and hole, and between bit and rock as in petroleum engineering, and the quasi-static contact between bridge and concrete base and rolling contact between train wheel and track as in rail engineering are some special examples of contact problems. The most difficult and crucial issue in solving such problems is to establish contact variational function and solution method. In this paper, the current literature related to the theories and methods of variational principles of contact mechanics is reviewed, analyzed and compared, which sets a foundation for the establishment of variational principles specific to the rotary shouldered connection problem.