接触问题数值分析方法的研究现状与发展

Progress and Current Situation of Numerical Analysis Methods in Contact Problems

接触问题涉及到应力集中、边界非线性、甚至材料或几何非线性，问题很复杂但又十分重要。随着电子计算机的发展，有限元与边界元理论与数值方法也取得了很大进展。目前，这两种方法已成为工程接触问题十分有效的研究和数值分析手段。本文综述了接触问题中的有限元法与边界元法及其工程应用方面所取得的进展，着重围绕小变形弹性接触、小变形弹塑性接触以及大变形接触等方面的内容。此外，文中还对今后研究的发展方向作了展望。二十多年来，在小变形弹性接触问题中的有限元法和边界元法发展的比较成熟，并在工程中获得广泛应用；小变形弹塑性接触问题中的有限元法发展的也比较成熟。然而，它们在如下方面还必须开展进一步的研究，例如，不同材料非线性模式的接触、不同蠕变模式的接触、大变形弹塑性接触、基于实验力学的反迭代分析、以及复杂的工程构件的接触分析等。

The contact problems in engineering are very important but rather complicated because they deal with stress concentration,boundary nonlinear,and even material or geometric nonlinear problems. With the development of electronic computers,great progress has been made in the theory and the numerical approaches of finite element methods(FEM)and boundary element methods (BEM). Now, the two methods have become the very useful and efficient tools for the investigation and the numerical analysis of engineering contact problems. The progress of FEM and BEM for contact problems as well as their engineering applications is summarized in this paper,particularly including the small deformafion elastic and elastoplastic contact problems,and the large deformation contact problems. In addition,a view for the continuing study of the contact problems in future is forecact. For more than twenty years,FEM and BEM for the elastic contact problems,as well as FEM for the elastoplastic contact problems of small deformation, have all been matured,and widely used in engineering. However,FEM and .BEM for the following contact problems will have to be further studied,such as the different material nonlinear contact,the different creep contact,the elastoplasctic contact of large deformation,anti-iterative approaches depending on experimental mechanics and the contact analysis of the complicated engineering components.