二维多体机械系统多区域接触问题的研究

RESEARCH OF MULTIAREA CONTACT PROBLEMS IN TWO DIMENSIONAL MULTIBODY MECHANICAL SYSTEMS

传统上，人们大多研究物体局部区域或简单结构间的接触问题及其详细力学性态；本文将接触问题放入机械系统中进行研究，不仅考虑物体间的接触，更关注机械系统中各物体的总体弹性变形与物体接触边界间的耦合影响。本文应用势能最小原理，建立了一类描述机械系统中多区域接触问题的力学模型，用一组代数方程组描述接触体间点的约束关系，获得一组包含力学模型和约束方程的代数方程组。用Ｎｅｗｔｏｎ－Ｒａｐｈｓｏｎ 法求解之。

People have manly studied simple local areas contact problems traditionally. They cared for detail mechanics characters of local contact area mostly. Contact problems in the mechanical systems are studied in this paper. Not only the local contact problems but also the coupling between the contact boundaries and the deformation of bodies are considered. Using the principle of potential energy minimization, a mechanics model to describe the multiarea contact problem in the mechanical system is presented. A set of algebraic constrain equations are used to describe the constrain relationship between the boundary points of the contact bodies. We can obtain a set of algebraic equations including the mechanics and the constrain equations. Through the model, we can obtain the contact status among the contact bodies in the mechanical systems