变形体的虚功原理及其在求解接触问题中的应用

The Principle of Virtual Work for Deformable Bodies and Its Application to Contact Problems

研究了变形体虚功原理的理论和建立方法 ,并将其用于建立接触问题有限元法计算公式。其基本原理是将构成变形体的微单元体视为质点 ,变形体成为质点系。应用分析力学中质点系的虚位移原理 ,即可得到变形体的虚功原理。应用该法建立了固体力学小变形、大变形问题的虚功原理 ,并推广用于变形体的接触问题 ,建立了相应的虚功原理。在对接触问题的分析中 ,还研究了变形体 -刚体的接触问题及带有外接触边界的固体力学问题 ,建立了相应的虚功原理 。

The theory of virtual work principles of deformable bodies and the technique to derive their expressions are studied and applied to contact problems to build FEM formulas. An infinitesimal element that constitutes a deformable body is taken as a particle, which is constrained elastically by the other particles around it but loses no degree of freedom. Accordingly, the whole deformable body becomes a particle system. The principles of virtual work for deformable bodies can be obtained with facility by taking advantage of the well known principle of virtual displacement in analytical mechanics. The principles of virtual work is applied to solve contact problems. Especially, the study focuses on the contact between a body with small stiffness and another with very large stiffness, which leads to two special instances:(1) that between a deformable and a rigid bodies; and (2) that containing so called external contact boundary between a deformable and a fixed rigid bodies. It would be convenient to solve some special contact problems in engineering with the method presented in this paper.