用边界单元法解线弹性接触问题

本文以边界单元法求解二维无摩擦弹性接触问题,分析不同接触情况中边界上满足平衡与协调的条件后,提出了可能接触与已接触两种状态的边界条件,然后应用弹性力学边界积分方程并将边界离散为若干直线段集合使之变为代数方程以求其数值解,将判定边界间是否嵌入和受拉的条件仅限于可能接触的边界,因而简化了迭代计算,最后所得解包括全部边界上的面力与位移,以及接触压力的分布,通过二算例表明,此法比有限单元法节点总数少、数据准备简单、计算速度快且精度更高。

Boundary Element Method in Application to Linear Elastic Contact Problems

Deals wiih the two-dimensional frictionlcss clastic contact problems by way of boundary element method. Analyzing both the conditions of equilibrium and coordination to be satisfied in the different cases of contact, the boundary conditions are expressed in cither case that a boundary is possibly or has already been in contact with, the other. A boundary integral equation based on elastic mechanics is then applied and it becomes algebraic for numerical solution by discretizing the boundary into several linear sets. The iteration computation is simplified in such a way that the criteria of the states of inset and normal pull between two boundaries are merely limited to the case of possible contact boundary. The final solution obtained involve the contact zone and the tractions and displacements on the whole boundary especially the distribution of contact pressure. With two instances included the result is proved Jess number of nodes, simpler data preparation. more rapid computation speed and higher precision in comparison with finite element method.