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边界元法源于经典的积分方程和有限元法。新方法综合了二者优点,摒弃其缺点。特别是在地下工程中,计算域趋向无限大时,边界元法更为优越。本文介绍了全平面应变问题的基本概念。和一般平面应变相比较,全平面应变能处理三维应力场,且仅用两个自变量处理任意倾斜主轴坑峒的应力分析。文中描述全平面应变问题的间接边界元法,详细地推导了三维应力场中园柱形长孔应力位移的边界积分公式。这样就可以方便地比较解析解与数值解的结果和认识这种新方法的实质。某些数字结果以表格形式给出。
The boundary element method originates from classical integral equations and finite element methods. The new method combines the advantages of the two and abandons its shortcomings. Especially in underground engineering, the boundary element method is superior when the computational domain tends to be infinitely large. This article describes the basic concepts of the full plane strain problem. Compared with the general plane strain, the full plane strain can handle the three-dimensional stress field, and only two independent variables are used to deal with the stress analysis of an arbitrary tilted spindle pit. In this paper, the indirect boundary element method is described for the full-plane strain problem. The boundary integral formulas for the stress-displacement of cylindrical long holes in a three-dimensional stress field are deduced in detail. This allows you to easily compare the results of analytical and numerical solutions and to understand the essence of this new method. Some of the numerical results are given in tabular form.