圆外平面弹性问题的边界积分公式  

Boundary Integral Formula for the Elastic Plane Problem of Exterior Circular Domain

作　　者：董正筑[1] 李顺才[1] 余德浩[2] 

机构地区：[1]中国矿业大学理学院,江苏徐州221008 [2]中国科学院计算数学与科学工程计算研究所,北京100080

出　　处：《应用数学和力学》2006年第7期867-873,共7页Applied Mathematics and Mechanics

摘　　要：将边界上的应力函数及其法向导数展开为罗朗级数,与复应力函数的罗朗级数的表达式对比,可以确定罗朗级数的各系数,再利用傅利叶级数和卷积的几个公式进行计算,得到应力函数边界积分公式.通过边界的应力函数及其法向导数的积分,直接得到圆外应力函数值,并给出几个算例,表明结果用于求解单位圆外平面弹性问题十分方便.After the stress function and its normal derivative on the boundary for the plane problem of exterior circular domain ate expanded into Laurent series, comparing them with the Laurent series of the complex stress function and making use of some formulas in Fourier series and in the convolutions, the boundary integral formula of the stress function is derived further. Then the stress function can be obtained directly by the integration of the stress function and its normal derivative on the boundary. Some examples are given. It shows that the boundary integral formula of the stress function is convenient to be used for solving the elastic plane problem of exterior circular domain.

关 键 词：圆外平面弹性问题 双调和方程 傅利叶级数 应力函数 边界积分公式 

分 类 号：O343.1[理学—固体力学]