半平面体弹性问题的边界积分公式及应用  

Boundary Integral Formula of Semi-Plane Elasticity Problem and Its Application

作　　者：彭维红[1] 董正筑[1] 李顺才[2] 

机构地区：[1]中国矿业大学理学院,江苏徐州221008 [2]徐州师范大学机械系,江苏徐州221008

出　　处：《中国矿业大学学报》2005年第3期400-404,共5页Journal of China University of Mining & Technology

摘　　要：从格林函数和双调和函数的基本解出发,将双调和方程的边值问题转化为一个只与边界面力有关的边界积分方程,进而求得具体面力条件下半平面弹性问题的解析解.并用以研究底板岩层中的应力分布,得到了底板应力增量分布的解析计算公式,该公式直观、简洁,便于进行数值计算.Based on the Green function and the basic solution of bi-harmonic functions, a boundary integral formula was acquired from the bi-harmonic equations. On the basis of the formula, the analytical solutions to a semi-plane elasticity problem under specific plane loads can be obtained. The bounary integral formula was applied to investigate the distribution of stresses in seam floor, and as a result, the mathematical expression of the increment of stresses in seam floor was obtained. It can be realized that the conclusion is directly perceived through the senses, simple, and convenient for numerical calculating.

关 键 词：积分公式 平面体 应用 边界积分方程 平面弹性问题 解析计算公式 双调和函数 双调和方程 格林函数 问题转化 应力分布 底板岩层 应力增量 数值计算 基本解 界面力 解析解 边值 

分 类 号：O172.2[理学—数学] TB237[理学—基础数学]