复变函数法求工作面周边应力分布  

Complex-variable function method for the stress distribution around the working face

作　　者：李文敏[1] 

机构地区：[1]安徽理工大学能源与安全学院,安徽淮南232001

出　　处：《矿业工程研究》2013年第1期17-19,共3页Mineral Engineering Research

基　　金：国家自然科学基金项目(51074003;51074005);国家自然科学基金委员会与神华集团有限公司联合资助项目(51174255);安徽省优秀青年科技基金资助项目(10040606Y31);中国博士后科学基金资助项目(2011M501037)

摘　　要：为了研究采煤工作面周边应力分布规律,利用应力分布规律准确的指导现场实践,将工作面在倾斜方向看做矩形,应用复变函数保角映射函数,将ζ平面上的矩形小孔,映射为z平面上的单位圆.通过弹性力学的方法,将问题简化矩形单孔问题在无限域内孔周边的应力分布问题.并运用数学软件,将表达式图形化,直观的看出利用力学方法求解得到的工作面周边应力分布情况.为了比较得到的结果,利用FLAC3D数值模拟软件,相同地质条件下的工作面做数值模拟,以便于对力学分析结果进行比较,比较结果证明,力学分析方法得到的解析解与数值模拟结果误差可以接受.In order to study the coalface peripheral stress distribution law, and use this law to accurately guide the actual practice, this paper takes the sloping direction as a rectangular, applies complex -variable function conformal to map function, mapping plane of the rectangular openings to the plane of the unit circle. By using the method of elastic mechanics, the problem comes down to rectangular single - arch problem in the infinite simplified field surrounding the stress distribution of the holes. And it uses mathematical software to intuitively get the stress distribution around the face. In order to compare with the results, this paper, by using FLAC3D numerical simulation software, does the numerical simulation at the same geological conditions of the working face so as to compare the results of the mechanics analysis. The comparison results prove that the analytical solution got by the mechanics analysis method and the error of numerical simulation result can be accepted.

关 键 词：复变函数 弹性力学 孔周边应力分布 

分 类 号：TD323[矿业工程—矿井建设]