采用逐次渐进法求解非圆形地下洞室映射函数  

Solving the Mapping Function of Noncircular Underground Cavern with the Method of Successive Approximation

作　　者：陈峰宾[1,2] 张顶立[2] 张素磊[2] 

机构地区：[1]河南理工大学土木工程学院,河南焦作454000 [2]北京交通大学土木建筑工程学院,北京100044

出　　处：《中国铁道科学》2013年第2期80-86,共7页China Railway Science

基　　金：国家"九七三"计划项目(2010CB732102);铁道部科技研究开发计划项目(2009G005)

摘　　要：基于多角形映射理论,推导出单位圆外域到多角形外域的映射函数项数的一般表达式。采用逐次渐进法求解表达式,得到非圆形地下洞室的映射函数,编制计算机程序实现该算法。算例计算结果表明:该方法不仅适用于有对称轴的孔形,也适用于一般孔形;映射函数项数越多,映射精度越高;对于曲边孔形,映射函数取很少的项(4或5项)就能得到较为理想的映射孔形;对于含有较多角点的复杂洞形,映射函数需要取较多项才能得到较为理想的近似映射孔形,但在角点处误差较大;若对称图形的对称轴与x轴重合,则映射函数的各项为实数;运用程序计算时,只需要输入映射函数的项数和非圆形地下洞室洞形的DXF格式文件,就可得到非圆形地下洞室的映射函数。Based on polygonal mapping theory,the general expression for the number of terms in the mapping function from the outer domain of unit circle to polygon outer domain was deduced.Successive approximation method was adopted to solve the expression to obtain the mapping function of noncircular underground cavern,and computer program was compiled to realize the method.Calculation results of examples show that the method is not only suitable for cavern shape with symmetry axis but also suitable for general cavern shape.The more number of terms of mapping function is the higher mapping accuracy will be.For curved side cavern shape,taking few items（four or five） of the mapping function can get a relatively ideal mapping cavern shape.For complex cavern shape with more angular points,only taking more items of mapping function can get a relatively ideal approximate mapping cavern shape,but the error is larger at angular point.If the symmetry axis of symmetric figure is coincident with x axis,all the terms of mapping function will be real numbers.Computer program can get the mapping function of noncircular underground cavern by only inputting items of the mapping function and the DXF formatted file of noncircular underground cavern shape.

关 键 词：非圆形地下洞室 映射函数 等幅角修正 逐次渐进法 

分 类 号：U451.2[建筑科学—桥梁与隧道工程]