|
|
|
| RESEARCH ON ANALYTICAL SOLUTION OF STRESS FIELD OF SURROUNDING ROCK OF SINGLE HOLE WITH ARBITRARY SHAPE BASED ON HIGHLY-EFFICIENT CONFORMAL MAPPING |
| HUANGFU Pengpeng，ZHANG Luqing，WU Faquan |
| (Key Laboratory of Engineering Geomechanics，Institute of Geophysics，Chinese Academy of Sciences，Beijing 100029，China) |
|
|
|
|
Abstract The general steps of calculating analytical solution of stress field of the surrounding rock of single hole with arbitrary shape and analytical expression of the two potentials were obtained，based on highly-efficient conformal mapping of external area of underground cavern with arbitrary shape based on searching mapped points on the boundary，Cauchy integral formula，combined with complex function method. Then，the stresses at any point z inside the surrounding rock can be computed by using the Kolosov-Muskhelishvili formulae fast. Compared with numerical result，the result acquired by this analytical algorithm could be much more precise than that of the numerical simulation，and the former is much more efficient，too. Then，the analytical result of stress field of the surrounding rock of hole with straight wall and horseshoe shape under three cases of remote loading were obtained using this method，and zones of stress concentration were denoted emphatically. Finally，using this method，the analytical solution of stress field of the surrounding rock of the main power house of Jinping I hydropower station was calculated.
|
|
Received: 05 July 2010
|
|
|
|
| [1] 陆明万，罗学富. 弹性理论基础[M]. 北京：清华大学出版社，1990：297–308.(LU Mingwan，LUO Xuefu. Foundations of elasticity[M]. Beijing：Tsinghua University Press，1990：297–308.(in Chinese))
[2] УСХЕПИШВИПИ H И M. 数学弹性力学中的几个基本问题[M]. 赵惠元译. 北京：科学出版社，1958：196–211.(УСХЕПИШВИПИ H И M. Some basic problem of the mathematical theory of elasticity[M]. Translated by ZHAO Huiyuan. Beijing：Science Press，1958：196–211.(in Chinese))
[3] 吕爱钟，张路青. 地下隧道力学分析的复变函数方法[M]. 北京：科学出版社，2007：28–30.(LU Aizhong，ZHANG Luqing. Complex-variable method for mechanical analysis around underground tunnel[M]. Beijing：Science Press，2007：28–30.(in Chinese))
[4] THEOCARIS P S，IOAKIMIDIS N I. The inclusion problem in plane elasticity[J]. Quarterly Journal of Mechanics and Applied Mathematics，1977，30(4)：437–448.
[5] THEOCARIS P S，IOAKIMIDIS N I. The problem of interaction between a misfiting inclusion and a crack in an infinite elastic plane[J]. Journal of Elasticity，1979，9(1)：97–103.
[6] LINKOV A M. Plane problems of the static loading of a piecewise homogeneous linearly elastic medium[J]. Journal of Applied Mathematics and Mechanics，1983，47(4)：527–532.
[7] LINKOV A M，MOGILEVSKAYA S G. Complex hypersingular integrals and equations of plane elasticity problem[M]. [S.l.]：[s.n.]，1991：17–34.
[8] LINKOV A M，MOGILEVSKAYA S G. Complex hypersingular integrals and integral equations in plane elasticity[J]. Acta Mechanica，1994，105(1/4)：189–205.
[9] SIMHA K R Y，MOHAPATRA S S. Stress concentration around irregular holes using complex variable method[J]. Sadhana，1998，23(4)：393–412.
[10] WANG J L，CROUCH S L，MOGILEVSKAYA S G. A complex boundary integral method for multiple circular holes in an infinite plane[J]. Engineering Analysis with Boundary Elements，2003，27(8)：789–802.
[11] THEOCARIS P S，PETROU L. Stress distributions and intensities atcorners of equilateral triangular holes[J]. International Journal of Fracture，1986，31(4)：271–189.
[12] THEOCARIS P S，PETROU L. From the rectangular hole to the idealcrack[J]. International Journal of Solids and Structures，1989，25(3)：213–233.
[13] PAN E，YANG B，CAI G，et al. Stress analyses around holes in composite using boundary element method[J]. Engineering Analysis with Boundary Elements，2001，25(1)：31–40.
[14] UKADGAONKER V G，RAO D K N. A general solution for stresses around holes in symmetric laminates under inplane loading[J]. Composite Structures，2000，49(3)：339–354.
[15] HELSING J，JONSSON A. Complex variable boundary integral equations for perforated infinite planes[J]. Engineering Analysis with Boundary Elements，2001，25(3)：191–202.
[16] ROKHLIN V. Rapid solution of integral equations of classical potential theory[J]. Journal of Computational Physics，1985，60(2)：187–207.
[17] 皇甫鹏鹏，伍法权，郭松峰，等. 基于边界点搜索的洞室外域映射函数求解法[J]. 岩土力学，2011，32(5)：1 418–1 424.(HUANGFU Pengpeng，WU Faquan，GUO Songfeng，et al. A new method for calculating mapping function of external area of cavern with arbitrary shape based on searching points on boundary[J]. Rock and Soil Mechanics，2011，32(5)：1 418–1 424.(in Chinese))
[18] 陈子荫. 围岩力学分析中的解析方法[M]. 北京：煤炭工业出版社，1994：97–102.(CHEN Ziyin. Analytical method for mechanics of surrounding rock[M]. Beijing：China Coal Industry Publishing House，1994：97–102.(in Chinese)) |
|
|
|
2011, Vol. 30 
