Analytics study on the problem of two holes having arbitrary shapes and arrangements in plane elastostatics

  • Zhang LuqingEmail author
  • Yang Zhifa
  • Lü Aizhong


By using Schwarz alternating method, this paper presents a simplified alternating algorithm for the problems of two holes having arbitrary shapes and arrangements in an isotropic homogeneous linear elastic infinite region, and obtains stress and displacement fields for random times of iteration. After precision analysis it is found that the results for twenty times of iteration are of very high precision, and those with higher precision can be acquired if the iteration solving is further conducted. The comparison of the results from FEM further proves the reliability of the simplified alternating algorithm presented by this paper.


Schwarz alternating method two holes having arbitrary shapes arbitrary arrangements simplified alternating algorithm iteration stress field displacement field precision analysis 


  1. 1.
    Pan Jiazheng, Stress analysis for two neighbor hydraulic tunnels, Underground Engineering (in Chinese), 1979, (2): 2.Google Scholar
  2. 2.
    Liu Xinyu, Hou Xueyuan, Stress analysis for parallel circular tunnels, Journal of Tongji University (in Chinese), 1985, (3): 15.Google Scholar
  3. 3.
    Salerno, V. L., Mahoney, J. B., Stress solution for an infinite plate containing two arbitrary circular holes under equal biaxial stresses, Journal of Engineering for Industry, Transactions of ASME, 1968, 35: 656.Google Scholar
  4. 4.
    Ukadgaonker, V. G., Stress analysis of a plate containing two circular holes having tangential stresses, AIAA Journal, 1980, 18: 125.CrossRefGoogle Scholar
  5. 5.
    Kim, T. J., Ukadgaonker, V. G., Plane stress analysis of two rigid circular inclusions, AIAA Journal, 1971, 9: 2294.CrossRefGoogle Scholar
  6. 6.
    Ukadgaonker, V. G., Interaction effect of two arbitrarily oriented cracks, part I, International Journal of Fracture, 1991, 51: 219.CrossRefGoogle Scholar
  7. 7.
    Zhang Luqing, Lü Aizhong, Study of alternating method for stress analysis on surrounding rock of two circular holes, Chinese Journal of Rock Mechanics and Engineering (in Chinese), 1998, 17(5): 534.Google Scholar
  8. 8.
    Yu, I. W., Sendeckyj, G. P., Multiple circular inclusion problems in plane elastostatics, Journal of Applied Mechanics, Transactions of ASME, 1974, 41: 215.Google Scholar
  9. 9.
    Mikhlin, S. G., Method of successive approximation in solutions to biharmonic equations, Trudy, Seisomological, USSR, 1934, 39.Google Scholar
  10. 10.
    Soboleff, S., Schwarz algorithm in the theory of elasticity, Reports from Academy of Science, USSR, 1936, IV.Google Scholar
  11. 11.
    Chen Ziyin, Analytic Method of Mechanical Analysis for the Surrounding Rock (in Chinese), Beijing: Coal Industry Publishing House, 1994, 70–76.Google Scholar
  12. 12.
    Lü Aizhong, Jiang Binsong, Reverse Problems in Rock Mechanics (in Chinese), Beijing: Coal Industry Publishing House, 1998, 164–171.Google Scholar

Copyright information

© Science in China Press 2001

Authors and Affiliations

  1. 1.Engineering Geomechanics Laboratory Institute of Geology and GeophysicsChinese Academy of SciencesBeijingChina
  2. 2.Shandong University of Science and TechnologyTai’anChina

Personalised recommendations