A complex boundary integral method for multiple circular holes in an infinite plane

Jianlin Wang, Steven L. Crouch, Sofia G. Mogilevskaya

Research output: Contribution to journalArticlepeer-review

63 Scopus citations


A complex boundary integral equation method, combined with series expansion technique, is presented for the problem of an infinite, isotropic elastic plane containing multiple circular holes. Loading is applied at infinity or on the boundaries of the holes. The sizes and locations of the holes are arbitrary provided they do not overlap. The analysis procedure is based on the use of a complex hypersingular integral equation that expresses a direct relationship between all the boundary tractions and displacements. The unknown displacements on each circular boundary are represented by truncated complex Fourier series, and all of the integrals involved in the complex integral equation are evaluated analytically. A system of linear algebraic equations is obtained by using a Taylor series expansion, and the block Gauss-Seidel algorithm is used to solve the system. Several numerical examples are considered to demonstrate the accuracy, versatility, and efficiency of the approach.

Original languageEnglish (US)
Pages (from-to)789-802
Number of pages14
JournalEngineering Analysis with Boundary Elements
Issue number8
StatePublished - Sep 2003

Bibliographical note

Copyright 2008 Elsevier B.V., All rights reserved.


  • Complex Fourier series
  • Complex boundary integral equation method
  • Complex hypersingular integral equation
  • Galerkin method
  • Multiple circular holes
  • Taylor series expansion


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