Complex variables boundary element analysis of three-dimensional crack problems

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This paper presents a new boundary element-based approach for solving three-dimensional problems of an elastic medium containing multiple cracks of arbitrary shapes. The medium could be loaded by far-field stress (for infinite domains), surface tractions (including those at the cracks surfaces), or point loads. Constant body forces are also allowed. The elastic fields outside of the cracks are represented by integral identities. Triangular elements are employed to discretize the boundaries. Integration over each element is performed analytically. In-plane components of the fields are combined in various complex combinations to simplify the integration. No singular integrals are involved since the limit, as the field point approaches the boundary, is taken after the integration. The collocation method is used to set up the system of linear algebraic equations to find the unknown boundary displacements and tractions. No special procedure is required to evaluate the fields outside of the boundaries, as the integration is performed before the limit is taken. Several numerical examples are presented to demonstrate the capacity of the method.

Original languageEnglish (US)
Pages (from-to)1532-1544
Number of pages13
JournalEngineering Analysis with Boundary Elements
Issue number11
StatePublished - 2013

Bibliographical note

Funding Information:
Partial support was provided by DOE Grant DE-FE0002020 funded through the American Recovery and Reinvestment Act.


  • Analytical integration
  • Boundary
  • Complex variables
  • Element
  • Method
  • Three-dimensional cracks


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