Singular boundary elements for three-dimensional elasticity problems

Bojan B. Guzina, Ronald Y.S. Pak, Alejandro E. Martínez-Castro

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


The focus of this paper is a set of semi-discontinuous, traction-singular surface elements introduced to help the rigorous boundary integral analysis of problems in three-dimensional solid mechanics. In contrast to the singular boundary elements developed for linear fracture mechanics where the square-root singularity is of primary interest, traction shape functions featuring the proposed four- and eight-node boundary elements can be used to represent power-type singularities of arbitrary order, such as those arising at non-smooth material boundaries and interfaces. Apart from being capable of rigorously handling traction singularities and discontinuities across the domain boundaries and interfaces, these elements also permit a smooth transition to adjacent regular elements. Complemented with a family of suitable displacement and geometry shape functions, the singular surface elements are incorporated into a regularized boundary integral equation method and shown, through a set of benchmark results, to perform well for both static and dynamic problems.

Original languageEnglish (US)
Pages (from-to)623-639
Number of pages17
JournalEngineering Analysis with Boundary Elements
Issue number8
StatePublished - Aug 2006

Bibliographical note

Funding Information:
The support of the National Science Foundation through CAREER Award no. CMS-9875495 to Bojan Guzina and Grant no. CMS-9712835 to Ronald Pak is gratefully acknowledged. The authors are also thankful to the Ministry of Education, Spain for providing the opportunity for Alejandro Martínez-Castro to visit the University of Minnesota through F.P.U. Grant AP2001-2198, and to Dr. Rafael Gallego for insightful comments during the course of this study.


  • Boundary element
  • Corner singularity
  • Edge singularity
  • Singular stresses


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