A variationally coupled FE-BE method for elasticity and fracture mechanics

Y. Y. Lu*, T. Belytschko, W. K. Liu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

25 Scopus citations


A new method for coupling finite element and boundary element subdomains in elasticity and fracture mechanics problems is described. The essential feature of this new method is that a single variational statement is obtained for the entire domain, and in this process the terms associated with tractions on the interfaces between the subdomains are eliminated. This provides the additional advantage that the ambiguities associated with the matching of discontinuous tractions are circumvented. The method leads to a direct procedure for obtaining the discrete equations for the coupled problem without any intermediate steps. In order to evaluate this method and compare it with previous methods, a patch test for coupled procedures has been devised. Evaluation of this variationally coupled method and other methods, such as stiffness coupling and constraint traction matching coupling, shows that this method is substantially superior. Solutions for a series of fracture mechanics problems are also reported to illustrate the effectiveness of this method.

Original languageEnglish (US)
Pages (from-to)21-37
Number of pages17
JournalComputer Methods in Applied Mechanics and Engineering
Issue number1
StatePublished - Jan 1991

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Physics and Astronomy(all)
  • Computer Science Applications

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