A boundary element formulation for the inverse elastostatics problem (iesp) of flaw detection

Luciano M. Bezerra, Sunil Saigal

Research output: Contribution to journalArticlepeer-review

43 Scopus citations


A boundary integral formulation is presented for the detection of flaws in planar structural members from the displacement measurements given at some boundary locations and the applied loading. Such inverse problems usually start with an initial guess for the flaw location and size and proceed towards the final configuration in a sequence of iterative steps. A finite element formulation will require a remeshing of the object corresponding to the revised flaw configuration in each iteration making the procedure computationally expensive and cumbersome. No such remeshing is required for the boundary element approach. The inverse problem is written as an optimization problem with the objective function being the sum of the squares of the differences between the measured displacements and the computed displacements for the assumed flaw configuration. The geometric condition that the flaw lies within the domain of the object is imposed using the internal penalty function approach in which the objective function is augmented by the constraint using a penalty parameter. A first‐order regularization procedure is also implemented to modify the objective function in order to minimize the numerical fluctuations that may be caused in the numerical procedure due to errors in the experimental measurements for displacements. The flaw configuration is defined in terms of geometric parameters and the sensitivities with respect to these parameters are obtained in the boundary element framework using the implicit differentiation approach. A series of numerical examples involving the detection of circular and elliptical flaws of various sizes and orientations are solved using the present approach. Good predictions of the flaw shape and location are obtained.

Original languageEnglish (US)
Pages (from-to)2189-2202
Number of pages14
JournalInternational Journal for Numerical Methods in Engineering
Issue number13
StatePublished - Jul 15 1993
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • General Engineering
  • Applied Mathematics


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