A variation of the extended finite element method for 3D fracture mechanics is proposed. It utilizes global enrichment and point-wise as well as integral matching of displacements of the standard and enriched elements in order to achieve higher accuracy, optimal convergence rates and improved conditioning for two and three Preprint submitted to Elsevier Science 29 January 2015
A numerical scheme is proposed for the detection of multiple cracks in three dimensional (3D) structures. The scheme is based on a variant of the extended finite element method (XFEM) and a hybrid optimizer solution. The proposed XFEM variant is particularly well-suited for the simulation of 3D fracture problems, and as such serves as an efficient solution to the so-called forward problem. A set of heuristic optimization algorithms are recombined into a multiscale optimization scheme. The introduced approach proves effective in tackling the complex inverse problem involved, where identification of multiple flaws is sought on the basis of sparse measurements collected near the structural boundary. The potential of the scheme is demonstrated through a set of numerical case studies of varying complexity.
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