3 D CRACK DETECTION USING AN XFEM VARIANT AND GLOBAL OPTIMIZATION ALGORTITHMS

In the present work, a scheme is presented for the detection of cracks in three dimensional (3D) structures. The scheme is based on the combination of a newly introduced variation of the extended finite element method (XFEM) and global optimization algorithms. As with existing crack detection schemes, optimization algorithms are employed to minimize the norm of the difference between measured response of the structure, typically strains in some specific points along the boundary, and the response predicted numerically by XFEM. During the optimization procedure the crack geometry is parametrized and the parameters serve as design variables. The whole procedure involves the solution of a very large number of forward problems, which constitute the main computational effort. Therefore, emphasis is given in the reduction of the computational cost associated with the solution of each individual forward problem since it can directly affect the total computational time. The employed XFEM variant can provide increased accuracy for the forward problems at a reduced computational toll, thus decreasing the overall analysis time associated with the crack detection scheme. This reduction is a result of the improved conditioning of the system matrices which leads to a decrease in the time needed to solve the corresponding systems which ranges from 40% up to a few orders of magnitude depending on the enrichment strategy used. Since during the optimization procedure cracks are randomly generated, cracks that lie beyond the boundaries of the structure can occur. In order to exclude those cracks, implicit functions are defined in order to localize the cracks within the structure. In some cases those functions are modified so as to exclude also cracks lying in further invalid locations within the search space. The potential of the proposed scheme is demonstrated through numerical examples involving the detection of cracks in 3D structures. 1 DOI 10.21012/FC9.261 Konstantinos Agathos, Eleni Chatzi and Stéphane P. A. Bordas

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