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XFEM-based crack detection scheme using a genetic algorithm. (English) Zbl 1194.74309
Summary: A new computational tool is developed for the accurate detection and identification of cracks in structures, to be used in conjunction with non-destructive testing of specimens. It is based on the solution of an inverse problem. Based on some measurements, typically along part of the boundary of the structure, that describe the response of the structure to vibration in a chosen frequency or a combination of frequencies, the goal is to estimate whether the structure contains a crack, and if so, to find the parameters (location, size, orientation and shape) of the crack that produces a response closest to the given measurement data in some chosen norm. The inverse problem is solved using a genetic algorithm (GA). The GA optimization process requires the solution of a very large amount of forward problems. The latter are solved via the extended finite element method (XFEM). This enables one to employ the same regular mesh for all the forward problems. Performance of the method is demonstrated via a number of numerical examples involving a cracked flat membrane. Various computational aspects of the method are discussed, including the a priori estimation of the ill-posedness of the crack identification problem.
74R10Brittle fracture
74H45Vibrations (dynamical problems in solid mechanics)
74S05Finite element methods in solid mechanics