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Solution of identification inverse problems in elastodynamics using semi-analytical sensitivity computation. (English) Zbl 1195.74255

Summary: The purpose of this work is to study a class of inverse problems that arises in solid mechanics areas such as quantitative non-destructive testing (QNDT) or shape optimization. The technique is based on the boundary integral equations (BIEs) used in the classical boundary element method (BEM), which are differentiated semi-analytically with respect to variations of the boundary geometry and used in an iterative search algorithm. The extension of this strategy is presented here for the case of elasticity in dynamics using the displacement or singular BIE, which allows to apply this strategy to QNDT problems based on vibrations or ultrasonics.
The central point is the evaluation of the capability of solving numerically a QNDT problem such as the location and characterization of cavity and inclusion-type defects by measuring the dynamic response at an accessible boundary of the specimen. To test this capability, comprehensive convergence tests are made for the badness of the initial guess, the amount of supplied measurements, and simulated errors on measurements, geometry, elastic constants and frequency.

MSC:

74S15 Boundary element methods applied to problems in solid mechanics
74H15 Numerical approximation of solutions of dynamical problems in solid mechanics
74P10 Optimization of other properties in solid mechanics
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