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Boundary integral formulae for the reconstruction of imperfections of small diameter in an elastic medium. (English) Zbl 1028.74021
The paper proposes a procedure for the reconstruction (identification) of a finite number of imperfections of small diameter with Lamé coefficients, known or unknown, different from the ones of the background (matrix) material. The method is based on the integration of the solution against special test functions, and on asymptotic arguments for small imperfections. It is a further, nontrivial extension from an analogous method for scalar differential equations (conduction problems) to matrix differential equations (elasticity). A schematic identification algorithm is proposed without numerical results.

MSC:
74G75 Inverse problems in equilibrium solid mechanics
74E05 Inhomogeneity in solid mechanics
74G10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics
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