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Reconstruction of an ellipsoidal defect in anisotropic elastic solid, using results of one static test. (English) Zbl 1308.74026
Summary: A problem of identification of an ellipsoidal defect (a cavity or inclusion) in an infinite anisotropic linear elastic solid is considered in this article. It is assumed that arbitrary constant stresses are applied at the infinity and the loads and displacements are known on some closed surface containing the defect inside. An analytical method for identification of the geometrical parameters of the ellipsoidal defect (coordinates of its centre, the magnitudes and directions of the axes) using the available data is developed. The results, obtained for the case of an infinite solid, are applied to the bounded elastic body. Numerical examples showing the efficiency of the proposed identification method are considered.

MSC:
74B05 Classical linear elasticity
65N21 Numerical methods for inverse problems for boundary value problems involving PDEs
74G75 Inverse problems in equilibrium solid mechanics
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