Application of Reciprocity Gap Functional for Elastostatic Inverse Problem of Small Well-separated Defects Identification

AbstractAn inverse problem of identification of a finite number of small, well-separated defects in an anisotropic elastic body using the results of one static test is considered. It is supposed that the defects are cavities (in particular, cracks) or inclusions (rigid or linear elastic). If the defects are cavities then their boundaries are supposed unloaded. If the defects are inclusions it is supposed complete bonding between the matrix and inclusions. It is assumed also that in a static test the loads and displacements are measured on the external boundary of the body. Under these assumptions a method for determination of centers of the defects projections on an arbitrary plane is developed. In case of ellipsoidal defects their geometrical parameters (directions and magnitudes of the ellipsoids axes) are also determined