Identification of a spheroidal defect in an elastic solid using a reciprocity gap functional

Abstract

The elastostatic problem of identification of a spheroidal cavity or inclusion in an elastic solid is considered. It is shown that the parameters of the spheroidal defect (coordinates of its center, the magnitudes of the semiaxes, the direction of the axis of rotation and elastic moduli in the case of elastic inclusion) can be determined using one uniaxial tension (compression) test. The explicit formulas expressing the unknown defect parameters by means of the values of the reciprocity gap functional (RGF) are obtained. The values of the RGF can be calculated from experimental data if both applied loads and displacements are measured on the external surface of the elastic body in the static test. Numerical analysis of the obtained explicit formulas is fulfilled.