An application of Betti's reciprocal theorem for the analysis of an inclusion problem (Q1592575)

The paper deals with an axisymmetric contact boundary value problem of classical elasticity, where the isotropic homogeneous elastic infinite space is bounded internally by a rigid disc inclusion. The interface between the elastic medium and the rigid disc exhibits complete bonding which guarantees the continuity of displacements and tractions. The infinite elastic medium is subjected to an axisymmetric internal load uniformly distributed on a finite circular domain. The author proposes a direct integral equation formulation, whose full solution can be obtained only by numerical methods. However, by the application of Betti's reciprocal theorem, the author is able to derive an exact closed-form relation for rigid displacement of the disc inclusion caused by axisymmetric circular load.