Inversion Symmetry of the Solutions of Boundary-Value Problems of Elasticity for a Half-Space

The inversion symmetry of the components of the displacement vector and stress tensor in the solution of the first boundary-value problem of elasticity for a half-space is studied. The case where one component of loading on the half-space boundary has inversion symmetry and the other two components are equal to zero is considered. Inversion symmetry is also studied for the mixed problem where normal forces act and tangential forces are equal to zero one part of the half-space boundary, while the conditions of smooth contact are prescribed on the other part, and the problem of the torsion of an elastic half-space with tangential stresses given on its boundary.