Nonexistence of Solution for Horizontally Rigid Half-Space

Abstract

The Westergaard expressions for stresses and displacements in a half-space of Westergaard material are shown to be invalid because the vertical shear stress does not vanish at the plane boundary of the half-space. The same inadequacy is discovered in the solution for a horizontally rigid cross-anisotropic half-space deduced from Michell’s expressions. A surprising conclusion is drawn, namely, that there is currently no exact elastic solution for the stresses and displacements in a horizontally rigid cross-anisotropic half-space. The Westergaard theory should cease to be regarded as an exact elastic solution for a problem of the theory of elasticity.