Point and circular loads applied within a cross anisotropic elastic half space

Abstract

Solutions are presented for the full range of load types applied to circular areas located with a cross anisotropic elastic half space. For the half space, the bounding plane is parallel both the located area and to the plane of isotropy in the material properties. The five load types are: vertical force, horizontal force, moment about a horizontal axis, moment about a vertical axis, and radial shear stress. For general distributions of loading stresses integral transform techniques are used to derive solutions for all displacement and strain components, the latter readily giving all stress components. The practically important cases of loading in the form of point loads or as the polynomial stress distributions (1 − R 2 ) q and R (1 − R 2 ) t are examined. The solutions produced can be used to extend the boundary element method to three-dimensional cases involving cross-anisotropic half spaces