Explicit expressions of the Barnett-Lothe tensors for anisotropic materials

The three Barnett-Lothe tensorsS, H, andL appear frequently in the real form solutions of two-dimensional anisotropic elasticity problems. Explicit expressions for the components of these tensors are presented for general anisotropic materials. The special cases of monoclinic materials with the plane of material symmetry at x₃=0, x₂=0, and x₁=0 are then deduced. For monoclinic materials with the symmetry plane at x₂=0 or x₁=0, the locations of image singularities for the Green's functions for a half-space have a special geometry.