A BEM formulation for anisotropic half-plane problems

This article presents a boundary element formulation for cracked anisotropic elastic half-planes and shows how the formulation can efficiently be applied to solve various practical problems. The complete Green's functions for the anisotropic half-plane are obtained and the corresponding boundary integral equations are derived. Also presented are particular solutions associated with the body force of gravity and far-field stresses, which are incorporated rigorously into the boundary element formulation by superposition. For half-plane problems, this new formulation is more efficient than the finite element method or even the boundary element formulation using Green's functions for the infinite plane. Numerical examples are presented for the calculation of the stresses and the stress intensity factors. For the isotropic case, our numerical results are in excellent agreement with those obtained with previously published analytical solutions. For the anisotropic case, our results show clearly that material anisotropy can have a great effect on the stress distribution and on the magnitude of stress intensity factors.