Novel semi-analytical solution strategy for stress analysis of linear elastic half-plane containing an isolated hole

A semi-analytical method for computation of stress and displacement field due to surface loading on a linear elastic, isotropic and homogeneous half-plane containing a hole is presented. The method relies on the principle of superposition and comprises of three parts, viz. half-plane with no hole subjected to the intended surface loading, infinite plane containing a hole subjected to unspecified traction on the hole surface and lastly half-plane with no hole subjected to corrective loading on the surface. The loadings in the latter two cases are sought to ensure that all the boundary conditions are satisfied. Michell solution and combination of Airy stress function approach and Fourier transforms are the tools utilized for the second and third part, respectively. The complete method is thoroughly validated through three distinct examples from literature.