Parametric Study for Calculating Surface Deflection Using the Method of Images

Abstract

The solution of the elastic field for inclusions in an elastic half space has been applied widely in many contact analyses and engineering designs. A popular method to solve the half-space inclusion problem resorts to the method of images, where the solution is decomposed into 3 components consisting of the full space inclusion, mirrored inclusion, and the surface traction cancellation. In the process of cancelling the redundant surface tractions determined from a full space inclusion problem, the computation domain is supposed to be limited in a finite size and there is inevitably truncation error. It has not been quantitatively investigated how the truncation error will influence the accuracy of the numerical computations based on the method of images. This work studies the deflection of the boundary surface of a half-space containing an Eshelby inclusion. Errors due to mesh refinement and domain truncation are quantitatively analyzed. Parametric studies are performed for a systematic examination of surface redundant tractions and their influences.