An Automated Procedure for Determining Asymptotic Elastic Stress Fields at Singular Points

The paper describes an analytical tool in MATLAB for determining the nature of the stress and displacement fields near a fairly general singular point in linear elasticity. The user is prompted to input the local geometry of the system, the material properties, and the boundary conditions (and interface conditions in the case of composite bodies or problems involving contact between two or more bodies). The tool then computes the dominant eigenvalue and provides as output the equations defining the singular stress and displacement fields and contour plots of these fields. No knowledge of the asymptotic analysis procedure is required of the user. The tool is tested against previously published results where available and proves to be robust and accurate. It is potentially useful for the development of special finite elements for singular points or for characterizing failure at such points. It can be downloaded from the website http://www-personal.umich.edu/∼jbarber/asymptotics/intro.html