The paper gives an account of different approaches to deal with the weak singularity in numerical methods of contact stress problems when the methods are based on the fundamental equation relating the elastic displacement with pressure. Singularity consideration in a new method to simultaneously determine the shape of the contact area and the pressure distribution, particularly in non-Hertzian contact problems, has been dealt with using elliptic functions. Necessity of proper analysis of singularity is discussed and the final results when compared with Hertz solution have been shown to be satisfactory.

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