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The numerical solution of some singular contact problems using a Hilbert transform

Abstract This paper presents a numerical solution method for frictionless, two dimensional contact problems involving punches with slope discontinuities or sharp corners. The solution method presented employs a finite Hilbert transform to remove computational difficulties associated with the logarithmic pressures encountered within such contacts. A complementary (smooth) problem may then be solved using a rapidly convergent Chebyshev expansion which requires relatively few terms to achieve accurate results. The algebraic (square root) pressure singularities encountered at the ends of certain contacts are also easily resolved, being implicit in the series solution used. The solutions to several problems on the half plane are compared with those obtained directly, and a comparison with analytic solutions is made. In the knowledge that the method gives efficient and accurate half plane solutions, it is then extended to problems involving layers of finite depth. In particular, symmetric wedge indentation on both unbonded and bonded layers is investigated, and results for contact width in relation to applied load are given.