The method of integral equation formulation and the unbounded solutions of elastic contact problems

It is shown that a modification of the integral equation formulation [1] can be used to find an expression of the unbounded contact stress of problems in the theory of elasticity. The modifications consist in reducing the problem to a Hilbert-type singular integral equation rather than that of the Cauchyʹs kernel one. The reduction is carried out in analogous procedures to that followed in [1], but here the unknown function is the contact stress, in contrast to the previous formulation in which the unknown function was a necessarily continuous displacement. The Hilbert equation is inverted to define the contact stress and further reduced to an infinite algebraic system, its solution completes the definition with the aid of the physical conditions. The truncation of the algebraic system is justified and the error is estimated.