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 o f problems in the theory of elasticity. The modifications consist in r educing the problem to a Hilbert-type singular integral equation rathe r than that of the Cauchy's kernel one. The reduction is carried out i n analogous procedures to that followed in [1], but here the unknown f unction is the contact stress, in contrast to the previous formulation in which the unknown function was a necessarily continuous displaceme nt. The Hilbert equation is inverted to define the contact stress and further reduced to an infinite algebraic system, its solution complete s the definition with the aid of the physical conditions. The truncati on of the algebraic system is justified and the error is estimated. (C ) 1998 Elsevier Science Ltd. All rights reserved.