New Variational Solution for the Space Contact Problem

In the recent thirty years, a great of investigations have been made in the Wiener-Hopf equations and variational inequalities as two mutually independent problems. In this paper, we investigate the equivalence of the solution of variational inequality and the inversion of the Toeplitz operator when the projection operators P, Q are linear. The solution of general Wiener-Hopf equation is concluded as the solution of a variational problem. Thus an approximation method of obtaining the maximum value by variational is proposed to obtain the approximation of general Wiener-Hopf equation and apply it to the space contact problems in the elasticity theory. Especially, the solution representation is given in case that the projection of contact surface is round. The closing-form solution is also given when the known displacement is a polynomial of even power.