Bilateral Asymptotic Solution of One Class of Dual Integral Equations of the Static Contact Problems for the Foundations Inhomogeneous in Depth

Abstract

An article is devoted to the method of reduction of one class of dual integral equations, which appear while solving the mixed problems of elastic theory, to the solution of infinite algebraic equation systems in accordance with the method described by Alexandrov V.M. For example, such dual equations arise in solving the contact problems of elasticity theory for the layer inhomogeneous in depth or inhomogeneous half-space. The approximate solution of such equations is reduced to the solution of finite algebraic equation systems. It is proved that the solution, constructed in such way, is asymptotically exact as for small, as for large values of dimensionless geometrical parameter of the problem. The equations generated by the Fourier and Hankel integral transforms are provided as an example.