AN EFFICIENT SOLUTION OF PRANDTL-TYPE INTEGRODIFFERENTIAL EQUATIONS IN A SECTION AND ITS APPLICATION TO CONTACT PROBLEMS FOR A STRIP

Two Prandtl-type integrodifferential equations are solved exactly, one equation arising from the antiplane problem for an elastic layer, one of whose boundaries is rigidly attached, the other boundary being rig idly attached everywhere except along a section where it is elasticall y attached, the other equation arising from the plane problem of a str ip-shaped membrane uniformly extending at infinity and strengthened by elastic inclusions. In both cases the integral equation leads, with t he help of a Fourier transformation, to a vector Riemann problem, whic h reduces by a method similar to one presented earlier [1] to an infin ite Poincare-Koch algebraic system. Explicit formulae are found for th e system unknowns together with recurrence relations that are convenie nt for numerical implementation. Computational formulae are found for the axial forces at the ends of the stringer, together with tangential contact stresses and their intensity factors. In the neighbourbood of the ends of the stringer an asymptotic expansion for the contact stre sses is constructed, which, besides powers of radicals, contains produ cts of radicals in integer powers of logarithms. Numerical results are presented.