Singular integrodifferential equation for infinite thermoelastic plate

Muskhelishviliʹs method of complex variables in solving two-dimensional elasticity problems has been applied to derive exact expressions for Gaursatʹs functions for the first and second fundamental problems of thermoelastic infinite plate weakened by a hole having many poles and arbitrary shape. The plate is conformally mapped on the domain outside a unit circle by means of a general rational mapping function. Some applications are investigated and some interesting cases when the hole takes different shapes are included as special cases.