A refined decay condition for a high-contrast sandwich plate subject to antiplane shear

A three-layered elastic semi-infinite strip subject to antiplane shear is considered. The relative stiffness ratio is assumed to be a small parameter. The so-called decay conditions generalising the Saint-Venant’s principle are studied. A first-order asymptotic correction to the complementary condition prohibiting slowly decaying boundary layers is derived using an asymptotic layer-wise procedure. The established refined formula involves functions of the thickness coordinate expressed through infinite series. Their convergence is analysed numerically for various values of the thickness ratio. An example of a removable singularity in the general solution is also presented.