Asymptotic analysis of three-dimensional boundary-value problems for three-layered high-contrast plates

Abstract Two-dimensional leading-order equations governing the elastic bending of a thin three-layered plate with a high contrast in the stiffness of core and skin layers are derived from the original three-dimensional framework. These equations support slowly decaying stress states along with flexural behaviour specific to the classical Kirchhoff plate theory. Asymptotically consistent boundary conditions are formulated using decay relations for an elastic semi-infinite strip, which generalize Saint-Venant’s principle by imposing additional constraints owing to contrast. The developed asymptotic results are tested by comparison with the exact solutions for several parametric set-ups.