Asymptotic solution of the problem of the interaction of a plate with a foundation inhomogeneous in depth
The equations of the contact problem of a circular plate interacting with a half-space inhomogeneous in depth are considered. The Lamé coefficients vary with depth in the half-space according to a general law -- that of a gradient (continuously inhomogeneous) or laminated half-space. Use is made of the series expansions of the contact pressures under the plate and of its deflections, the terms of the series being the eigenfunctions of the equation of the bending of the plate with boundary conditions representing support conditions for the plate. To solve the dual integral equation, the two-sided asymptotic method is used. An analysis is made of how different laws of variation of the Lamé coefficients with depth in the half-space may affect the distribution of contact pressures under the plate, its deflection and the settlement of the surface of the half-space outside the contact zone.
scientific article; zbMATH DE number 1077434