The problem of a round plate equilibriwn under a constant concentrated force applied at the plate center has been solved. The plate consists of a homogeneous isotropic base and a fairly inhomogeneous (in particular, multilayer) coating much thinner than the base. The concentrated force magnitude is such that the plate sag and the coating thickness are of the same order. The sag is determined by the asymptotic method. The calculation results can be applied in approximate determination of elastic characteristics of thin coatings.
Department of Mathematics, Faculty of Physics, Moscow State University, Leninskie Gory, Moscow, 119992, Russia
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