Asymptotic of the Solution of the Contact Problem
for a Thin Elastic Plate and a Viscoelastic Layer1
G. P. Panasenkoa,b,* and A. E. Elbertc
a National Research University “Moscow Power Engineering Institute”, Moscow, Russia
b University of Lyon, France
cInstitute of Mechanics and Mathematics, Ural Branch, Russian Academy of Sciences, Yekaterinburg, Russia
Correspondence to: * e-mail: grigory.panasenko@univ-st-etienne.fr
1The article was translated by the authors.
Received 28 June, 2017
Abstract—The contact problem for a thin elastic rigid plate described by the elasticity equations and a viscoelastic layer is solved. The ratio of the thicknesses of the plate and the layer is a small parameter, while the ratio of the Young’s moduli of the layer and the plate is proportional to the cube of this parameter. The asymptotic expansion of the solution is constructed. A theorem on the estimate of the error of asymptotic approximation is formulated. Such problem appears in geophysics, in modeling of the Earth crust–magma interaction.
DOI: 10.1134/S1064562418020023