Asymptotic Analysis of a Thin Elastic Plate--Viscoelastic Layer Interaction

International audienceThe paper is devoted to an asymptotic analysis of a problem on interaction between a thin purely elastic plate and a thick viscoelastic layer described by the Kelvin-Voigt model. Such a problem appears in modeling of the earth crust-magma interaction. The small parameter is the ratio of the thicknesses of the elastic part and the viscoelastic one. At the same time the plate has a high Young's modulus, that is, an inverse to the third power of the small parameter. The complete asymptotic expansion of the solution is constructed. The error estimate is proved for the difference of the exact solution and a truncated expansion. The limit problem is the Kelvin-Voigt equations with a special boundary condition. This limit problem is solved numerically by a finite element scheme. The difference between the initial and limit problems is studied theoretically and by numerical computations