Asymptotic modeling of the elastodynamics of a multi-structure. (English) Zbl 0777.73033

Raoult, Annie

Asymptotic Anal. 6, No. 1, 73-108 (1992).

Summary: We consider a structure consisting of two parts: a three-dimensional linearly elastic body and a linearly elastic plate. The plate is inserted into the three-dimensional body. We perform an asymptotic analysis of the time-dependent behavior of the structure during the time-interval \([0,T]\) when the thickness of the plate goes to zero. Under specific assumptions on the data (Lamé constants, mass densities, loads), we establish the existence of a limit problem. This limit problem is a system of coupled partial differential equations posed over a three-dimensional body with a slit and the middle surface of the plate. Strong convergence in \(L^ 2(0,T;H^ 1)\) of the time-dependent displacements (with appropriate scaling) is proved.

MSC:

74H45	Vibrations in dynamical problems in solid mechanics
74K20	Plates
74B05	Classical linear elasticity

Keywords:

linearly elastic body; linearly elastic plate; existence; limit problem; convergence