Asymptotic modeling of the elastodynamics of a multi-structure
A. Raoult · Asymptotic Analysis · 1992
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 (Lame 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.