Exact controllability and asymptotic limit for thin plates. (English) Zbl 0854.73029

Figueiredo, Isabel; Zuazua, Enrique

Asymptotic Anal. 12, No. 3, 213-252 (1996).

Summary: We consider the exact controllability problem for a three-dimensional linear elastic thin plate, with thickness \(2\varepsilon\) and a polygonal middle surface. Controls are imposed on the lateral surface and at the top and bottom of the plate. The asymptotic limit when \(\varepsilon\to 0\) is computed. We obtain that the displacements converge to a controlled Kirchhoff-Love displacement, where the normal displacement satisfies the usual two-dimensional evolution equation for a linear plate, with controls on the boundary and in the interior of the plate.

MSC:

74K20	Plates
74M05	Control, switches and devices (“smart materials”) in solid mechanics
35Q72	Other PDE from mechanics (MSC2000)
93C20	Control/observation systems governed by partial differential equations

Keywords:

controls on boundary; controlled Kirchhoff-Love displacement; two-dimensional evolution equation