Abstract
We consider a thin shell whose elastic deformations are described by the system of Koiter linear partial differential equations. The shell is controlled by functions acting along its boundary. We show, using the HUM method (Hilbert Uniqueness Method) of J.L. Lions, that when the middle surface of the shell satisfies specific geometrical assumptions, it is possible to obtain exact controllability which consists in driving the system to rest in finite time. In particular we identify the function spaces where the initial Cauchy data (initial displacement and velocity fields) have to be taken and the function space where the control can be chosen in order to get the exact controllability.
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Miara, B., Valente, V. Exact Controllability of a Koiter Shell by a Boundary Action. Journal of Elasticity 52, 267–287 (1998). https://doi.org/10.1023/A:1007540610612
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DOI: https://doi.org/10.1023/A:1007540610612