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An optimal design of an elastic plate in a dynamic contact with a rigid obstacle
Author(s) -
Bock Igor,
Kečkemétyová Mária
Publication year - 2019
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201900183
Subject(s) - variational inequality , obstacle , perpendicular , boundary value problem , variable (mathematics) , mathematics , mathematical analysis , boundary (topology) , obstacle problem , set (abstract data type) , vibration , mathematical optimization , computer science , geometry , physics , quantum mechanics , political science , law , programming language
We deal with an optimal design problem governed by an initial‐boundary value problem for a hyperbolic variational inequality describing the perpendicular vibrations of a simply supported anisotropic elastic plate against a rigid obstacle. A variable thickness of a plate plays the role of a control variable. The set of admissible thicknesses for the design problem consists of solutions of a state problem gained as limits of the sequences of functions solving penalized problems.