Geodesic
The unilateral contact problem for a Timoshenko plate and a thin elastic obstacle
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 364-379.

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The paper deals with the problem of contact between a plate and a beam acting as an obstacle to the plate. The plate is described in the framework of Timoshenko theory of plates. It is assumed that no mutual penetration between the plate and the obstacle can occur, and so an appropriate non-penetration condition is used. We study the existence and uniqueness of a solution for the equilibrium problem as well as passages to the limit with respect to the shear rigidity parameter. The accompanying optimal control problem is investigated in which the rigidity parameter acts as a control parameter, cost functional characterizes the difference between known functions and the displacements obtained by equilibrium problem solving.
Keywords: contact, equilibrium, Timoshenko plate, beam, thin obstacle, non-penetration condition, minimization problem, variational inequality, rigidity parameter, optimal control. 
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     title = {The unilateral contact problem for a {Timoshenko} plate and a thin elastic obstacle},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {364--379},
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}
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A. I. Furtsev. The unilateral contact problem for a Timoshenko plate and a thin elastic obstacle. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 364-379. http://geodesic.mathdoc.fr/item/SEMR_2020_17_a86/

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