This article is cited in 9 papers

Differentical equations, dynamical systems and optimal control

The unilateral contact problem for a Timoshenko plate and a thin elastic obstacle

A. I. Furtsev

Lavrentyev Institute of Hydrodynamics, 15, Lavrent'ev ave., Novosibirsk, 630090, Russia

Abstract: 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.

UDC: 539.3,517.958

MSC: 35Q74, 74G65, 74M15

Received December 18, 2019, published March 10, 2020

DOI: 10.33048/semi.2020.17.023

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