Mathematics

Equilibrium problems for elastic plate with thin rigid inclusion and free edge

A. M. Khludnev<sup>ab

a</sup> Lavrentiev Institute of Hydrodynamics, 15 Lavrentiev Avenue, Novosibirsk 630090, Russia
^b Novosibirsk State University, 1 Pirogov Street, Novosibirsk, 630090, Russia

Abstract: The paper investigates equilibrium problems for an elastic plate containing a thin rigid inclusion in the case of free edge. The inclusion may be delaminated from the elastic plate thus forming an interfacial crack. The considered boundary conditions lead to non-coercive boundary value problems. The cases of possible fixing of the plate at one or two given points are analyzed. Necessary and sufficient conditions for the existence of solutions to the problems under consideration are found.

Keywords: elastic plate, thin rigid inclusion, delamination, non-coercive boundary value problem.

UDC: 539.3+517.958

Received: 28.01.2021
Revised: 28.02.2021
Accepted: 26.08.2021

DOI: 10.25587/SVFU.2021.64.10.007

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