This article is cited in 11 papers

Choosing an optimal shape of thin rigid inclusions in elastic bodies

V. V. Shcherbakov<sup>ab

a</sup> Lavrent’ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
^b Novosibirsk State University, Novosibirsk, 630090, Russia

Abstract: The optimal control problem for a three-dimensional elastic body containing a thin rigid inclusion as a surface is studied. It is assumed that the inclusion delaminates, which is why there is a crack between the elastic domain and the inclusion. The boundary conditions on the crack faces that exclude mutual penetration of the points of the body and inclusion are considered. The cost functional that characterizes the deviation of the surface force vector from the function prescribed on the external boundary is used; in this case, the inclusion shape is considered as a control function. It is proven that a solution of the described problem exists.

Keywords: thin rigid inclusion, crack, nonlinear boundary conditions, variational inequality, optimal control.

UDC: 539.3+517.977

Received: 15.03.2013
Revised: 27.02.2014

DOI: 10.15372/PMTF20150218

 English version: Journal of Applied Mechanics and Technical Physics, 2015, 56:2, 321–329

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