This article is cited in 5 papers

Differentiation of the energy functional in the equilibrium problem for a Timoshenko plate containing a crack

N. P. Lazarev<sup>ab

a</sup> Research Institute of Mathematics, Ammosov North-East Federal University, Yakutsk, 677000, Russia
^b Lavrentyev Institute of Hydrodynamics of Siberian Branch of the Russian Academy of Sciences, Novosibirsk

Abstract: The variational formulation of the equilibrium problem for a Timoshenko plate containing a vertical plane crack is considered. Nonpenetration conditions in the form of inequalities (Signorini type conditions) are specified on the crack faces. The behavior of the solution and the corresponding energy functional of the plate with variation in the crack length is analyzed. A formula for the derivative of the energy functional along the crack length is obtained. The solutions are found to continuously depend on the parameter characterizing the crack length.

Keywords: crack, variational inequality, Timoshenko plate, energy functional, derivative of the energy functional.

UDC: 539.375

Received: 02.02.2011
Accepted: 01.07.2011

 English version: Journal of Applied Mechanics and Technical Physics, 2012, 53:2, 299–307

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