This article is cited in 9 papers

The Griffith formula for a Timoshenko-type plate with a curvilinear track

N. P. Lazarev<sup>ab

a</sup> Institute for Mathematics of NEFU, 58 Belinskii st., 677000 Yakutsk, Republic of Sakha, Russia
^b Lavrent'ev Institute of Hydrodynamics SB RAS, 15 Lavrent'ev av., 630090 Novosibirsk, Russia

Abstract: We consider an equilibrium problem for an elastic transversely isotropic Timoshenko-type plate with a curvilinear crack. Nonpenetration conditions on the faces of the crack having the form of inequalities (conditions of the Signorini type) are given. It is proved that the solutions to the equilibrium problems with a perturbed crack converge to the solution to the equilibrium problem with the unperturbed crack in the corresponding space. The derivative of the energy functional with respect to the crack length is obtained.

Keywords: Timoshenko-type plate, crack, nonpenetration condition, Griffith criterion, variational inequality, derivative of the energy functional, nonsmooth domain.

UDC: 539.375

Received: 19.01.2012

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