This article is cited in 1 paper

Energy functional derivative of the length of a curvilinear oblique cut in the problem of equilibrium of a Timoshenko plate

N. P. Lazarev<sup>ab

a</sup> Lavrentyev Institute of Hydrodynamics, Russian Academy of Sciences, Novosibirsk, 630090, Russia
^b Scientific Research Institute of Mathematics of the North-Eastern Federal University, Yakutsk, 677000, Russia

Abstract: This paper describes the dependence of the solution of the problem of equilibrium of a Timoshenko plate and the total energy functional of the plate on the surface perturbation, which is an oblique crack. The nonlinearity of the problem is caused by the boundary conditions in the form of inequalities (conditions such as the Signorini conditions), which simulate mutual nonpenetration of the opposite crack faces. The continuous dependence of the solution of the problem on the perturbation of the crack length is established. A formula for the energy functional derivative of the perturbation of the crack length is obtained.

Keywords: oblique crack, variational inequality, Timoshenko plate, nonpenetration condition, energy functional derivative.

UDC: 539.375

Received: 30.06.2014
Revised: 28.10.2015

DOI: 10.15372/PMTF20150614

 English version: Journal of Applied Mechanics and Technical Physics, 2015, 56:6, 1038–1048

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