N. P. Lazarev, “The Griffith formula for a Timoshenko-type plate with a curvilinear track”, Sib. Zh. Ind. Mat., 16:2 (2013), 98

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Sibirskii Zhurnal Industrial'noi Matematiki, 2013, Volume 16, Number 2, Pages 98–108 (Mi sjim783)

This article is cited in 9 scientific papers (total in 9 papers)

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

N. P. Lazarev^ab

^a 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

Full-text PDF (270 kB) Citations (9)

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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.

Received: 19.01.2012

Bibliographic databases:

Document Type: Article

UDC: 539.375

Language: Russian

Citation: N. P. Lazarev, “The Griffith formula for a Timoshenko-type plate with a curvilinear track”, Sib. Zh. Ind. Mat., 16:2 (2013), 98–108

Citation in format AMSBIB

\Bibitem{Laz13}

\by N.~P.~Lazarev

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

\jour Sib. Zh. Ind. Mat.

\yr 2013

\vol 16

\issue 2

\pages 98--108

\mathnet{http://mi.mathnet.ru/sjim783}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3203345}

Linking options:

https://www.mathnet.ru/eng/sjim783

https://www.mathnet.ru/eng/sjim/v16/i2/p98

This publication is cited in the following 9 articles:

I. V. Fankina, “O ravnovesii dvusloinoi konstruktsii s verkhnim sloem, nakryvayuschim vershinu defekta”, Sib. elektron. matem. izv., 17 (2020), 141–160
N. V. Neustroeva, N. P. Lazarev, “The derivative of the energy functional in an equilibrium problem for a Timoshenko plate with a crack on the boundary of an elastic inclusion”, J. Appl. Industr. Math., 11:2 (2017), 252–262
I. V. Frankina, “Optimal control of the rigid layer size of the construction”, J. Math. Sci., 237:4 (2019), 521–529
V. V. Scherbakov, O. I. Krivorotko, “Optimalnye formy treschin v vyazkouprugom tele”, Tr. IMM UrO RAN, 21, no. 1, 2015, 294–304
N. P. Lazarev, N. V. Neustroeva, N. A. Nikolaeva, “Optimalnoe upravlenie uglom naklona treschiny v zadache o ravnovesii plastiny Timoshenko”, Sib. elektron. matem. izv., 12 (2015), 300–308
A. M. Khludnev, “Optimalnoe upravlenie vklyucheniyami v uprugom tele, peresekayuschimi vneshnyuyu granitsu”, Sib. zhurn. industr. matem., 18:4 (2015), 75–87
Lazarev N.P., “Energy Functional Derivative With Respect To the Length of a Curvilinear Oblique Cut in the Equilibrium Problem For a Timoshenko Plate”, J. Appl. Mech. Tech. Phys., 56:6 (2015), 1038–1048
Khludnev A.M., “Optimal Control of a Thin Rigid Inclusion Intersecting the Boundary of An Elastic Body”, Pmm-J. Appl. Math. Mech., 79:5 (2015), 493–499
V. V. Shcherbakov, “Existence of an optimal shape for thin rigid inclusions in the Kirchhoff–Love plate”, J. Appl. Industr. Math., 8:1 (2014), 97–105

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Сибирский журнал индустриальной математики

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