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Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2013, Volume 54, Issue 4, Pages 171–181
(Mi pmtf1168)
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This article is cited in 3 scientific papers (total in 3 papers)
Equilibrium problem for a Timoshenko plate with an oblique crack
N. P. Lazarev Institute of Mathematics, Ammosov Northeast Federal University, Yakutsk, 677000, Russia
Abstract:
The condition of mutual nonpenetration of the crack faces is proposed for a Timoshenko plate with an oblique crack, whose initial state is defined by a surface the normal to which makes a small angle with the middle plane. Unique solvability of the variational problem of plate equilibrium with the nonpenetration conditions for the crack faces specified on the curve describing the crack is proved. A differential formulation of the problem equivalent to the original formulation for sufficiently smooth solutions is proposed. For the one-dimensional case (beam with a cut), an analytical solution is obtained, and the cases of longitudinal tension and compression are examined.
Keywords:
plate, crack, cut, nonpenetration condition, variational problem.
Received: 08.02.2013
Citation:
N. P. Lazarev, “Equilibrium problem for a Timoshenko plate with an oblique crack”, Prikl. Mekh. Tekh. Fiz., 54:4 (2013), 171–181; J. Appl. Mech. Tech. Phys., 54:4 (2013), 662–671
Linking options:
https://www.mathnet.ru/eng/pmtf1168 https://www.mathnet.ru/eng/pmtf/v54/i4/p171
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