This article is cited in 7 scientific papers (total in 7 papers)
An equilibrium problem for the Timoshenko-type plate containing a crack on the boundary of a rigid inclusion
Nyurgun P. Lazarevab
a Institute of Hydrodynamics, SB RAS, Novosibirsk, Russia
b North-Eastern Federal University, Yakutsk, Russia
An equilibrium problem for an elastic Timoshenko type plate containing a rigid inclusion is considered. On the interface between the elastic plate and the rigid inclusion, there is a vertical crack. It is assumed that at both crack faces, boundary conditions of inequality type are considered describing a mutual non-penetration of the faces. A solvability of the problem is proved, and a complete system of boundary conditions is found. It is also shown that the problem is the limit one for a family of other problems posed for a wider domain and describing an equilibrium of elastic plates with a vertical crack as the rigidity parameter goes to infinity.
crack, Timoshenko-type plate, rigid inclusion, energy functional, mutual non-penetration condition.
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Received in revised form: 10.06.2012
Nyurgun P. Lazarev, “An equilibrium problem for the Timoshenko-type plate containing a crack on the boundary of a rigid inclusion”, J. Sib. Fed. Univ. Math. Phys., 6:1 (2013), 53–62
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\paper An equilibrium problem for the Timoshenko-type plate containing a~crack on the boundary of a~rigid inclusion
\jour J. Sib. Fed. Univ. Math. Phys.
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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
N. V. Neustroeva, “An equilibrium problem for an elastic plate with an inclined crack on the boundary of a rigid inclusion”, J. Appl. Industr. Math., 9:3 (2015), 402–411
N. P. Lazarev, “Optimal control of the size of rigid inclusion in equilibrium problem for inhomogeneous Timoshenko-type plate with crack”, J. Math. Sci., 228:4 (2018), 409–420
V. A. Puris, “The conjugation problem for thin elastic and rigid inclusions in an elastic body”, J. Appl. Industr. Math., 11:3 (2017), 444–452
N. Lazarev, N. Neustroeva, “Optimal control of rigidity parameter of elastic inclusions in composite plate with a crack”, Mathematics and Computing (ICMC 2018), Springer Proceedings in Mathematics & Statistics, 253, eds. D. Ghosh, D. Giri, R. Mohapatra, K. Sakurai, E. Savas, T. Som, Springer, 2018, 67–77
N. A. Nikolaeva, “O ravnovesii uprugikh tel s treschinami, peresekayuschimi tonkie vklyucheniya”, Sib. zhurn. industr. matem., 22:4 (2019), 68–80
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