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Sibirskii Zhurnal Industrial'noi Matematiki, 2011, Volume 14, Number 4, Pages 32–43
(Mi sjim695)
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This article is cited in 9 scientific papers (total in 9 papers)
An equilibrium problem for a Timoshenko plate with a through crack
N. P. Lazarevab a Mathematics Research Institute, Northeastern Federal University, Yakutsk, RUSSIA
b Lavrent'ev Institute of Hydrodynamics, Siberian Division of the RAS, Novosibirsk, RUSSIA
Abstract:
We study the equilibrium problem for an elastic plate (Timoshenko model) with a vertical crack. On the curve defining the through crack we impose a boundary condition as an inequality describing the nonpenetration of the opposite crack edges. We prove the unique solvability of the variational statement of the problem. From the variational statement we deduce a complete system of boundary conditions, which we use to obtain an equivalent differential statement. We establish additional smoothness of the solution in comparison with that given in the variational statement. We prove that the solution functions are infinitely smooth under additional assumptions on the function of external loads and the functions of displacements near the curve describing the through crack.
Received: 12.07.2010
Citation:
N. P. Lazarev, “An equilibrium problem for a Timoshenko plate with a through crack”, Sib. Zh. Ind. Mat., 14:4 (2011), 32–43
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https://www.mathnet.ru/eng/sjim695 https://www.mathnet.ru/eng/sjim/v14/i4/p32
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Abstract page: | 513 | Full-text PDF : | 184 | References: | 90 | First page: | 10 |
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