Numerical solution of an equilibrium problem for an elastic body with a thin delaminated rigid inclusion

被引：0
作者：
Rudoy E.M. [1 ,2 ]
机构：
[1] Lavrent’ev Institute of Hydrodynamics, pr. Akad. Lavrent’eva 15, Novosibirsk
[2] Novosibirsk State University, ul. Pirogova 2, Novosibirsk
来源：
Journal of Applied and Industrial Mathematics | 2016年 / 10卷 / 2期
关键词：
delamination crack; domain decomposition method; nonpenetration condition; thin rigid inclusion; Uzawa algorithm; variational inequality;
D O I：
10.1134/S1990478916020113
中图分类号：
学科分类号：
摘要：
Under consideration is a 2D-problem of elasticity theory for a body with a thin rigid inclusion. It is assumed that there is a delamination crack between the rigid inclusion and the elastic matrix. At the crack faces, the boundary conditions are set in the form of inequalities providing mutual nonpenetration of the crack faces. Some numerical method is proposed for solving the problem, based on domain decomposition and the Uzawa algorithm for solving variational inequalities.We give an example of numerical calculation by the finite element method. © 2016, Pleiades Publishing, Ltd.
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页码：264 / 276
页数：12
相关论文
共 33 条
  • [1] Cherepanov G.P., Mechanics of Brittle Fractur, (1979)
  • [2] Morozov N.F., Mathematical Problems of Crack Theor, (1984)
  • [3] Khludnev A.M., Elasticity Problems in Nonsmooth Domain, (2010)
  • [4] Khludnev A.M., Kovtunenko V.A., Analysis of Cracks in Solid, (2000)
  • [5] Rudoy E.M., Domain DecompositionMethod for aModel Crack Problem with a Possible Contact of Crack Edges, Zh. Vychisl. Mat. Mat. Fiz, 55, 2, pp. 310-321, (2015)
  • [6] Rudoy E., Domain Decomposition Method for Crack Problems with Nonpenetration Condition, ESAIM: M2A, (2015)
  • [7] Kovtunenko V.A., Numerical Simulation of the Nonlinear Crack Problem with Nonpenetration, Math. Meth. Appl. Sci, 27, 2, pp. 163-179, (2004)
  • [8] Hintermuller M., Kovtunenko V., Kunisch K., The Primal-Dual Active SetMethod for a Crack Problem with Nonpenetration, IMA J. Appl. Math, 69, 1, pp. 1-26, (2004)
  • [9] Vtorushin E.V., Numerical Investigation of a Model Problem for the Poisson Equation with Inequality Constraints in a Domain with a Cut, Sibirsk. Zh. Industr. Mat, 8, 1, pp. 41-49, (2005)
  • [10] Aleksandrov V.M., Smetanin B.I., Sobol' N.G., Thin Stress Concentrators in Elastic Solid, (1993)
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