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This article is cited in 30 scientific papers (total in 30 papers)
Mathematical and numerical simulation of equilibrium of an elastic body reinforced by a thin elastic inclusion
N. A. Kazarinova, E. M. Rudoyab, V. Yu. Slesarenkoa, V. V. Shcherbakovab a Lavrentyev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia
Abstract:
A boundary value problem describing the equilibrium of a two-dimensional linear elastic body with a thin rectilinear elastic inclusion and possible delamination is considered. The stress and strain state of the inclusion is described using the equations of the Euler-Bernoulli beam theory. Delamination means the existence of a crack between the inclusion and the elastic matrix. Nonlinear boundary conditions preventing crack face interpenetration are imposed on the crack faces. As a result, problem with an unknown contact domain is obtained. The problem is solved numerically by applying an iterative algorithm based on the domain decomposition method and an Uzawa-type algorithm for solving variational inequalities. Numerical results illustrating the efficiency of the proposed algorithm are presented.
Key words:
thin elastic inclusion, delamination crack, nonpenetration condition, variational inequality, domain decomposition method, Uzawa algorithm.
Received: 31.03.2017
Citation:
N. A. Kazarinov, E. M. Rudoy, V. Yu. Slesarenko, V. V. Shcherbakov, “Mathematical and numerical simulation of equilibrium of an elastic body reinforced by a thin elastic inclusion”, Zh. Vychisl. Mat. Mat. Fiz., 58:5 (2018), 790–805; Comput. Math. Math. Phys., 58:5 (2018), 761–774
Linking options:
https://www.mathnet.ru/eng/zvmmf10737 https://www.mathnet.ru/eng/zvmmf/v58/i5/p790
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