Abstract:
The equilibrium problem for two elastic bodies pasted together along some curve is considered. There exists a crack on a part of the curve. Nonlinear boundary conditions providing a mutual non-penetration between crack faces are set. The main objective of the paper is to construct and to approve an algorithm for the numerical solution of the equilibrium problem. The algorithm is based on the two approaches: the domain decomposition method and the Uzawa method. The numerical experiment illustrates the efficiency of the algorithm.
Citation:
E. M. Rudoy, N. A. Kazarinov, V. Yu. Slesarenko, “Numerical simulation of the equilibrium of an elastic two-layer structure with a crack”, Sib. Zh. Vychisl. Mat., 20:1 (2017), 77–90; Num. Anal. Appl., 10:1 (2017), 63–73
This publication is cited in the following 11 articles:
E. V. Pyatkina, “Ravnovesie trekhsloinoi plastiny s treschinoi”, Sib. zhurn. industr. matem., 25:1 (2022), 105–120
E. V. Pyatkina, “Equilibrium of a Three-Layer Plate with a Crack”, J. Appl. Ind. Math., 16:1 (2022), 122
I. V. Fankina, “O ravnovesii dvusloinoi konstruktsii s verkhnim sloem, nakryvayuschim vershinu defekta”, Sib. elektron. matem. izv., 17 (2020), 141–160
E. V. Pyatkina, “a Contact of Two Elastic Plates Connected Along a Thin Rigid Inclusion”, Sib. Electron. Math. Rep., 17 (2020), 1797–1815
A. Furtsev, H. Itou, E. Rudoy, “Modeling of bonded elastic structures by a variational method: theoretical analysis and numerical simulation”, Int. J. Solids Struct., 182 (2020), 100–111
I. V. Frankina, “On the equilibrium of a two-layer elastic structure with a crack”, J. Appl. Industr. Math., 13:4 (2019), 629–641
E. V. Pyatkina, “A Problem of Glueing of Two Kirchhoff - Love Plates”, Sib. Electron. Math. Rep., 16 (2019), 1351–1374
I. V. Frankina, “The Equilibrium of a Two Layer Structure in the Presence of a Defect”, Sib. Electron. Math. Rep., 16 (2019), 959–974
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”, Comput. Math. Math. Phys., 58:5 (2018), 761–774
E. M. Rudoy, N. P. Lazarev, “Domain decomposition technique for a model of an elastic body reinforced by a Timoshenko's beam”, J. Comput. Appl. Math., 334 (2018), 18–26
E. V. Pyatkina, “A contact problem for two plates of the same shape glued along one edge of a crack”, J. Appl. Industr. Math., 12:2 (2018), 334–346
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