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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2017, Volume 20, Number 1, Pages 47–58
DOI: https://doi.org/10.15372/SJNM20170105 (Mi sjvm635) 		 
This article is cited in 10 scientific papers (total in 10 papers)

A modified dual scheme for solving an elastic crack problem

R. V. Namm, G. I. Tsoy

Computer Centre of Far Eastern Branch RAS, Kim Yu Chena str., 65, Habarovsk, 680063, Russia
Full-text PDF (1486 kB) Citations (10)
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DOI: https://doi.org/10.15372/SJNM20170105
Abstract: The dual scheme for solving a crack problem in terms of displacements is considered. The dual solution method is based on a modified Lagrangian functional. In addition, the method convergence is investigated under natural assumptions on $H^1$-regularity of the crack problem solution. The duality relation for the primal and dual problems has been proposed.
Key words: elastic crack problem, duality scheme, modified Lagrangian functional, sensitivity functional, duality relation, weak lower semicontinuity.
Funding agency Grant number
Russian Academy of Sciences - Federal Agency for Scientific Organizations 15-I-4-075
Received: 31.05.2016
Revised: 07.07.2016
English version:
Numerical Analysis and Applications, 2017, Volume 10, Issue 1, Pages 37–46
DOI: https://doi.org/10.1134/S1995423917010050
Bibliographic databases:
Document Type: Article
UDC: 519.853.2+519.632
Language: Russian
Citation: R. V. Namm, G. I. Tsoy, “A modified dual scheme for solving an elastic crack problem”, Sib. Zh. Vychisl. Mat., 20:1 (2017), 47–58; Num. Anal. Appl., 10:1 (2017), 37–46
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    • This publication is cited in the following 10 articles:
    1. A. V. Zhiltsov, N. N. Maksimova, “Dvoistvennyi metod dlya resheniya zadachi o ravnovesii tela, soderzhaschego tonkii defekt”, Sib. zhurn. vychisl. matem., 26:2 (2023), 183–198  mathnet  crossref
    2. R.V. Namm, G.I. Tsoy, “Solution of the static contact problem with Coulomb friction between an elastic body and a rigid foundation”, Journal of Computational and Applied Mathematics, 419 (2023), 114725  crossref
    3. R. V. Namm, G. I. Tsoi, “Duality method for solving 3D contact problems with friction”, Comput. Math. Math. Phys., 63:7 (2023), 1350–1361  mathnet  mathnet  crossref  crossref
    4. A. V. Zhiltsov, N. N. Maksimova, “A Dual Method for Solving an Equilibrium Problem of a Body Containing a Thin Defect”, Numer. Analys. Appl., 16:2 (2023), 154  crossref
    5. R. V. Namm, G. I. Tsoy, “Modified duality methods for solving an elastic crack problem with Coulomb friction on the crack faces”, Open Comput. Sci., 10:1 (2020), 276–282  crossref  mathscinet  isi  scopus
    6. Robert Namm, Georgiy Tsoy, Communications in Computer and Information Science, 1340, Advances in Optimization and Applications, 2020, 224  crossref
    7. R. V. Namm, G. I. Tsoy, G. Woo, “Modified Lagrange functional for solving elastic problem with a crack in continuum mechanics”, Commun. Korean Math. Soc., 34:4 (2019), 1353–1364  crossref  mathscinet  zmath  isi  scopus
    8. R. V. Namm, G. I. Tsoi, “Solution of a contact elasticity problem with a rigid inclusion”, Comput. Math. Math. Phys., 59:4 (2019), 659–666  mathnet  crossref  crossref  isi  elib
    9. Robert Namm, Georgiy Tsoy, Communications in Computer and Information Science, 1090, Mathematical Optimization Theory and Operations Research, 2019, 536  crossref
    10. Robert Namm, Georgiy Tsoy, Ellina Vikhtenko, Communications in Computer and Information Science, 974, Optimization and Applications, 2019, 35  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Sibirskii Zhurnal Vychislitel'noi Matematiki
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