A singular element of the graph model of an elastic medium in a cartesian coordinate system
DOI:
https://doi.org/10.7242/1999-6691/2011.4.4.47Keywords:
mathematical simulation, elasticity, directed graph, strain, stress intensity factorAbstract
A numerical method for analyzing mechanical fields in a deformable body is presented. The graph model of an elastic medium in the form of a directed graph is employed in the proposed method. To describe a singularity that appears near a crack tip of an isotropic elastic material, a new type of a unit cell is introduced.
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Morozov N.F. Matematiceskie voprosy teorii tresin. - M.: Nauka, 1984. - 256 s.
Rajs Dz. R. Matematiceskie metody v mehanike razrusenia // Razrusenie. / Pod red. G. Libovica. - M.: Mir. - T. 2. Matematiceskie osnovy teorii razrusenia. - 1975. - S. 205-335.
Vycislitel’nye metody v mehanike razrusenia. / Pod red. S. Atluri. - M.: Mir, 1990. - 392 s.
Mehanika razrusenia i procnost’ materialov: Sprav. posobie: V 4 t. / Pod obsej red. V.V. Panasuka. - Kiev: Naukova dumka. - T. 1. Osnovy mehaniki razrusenia. - 1988. - 488 s.
Semakin E.I. Naprazenno-deformirovannoe sostoanie v versine razreza pri antiploskoj deformacii uprugoplasticeskogo tela // PMTF. - 1974. - No 2. - S. 110-116.
Asbauh. Naprazenia v sloistyh kompozitah, soderzasih razorvannyj sloj // Tr. amer. ob-va inz.-meh. Seria E. - 1973. - T. 40, No 2. - S. 221-228.
Lusik O.N. Singularnye konecnye elementy: obzor i klassifikacia // Izv. RAN. MTT. - 2000. - No 2. - S. 103-114.
Borzenkov S.M., Matveenko V.P. Poluanaliticeskie singularnye elementy dla ploskih i prostranstvennyh zadac teorii uprugosti // Izv. RAN. MTT. - 1995. - No 6. - S. 48-61.
Kuzovkov E.G. Axisymmetric graph model of an elastic solid // Strength of Materials. - 1996. - V. 28, N. 6. - P. 470-485. DOI
Kuzovkov E.G. Grafovaa model’ uprugoj sredy v dekartovoj sisteme koordinat // Probl. procnosti. - 1993. - No 12. - S. 60-70.
Tyrymov A.A. Grafovaa model’ uprugoj sredy v polarnoj sisteme koordinat // Izv vuzov. Masinostroenie. - 1999. - No 1. - S. 3-15.
Trent H. Isomorphism between oriented linear graphs and lumped physical systems // JASA. - 1955. - V. 27, N. 3. - R. 500-527.
Evstigneev V.A., Kas’anov V.N. Tolkovyj slovar’ po teorii grafov v informatike i programmirovanii. - Novosibirsk: Nauka, 1999. - 291 s.; http://pco.iis.nsk.su/grapp (data obrasenia: 01.12.2011)
Krylov V.I. Priblizennoe vycislenie integralov. - M.: Nauka, 1967. - 500 s.
Svami M., Thulasiraman K. Grafy, seti i algoritmy. - M.: Mir, 1984. - 454 s.
Isida M. Effect of width and length on stress intensity factors of internally cracked plates under various boundary conditions // Int. J. Fract. Mech. - 1971. - V. 7, N. 3. - P. 301-316.
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