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This paper considers the doubly periodic problem of elasticity for anisotropic solids containing regular sets of thin branched inclusions. A coupling principle for continua of different dimension is utilized for modeling of thin inhomogeneities and the boundary element technique is adopted for numerical solution of the problem. The branches of the inclusion can interact both inside the representative volume element and at the interface of neighbor representative elements. A particular example of the elastic medium reinforced by a doubly periodic set of I-beams is considered. Stress intensity and stress concentration inside and outside thin inclusions are determined. The dependence of the effective mechanical properties of the reinforced composite material on the volume fraction of the filament and its rigidity is obtained.
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Rocznik
Tom
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48--52
Opis fizyczny
Bibliogr. 14 poz., wykr.
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autor
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- Bialystok Technical University, Wiejska Str. 45C, 15-351 Bialystok, Poland, h.sulym@pb.edu.pl
Bibliografia
- 1. Antipov Yu.A., Popov G.Ya., Yatsko S.I. (1987), Solution of the problem of stress concentration around intersecting defects by using the riemann problem with an infinite index, Journal of Applied Mathematics and Mechanics, 51(3), 357–365.
- 2. Dolgikh V.N., Fil'shtinskii L.A. (1979), Model of an anisotropic medium reinforced by thin tapes, Soviet Applied Mechanics, 15(4) 292–296.
- 3. Grigoryan E.H., Torosyan D.R., Shaghinyan S.S. (2002), A problem for an elastic plane containing a cross-like inclusion, Mechanics. Proceedings of National Academy of Sciences of Armenia, 55 (1), 6–16.
- 4. Kosmodamianskij A.S. (1976), Naprâžennoe sostoânie anizotropnyh sred s otverstiâmi ili polostâmi, Vyšča škola, Kyiv.
- 5. Osiv O.P, Sulym H.T. (2002), Antyploska deformaciâ seredovyšča zi zlučenymy pružnymy vklûčennâmy, Mehanika i fizyka rujnuvannâ budivelnuh materialiv i konstrukcij, 5, 154–164.
- 6. Osiv O., Sulym G. (2001), Antiplane deformation of isotropic medium with connected elastic ribbon-like inclusions, Abstracts of the Fourth Polish-Ukrainian Conference “Current Problems in Mechanics of Nonhomogeous Media” (Łódż, 4–8 Sept., 2001), Technol. Univ. of Łódż, Łódż.
- 7. Pasternak Ia. (2011), Coupled 2D electric and mechanical fields in piezoelectric solids containing cracks and thin inhomogeneities, Engineering Analysis with Boundary Elements, 35(4), 678–690.
- 8. Pasternak Ia. (2012), Doubly periodic arrays of cracks and thin inhomogeneities in an infinite magnetoelectroelastic medium, Engineering Analysis with Boundary Elements, 36(5), 799–811.
- 9. Pasternak Ia., Sulym H. (2011), Ploska zadača teorij pružnosti anizotropnogo tila z tonkymy gillâstymy pružnymy vklûčennâmy, Visnyk Ternopilskogo NTU, 16(4) 23–31.
- 10. Pasternak Ia., Sulym H. (2013), Stroh formalism based boundary integral equations for 2D magnetoelectroelasticity, Engineering Analysis with Boundary Elements, 37(1), 167–175.
- 11. Popov V.G. (1993), Dynamic problem of the theory of elasticity for a plane containing a rigid cruciform inclusion, Journal of Applied Mathematics and Mechanics, 57(1), 125–131.
- 12. Šackyj I.P, Kundrat A.M. (2004), Antyploska deformaciâ pružnogo prostoru zi zvâzanymy žorstkymy stričkovymy vklûčennâmy, Dopovivdi NAN Ukrajiny, 11, 55–60.
- 13. Sulym H.T. (2007), Osnovy matematyčnoj teorij termopružnoj rivnovagy deformivnyh til z tonkymy vklûčennâmy, Dosl.-vydav. centr NTŠ, L’viv.
- 14. Ting T.C.T. (1996), Anisotropic elasticity: theory and applications, Oxford University Press, New York.
Typ dokumentu
Bibliografia
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bwmeta1.element.baztech-article-BPBF-0003-0014