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JOURNALS // Izvestiya of Saratov University. Mathematics. Mechanics. Informatics

Izv. Saratov Univ. Math. Mech. Inform., 2022, Volume 22, Issue 1, Pages 48–61 (Mi isu921)

Nonlinear deformation of axisymmetrically loaded rotation shell based on FEM with different variants of definitional equations
A. Sh. Dzhabrailov, A. P. Nikolaev, Yu. V. Klochkov, N. A. Gureeva, T. R. Ishchanov

References

1. Amosov A. A., Technical Theory of Thin Elastic Shells, ASV, M., 2011, 304 pp. (in Russian)
2. Petrov V. V., Nonlinear Incremental Building Mechanics, Infa-Inzhenerija, M., 2014, 480 pp. (in Russian)
3. Cohen H., De Silva C. N., “Nonlinear theory of elastic surfaces”, Journal of Mathematical Physics, 7:2 (1966), 246–253  crossref  mathscinet  zmath  adsnasa  scopus
4. Kirillova I. V., Kossovich L. Y., “Elliptic boundary layer in shells of revolution under normal edge shock loading”, Multiscale Solid Mechanics, Advanced Structured Materials, 141, eds. H. Altenbach, V. A. Eremeyev, L. A. Igumnov, Springer, Cham, 2021, 249–260  crossref  scopus
5. Kabrits S. A., Mikhailovsky E. I., Tovstik P. E., Chernykh K. F., Shamina V. A., General Nonlinear Theory of Elastic Shells, Izd-vo S.-Peterburgskogo universiteta, St. Petersburg, 2002, 388 pp.
6. Kayumov R. A., “Postbuckling behavior of compressed rods in an elastic medium”, Mechanics of Solids, 52:5 (2017), 575–580  crossref  adsnasa  scopus
7. Badriev I. B., Paimushin V. N., “Refined models of contact interaction of a thin plate with postioned on both sides deformable foundations”, Lobachevskii Jurnal of Mathematics, 38:5 (2017), 779–793  crossref  mathscinet  zmath  scopus
8. Beirao da Veiga L., Lovadina C., Mora D., “A virtual element method for elastic and inelastic problems on polytope meshes”, Computer Methods in Applied Mechanics and Engineering, 295 (2015), 327–346  crossref  mathscinet  zmath  adsnasa  scopus
9. Aldakheel F., Hudobivnik B., Wriggers P., “Virtual element formulation for phase-field modeling of ductile fracture”, International Journal for Multiscale Computational Engineering, 17:2 (2019), 181–200  crossref  mathscinet  scopus
10. Magisano D., Leonetti L., Garcea G., “Koiter asymptotic analysis of multilayered composite structures using mixed solid-shell finite elements”, Composite Structures, 154 (2016), 296–308  crossref  scopus
11. Lomakin E. V., Minaev N. G., “Axisymmetric stress field near a circular cut in a solid with stress state dependent plastic properties”, Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 19:3 (2019), 317–325 (in Russian)  crossref  mathscinet  scopus
12. Karpov V. V., Ignatev O. V., Semenov A. A., “The stress-strain state of ribbed shell structures”, Magazine of Civil Engineering, 2017, no. 6(74), 147–160  crossref  scopus
13. Dzhabrailov A. Sh., Klochkov Yu. V., Marchenko S. S., Nikolaev A. P., “The finite element approximation of vector fields in curvilinear coordinates”, Russian Aeronautics, 50:2 (2007), 115–120  crossref  elib  scopus
14. Sedov L. I., Continuum Mechanics, in 2 vols., v. 1, Nauka, M., 1976, 492 pp. (in Russian)  mathscinet
15. Malinin N. N., Applied Theory of Plasticity and Creep, Mashinostroenie, M., 1975, 400 pp. (in Russian)
16. Ilyushin A. A., Plastic. Elastic-plastic Deformation, Lenand, St. Petersburg, 2018, 352 pp. (in Russian)
17. Klochkov Yu. V., Nikolaev A. P., Dzhabrailov A. Sh., “A finite element analysis of axisymmetric loaded shells of revolution with a branching meridian under elastic-plastic deforming”, Structural Mechanics of Engineering Constructions and Buildings, 2013, no. 3, 50–56 (in Russian)


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