The article regards the construction of a finite element for calculating the middle thickness of shells on the basis of a modification of three-dimensional isoparametric 8-node element through introduction of a hypothesis of infinitesimality of compression stress and usage of the technique of approximation order reduction. The method of double approximations on superconvergence points has been applied. Effectiveness of the given approach is shown on numerical examples.
оболочечный конечный элемент, упругие деформации, метод двойной аппроксимации, гипотеза малости напряжений обжатия, shell finite element, elastic strains, method of double approximation, hypothesis of infinitesimality of compression stress
1. Golovanov A.I. Sovremennye konechno-elementnye modeli i metody issledovanii tonkostennyh konstrukcii / A.I. Golovanov, A.V. Pesoshin, O.N. Tyuleneva. - Kazan': Kazan. gos. un-t, 2005. - 442 s.
2. Yang H.T.Y. A survey of recent shell finite elements / H.T.Y. Yang, S. Saigal, A. Masud, R.K. Kapania // Int. J. for numerical methods in engineering. - 2000. - V. 47. - P. 101-127.
3. Saharov A.S. Metod konechnyh elementov v mehanike tverdyh tel / A.S. Saharov, V.N. Kislookiy, V.V. Kirichevskiy, I. Al'tenbah, U. Gabbert, Yu. Dankert, X. Keppler, 3. Kochyk - Kiev: Vischa shk., 1982. - 480 s.
4. Berezhnoy D.V. Iskrivlennyy konechnyy element plastin i obolochek sredney tolschiny s uchetom obzhatiya / D.V. Berezhnoy // Trudy XVII mezhdunar. konf. no teorii obolochek i plastin. - Kazan': Kazan. gos. un-t, 1996. - T. 2. - S. 94-99.
5. Bazhenov V.A. Momentnaya shema metoda konechnyh elementov v zadachah nelineynoy mehaniki sploshnoy sredy /
6. Sze K.Y. Three-dimensional continuum finite element models for plate/shell analysis / K.Y. Sze // Prog. Struct. Engng Mater. - 2002. - V. 4. - P. 400-407.
7. Timoshenko S.P. Plastinki i obolochki / S.P. Timoshenko, S. Voynovskiy-Kriger - M.:Nauka, 1966. - 636 s.
8. Golovanov A.I. «Trehmernyy konechnyy element dlya rascheta tonkostennyh konstrukciy» / A.I. Golovanov, M.K. Sagdatullin // Uchenye zapiski Kazanskogo gosudarstvennogo universiteta. Seriya fiz. - mat. nauk. - Kazan' 2009. - T. 151, kn. 3, s. 121-129.
9. Perelygin O.A.Issledovanie prochnosti cilindricheskih obolochek s vmyatinami v oblasti radial'nyh soedineniy / O.A. Perelygin, Sh.Sh. Galyaviev, R.H. Zaynullin, D.V. Berezhnoy // Vestnik KGTU, Kazan', izd-vo KGTU, 2001, №1-2, S.75-77.
10. Perelygin O.A.Issledovanie prochnosti cilindricheskih obolochek pri nalichii uvoda ili smescheniya kromok svarnyh shvov / O.A. Perelygin, N.M. Tuykin, D.V. Berezhnoy, M.N. Serazutdinov // Vestnik KGTU, Kazan', izd-vo KGTU, 2001, №1-2, S.77-79.
11. Berezhnoy D.V. Mnogosloynyy ortotropnyy konechnyy element obolochek sredney tolschiny. / D.V. Berezhnoy, M.K. Sagdatullin, A.I. Golovanov // Vestnik Saratovskogo gosudarstvennogo tehnicheskogo universiteta. - 2011. -№3 (57). Vypusk 1. - S. 9-19.
12. Golovanov A.I. Metod konechnyh elementov v mehanike deformiruemyh tverdyh tel / A.I. Golovanov, D.V. Berezhnoy - Kazan': Izdatel'stvo «DAS», 2001. - 301s.
13. Berezhnoy D.V. Raschet kombinirovannyh konstrukciy metodom konechnyh elementov / D.V. Berezhnoy, M.K. Sagdatullin, A.A. Sachenkov // Nauchno-tehnicheskiy vestnik Povolzh'ya. - Kazan': Nauchno-tehnicheskiy vestnik Povolzh'ya, 2012. - № 4.- S.13-16.
14. Berezhnoy D.V. Universal'nyy konechnyy element dlya rascheta kombinirovannyh konstrukciy / D.V. Berezhnoy, M.K. Sagdatullin, A.A. Sachenkov // Vestnik Kazanskogo gosudarstvennogo tehnologicheskogo universiteta. - 2012. - №17. - S.150-157.
15. Sagdatullin M.K. Staticheskiy raschet prostyh i kombinirovannyh obolochechnyh konstrukciy MKE: dis. kand. fiz.-mat. nauk. Kazan. fed. un-t, Kazan', 2012.
16. Belytschko T. Implementation and application of a 9-node Lagrange shell element with spurious mode control / T. Belytschko, W.K. Liu, J.S.J. Ong, D. Lam // Computers and Structures. - 1985. - V. 20, №1-3. - P. 121-128.
17. Park K.C. A curved shell element based on assumed natural-coordinate strain / K.C. Park, G.M. Stanley // J. Appl. Mech. - 1986. - V. 53, №2. - P. 278-290.
