Geodesic
Comparison of scalar and vector FEM forms in the case of an elliptic cylinder
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 3, pp. 418-428 
T. A. Kiseleva; Yu. V. Klochkov; A. P. Nikolaev. Comparison of scalar and vector FEM forms in the case of an elliptic cylinder. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 3, pp. 418-428. http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_3_a5/
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     title = {Comparison of scalar and vector {FEM} forms in the case of an elliptic cylinder},
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Voir la notice de l'article provenant de la source Math-Net.Ru

An invariant vector approximation of unknown quantities is proposed and implemented to construct the stiffness matrix of a quadrilateral curved finite element in the form of a fragment of the mid-surface of an elliptic cylinder with 18 degrees of freedom per node. Numerical examples show that the vector approximation has significant advantages over the scalar one as applied to arbitrary shells with considerable mid-surface curvature gradients.

[1] Novozhilov V. V., Chernykh K. F., Mikhailovskii E. I., Lineinaya teoriya tonkikh obolochek, Politekhnika, L., 1991

[2] Galimov K. Z., Paimushin V. N., Teoriya obolochek slozhnoi geometrii, Izd-vo Kazansk. gos. un-ta, Kazan, 1985

[3] Grigolyuk E. I., Kabanov V. V., Ustoichivost obolochek, Nauka, M., 1978 | MR

[4] Grigolyuk E. N., Lopanitsyn E. A., Konechnye progiby, ustoichivost i zakriticheskoe povedenie tonkikh pologikh obolochek, MGTU “MAMI”, M., 2004

[5] Yakushev V. L., Nelineinye deformatsii i ustoichivost tonkikh obolochek, Nauka, M., 2004

[6] Bazhenov V. G., “Eksperimentalno-raschetnyi metod issledovaniya bolshikh uprugoplasticheskikh deformatsii tsilindricheskikh obolochek pri rastyazhenii do razryva i postroenie diagramm deformirovaniya pri neodnorodnom napryazhenno-deformirovannom sostoyanii”, Prikl. mekhan. i tekhn. fiz., 54:1 (2013), 116–124 | MR | Zbl

[7] Golovanov A. I., Tyuleneva O. N., Shigabutdinov A. F., Metod konechnykh elementov v statike i dinamike tonkostennykh konstruktsii, Fizmatlit, M., 2006

[8] Yakupov N. M., Serazutdinov M. N., Raschet uprugikh tonkostennykh konstruktsii slozhnoi geometrii, IMNRAN, Kazan, 1993

[9] Postnov V. A., Kharkhurim I. Ya., Metod konechnykh elementov v raschetakh sudovykh konstruktsii, Sudostroenie, L., 1974

[10] Bate K.-Yu., Metody konechnykh elementov, Fizmatlit, M., 2010

[11] Nikolaev A. P., Klochkov Yu. V., Kiselev A. P., Gureeva N. A., Vektornaya interpolyatsiya polei peremeschenii v raschetakh obolochek, FGBOU VPO Volgogradskii GAU, Volgograd, 2012, 244 pp.

[12] Sedov L. I., Mekhanika sploshnoi sredy, v. I, Nauka, M., 1976

[13] Klochkov Yu. V., Nikolaev A. P., Kiseleva T. A., “Sravnenie napryazhenii, vychislennykh na osnove skalyarnoi i vektornoi interpolyatsii MKE v sochlenennykh obolochkakh iz raznorodnykh materialov”, Stroitelnaya mekhan. i raschet sooruzhenii, 2013, no. 5(250), 70–76

[14] Belyaev N. M., Soprotivlenie materialov, Nauka, M., 1976