Geodesic
Numerical modeling of anisogrid structures deformation using schemes of high accuracy without saturation
Matematičeskoe modelirovanie i čislennye metody, no. 6 (2015), pp. 23-45 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The article describes a class of promising anisogrid structures representing mesh shell of unidirectional carbon. A brief analysis of existing approaches to modeling deformation of grid structures is presented. New mathematical and numerical models are proposed for reliable description of complex behavior of anisogrid structures under different kinds of loads. A high degree of accuracy and stability of the numerical model based on the ex-pansions of unknown functions in Chebyshev polynomials and Fourier series is caused by the lack of saturation of such approximations. Efficiency of the proposed models and techniques is demonstrated on the example of solving test boundary-value problems and a problem of axial compression of anisogrid cylindrical shell.
Keywords: anisogrid structure, cylindrical shell, continuum model, scheme with-out saturation, Fourier series, Chebyshev polynomial.
Mots-clés : carbon 
@article{MMCM_2015_6_a1,
     author = {S. Golushko and B. V. Semisalov},
     title = {Numerical modeling of anisogrid structures deformation using schemes of high accuracy without saturation},
     journal = {Matemati\v{c}eskoe modelirovanie i \v{c}islennye metody},
     pages = {23--45},
     year = {2015},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MMCM_2015_6_a1/}
}
TY  - JOUR
AU  - S. Golushko
AU  - B. V. Semisalov
TI  - Numerical modeling of anisogrid structures deformation using schemes of high accuracy without saturation
JO  - Matematičeskoe modelirovanie i čislennye metody
PY  - 2015
SP  - 23
EP  - 45
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/MMCM_2015_6_a1/
LA  - ru
ID  - MMCM_2015_6_a1
ER  - 
%0 Journal Article
%A S. Golushko
%A B. V. Semisalov
%T Numerical modeling of anisogrid structures deformation using schemes of high accuracy without saturation
%J Matematičeskoe modelirovanie i čislennye metody
%D 2015
%P 23-45
%N 6
%U http://geodesic.mathdoc.fr/item/MMCM_2015_6_a1/
%G ru
%F MMCM_2015_6_a1
S. Golushko; B. V. Semisalov. Numerical modeling of anisogrid structures deformation using schemes of high accuracy without saturation. Matematičeskoe modelirovanie i čislennye metody, no. 6 (2015), pp. 23-45. http://geodesic.mathdoc.fr/item/MMCM_2015_6_a1/

[1] Vasilyev V.V, Barynin V.A., Razin A.F., Petrokovskiy S.A., Halimanovich V.I., Composites and nanostructures, 2009, no. 3, 38–50

[2] Vasiliev V.V., Morozov E.V., Advanced Mechanics of Composite Materials, Elsevier, Ann Arbor, 2007, 491 pp.

[3] Obraztsov I.F., Rybakov L.S., Mishustin I.V., Mechanics of Composite Materials and Structures, 2:2 (1996), 3–14

[4] Babenko K.I., Fundamentals of Numerical Analysis, SRC Regular and chaotic dynamics Publ., Moscow; Izhevsk, 2002

[5] Boyd J., Chebyshev and Fourier Spectral Methods, University of Michigan, 2d edition., Ann Arbor, 2000 | MR

[6] Semisalov B.V., Journal of Computational Mathematics and Mathematical Physics, 54:7 (2014), 1110–1135 | DOI | Zbl

[7] Levin A., Proceedings of the universities. Construction and architecture, 1965, no. 9, 41–48

[8] Rybakov L.S., Mechanics of Solids, 1995, no. 5, 171–179

[9] Dean D.L., Ganga Rao H.V.S., “Macro approach to discrete field analysis”, J. Eng. Mech. Div., ASCE, 96:4 (1970), 377–394 pp.

[10] Azarov A.V., Mechanics of Composite Materials and Structures, 18:1 (2012), 121–130 | MR

[11] Bazant Z.P., Christensen M., “Analogy between micropolar continuum and grid frameworks under initial stress”, Int. J. Solids and St., 8:3 (1972), 327–346 | DOI

[12] Bunakov V.A., Protasov V.D., Mechanics of Composite Materials and Structures, 1989, 6, pp

[13] Bakhvalov N.S., Panasenko G.P., Averaging Processes in Periodic Medi, Nauka Publ., Mathematical Problems of the Mechanics of Composite Materials, Moscow, 1984, 352 pp. | MR

[14] Vlasov A.N., Mechanics of Composite Materials and Structures, 10:3 (2004), 424–441

[15] Dimitrienko Yu.I., Gubareva E.A., Sborschhikov S.V., Mathematical modeling and Numerical Methods, 2014, no. 1, 36–57

[16] Dimitrienko Yu.I., Gubareva E.A., Sborschikov S.V., Mathematical modeling and Numerical Methods, 2014, no. 2, 28–48

[17] Sheshenin S.V., Skoptsov K.A., Mathematical modeling and Numerical Methods, 2014, no. 2, 49–61

[18] Altufov N.A., Popov B.G., Mechanics of Solids, 1994, no. 6, 146–154

[19] Mityushov E.A., Mechanics of Composite Materials and Structures, 6:2 (2000), 151–161 | MR

[20] Svistkov A.L., Evlampieva S.E., Journal of Applied Mechanics and Technical Physics, 44:5 (2003), 151–161 | MR | Zbl

[21] Golushko S.K., Idimeshev S.V., Semisalov B.V., Metody resheniya kraevykh zadach mekhaniki kompozitnykh plastin i obolochek, ucheb. posobie po kursu «Pryamye i obratnye zadachi mekhaniki kompozitov». Elektron. tekstovye i graf. dannye, KTI VT SO RAN, Novosibirsk, 2014, 131 pp.

[22] Vasilyev V.V., Mechanics of Composite Material Structures, Mashinostroenie Publ., Moscow, 1988, 269 pp.

[23] Blokhin A.M., Ibragimova A.S., Semisalov B.V., Mathrmatical modeling, 21:4 (2009), 15–34 | MR | Zbl

[24] Timoshenko S., Woinowsky-Krieger S., Theory of plates and shells, McGraw-Hill Book Company Inc., Toronto; London, 1959