539.3:519.63 Numerical modeling of anisogrid structures deformation using schemes of high accuracy without saturation

Golushko S. K. (Design Technological Institute of Digital Techniques/Institute of Computational Technologies), Semisalov B. V. (Institute of Computational Technologies)

ANISOGRID STRUCTURE, CYLINDRICAL SHELL, CARBON, CONTINUUM MODEL, SCHEME WITHOUT SATURATION, FOURIER SERIES, CHEBYSHEV POLYNOMIAL


doi: 10.18698/2309-3684-2015-2-2345


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 expansions 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.


[1] Vasilyev V.V, Barynin V.A., Razin A.F. Petrokovskiy S.A., Halimanovich V.I. Kompozity i nanostruktury – Composites and nanostructures, 2009, no. 3, pp. 38–50.
[2] Vasilyev V.V., Morozov E.V. Advanced Mechanics of Composite Materials. Elsevier, 2007, 491 p.
[3] Obraztsov I.F., Rybakov L.S., Mishustin I.V. Mekhanika kompozitsionnykh materialov i konstruktsiy – Mechanics of Composite Materials and Structures, 1996, vol. 2, no. 2, pp. 3–14.
[4] Babenko K.I. Osnovy chislennogo analiza [Fundamentals of Numerical Analysis]. Moscow, Izhevsk, SRC Regular and chaotic dynamics Publ., 2002.
[5] Boyd J. Chebyshev and Fourier Spectral Methods. Second edition, University of Michigan, 2000.
[6] Semisalov B.V. Zhurnal vychislitelnoy matematiki i matematicheskoi fiziki RAN – Journal of Computational Mathematics and Mathematical Physics, 2014, vol. 54, no. 7, pp. 1110–1135.
[7] Levin A. Izvestiya vuzov. Stroitelstvo i arkhitektura – Proceedings of the universities. Construction and architecture, 1965, no. 9, pp. 41–48.
[8] Rybakov L.S. Mekhanika tverdogo tela – Mechanics of Solids, 1995, no. 5,
pp. 171–179.
[9] Dean D.L., Ganga Rao H.V.S. Macro approach to discrete field analysis.
J. Eng. Mech. Div., ASCE, 1970, vol. 96, no. EM4, pp. 377–394.
[10] Azarov A.V. Mekhanika kompozitsionnykh materialov i konstruktsiy – Mechanics of Composite Materials and Structures, 2012, vol. 18, no. 1,
pp. 121–130.
[11] Bazant Z.P., Christensen M. Analogy between micropolar continuum and grid frameworks under initial stress. Int. J. Solids and St. 1972, vol. 8, no. 3,
pp. 327–346.
[12] Bunakov V.A., Protasov V.D. Mekhanika kompozitsionnykh materialov i konstruktsiy – Mechanics of Composite Materials and Structures, 1989, no. 6, pp. 1046–1053.
[13] Bakhvalov N.S., Panasenko G.P Osrednenie protsessov v peroidicheskikh sredakh. Matematicheskie zadachi mekhaniki kompozitsionnykh materialov [Averaging Processes in Periodic Media. Mathematical Problems of the Mechanics of Composite Materials]. Moscow, Nauka Publ., 1984, 352 p.
[14] Vlasov A.N. Mekhanika kompozitsionnykh materialov i konstruktsiy – Mechanics of Composite Materials and Structures, 2004, vol. 10, no. 3,
pp. 424–441.
[15] Dimitrienko Yu.I., Gubareva E.A., Sborsсhhikov S.V. Matematicheskoe modelirovanie i chislennye menody – Mathematical modeling and Numerical Methods, 2014, no. 1, pp. 36–57.
[16] Dimitrienko Yu.I., Gubareva E.A., Sborschikov S.V. Matematicheskoe modelirovanie i chislennye menody – Mathematical modeling and Numerical Methods, 2014, no. 2, pp. 28–48.
[17] Sheshenin S.V., Skoptsov K.A. Matematicheskoe modelirovanie i chislennye menody – Mathematical modeling and Numerical Methods, 2014, no. 2,
pp. 49–61.
[18] Altufov N.A., Popov B.G. Mekhanika tverdogo tela – Mechanics of Solids, 1994, no. 6, pp. 146–154.
[19] Mityushov E.A. Mekhanika kompozitsionnykh materialov i konstruktsiy – Mechanics of Composite Materials and Structures, 2000, vol. 6, no. 2, pp. 151–161.
[20] Svistkov A.L., Evlampieva S.E. Prikladnaya mekhanika i tekhnicheskaya fizika – Journal of Applied Mechanics and Technical Physics, 2003, vol. 44, no. 5, pp. 151–161.
[21] Golushko. S.K., Idimeshev S.V., Semisalov B.V. Metody resheniya kraevykh zadach mekhaniki kompozitnykh plastin i obolochek: uchebnoe posobie po kursu “Pryamye i obratnye zadachi mekhaniki kompozitov” [Methods for Solving Boundary Value Problems of Mechanics of Composite Plates and Shells: Teaching Guide on the Curse «Direct and Inverse Problems of Composite Mechanics»]. ICT SB RAS Publ., Novosibirsk, 2014, 131 p. [electronic resource]. ISBN 978-5-9905791-0-1.
[22] Vasilyev V.V. Mekhanika konstruktsiy iz kompozitsionnykh materialov [Mechanics of Composite Material Structures]. Moscow, Mashinostroenie Publ., 1988, 269 p.
[23] Blokhin A.M., Ibragimova A.S., Semisalov B.V. Matematicheskoe modelirovanie – Mathrmatical modeling, 2009, vol. 21, no. 4, pp. 15–34.
[24] Timoshenko S., Woinowsky-Krieger S. Theory of plates and shells. 2nd ed.
N.Y.; Toronto; London: McGraw-Hill Book Company, Inc, 1959.


Golushko S., Semisalov B. Numerical modeling of anisogrid structures deformation using schemes of high accuracy without saturation. Маthematical Modeling and Coтputational Methods, 2015, №2 (6), pp. 23-45



Download article

Колличество скачиваний: 443