Geodesic
Axisymmetric bending of circular and annular sandwich plates with the nonlinear elastic core material
Matematičeskoe modelirovanie, Tome 29 (2017) no. 2, pp. 63-78.

Voir la notice de l'article provenant de la source Math-Net.Ru

This paper compares the analytical model with the FEM based numerical model of the axisymmetric bending of circular sandwich plates. Also, the paper describes equations of the bending of circular symmetrical sandwich plates with isotropic face sheets and the nonlinear elastic core material. The method for constructing an analytical solution of nonlinear differential equations has been described. The perturbation method for differential equations with small parameters is used to represent nonlinear differential equations as a sequence of linear equations. Linear differential equations are reduced to Bessel's equation. We compare results of analytical and FEM models with results of other researches using two problems: 1) the problem of axisymmetric transverse bending of a circular sandwich plate, 2) the problem of axisymmetric transverse bending of an annular sandwich plate. The effect of accounting nonlinear elastic core material on the strain state of the sandwich plate is described.
Keywords: circular sandwich plate, nonlinear elastic material, finite element method
Mots-clés : perturbation method. 
@article{MM_2017_29_2_a4,
     author = {A. V. Kudin and S. V. Choporov and S. V. Gomenyuk},
     title = {Axisymmetric bending of circular and annular sandwich plates with the nonlinear elastic core material},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {63--78},
     publisher = {mathdoc},
     volume = {29},
     number = {2},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2017_29_2_a4/}
}
TY  - JOUR
AU  - A. V. Kudin
AU  - S. V. Choporov
AU  - S. V. Gomenyuk
TI  - Axisymmetric bending of circular and annular sandwich plates with the nonlinear elastic core material
JO  - Matematičeskoe modelirovanie
PY  - 2017
SP  - 63
EP  - 78
VL  - 29
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2017_29_2_a4/
LA  - ru
ID  - MM_2017_29_2_a4
ER  - 
%0 Journal Article
%A A. V. Kudin
%A S. V. Choporov
%A S. V. Gomenyuk
%T Axisymmetric bending of circular and annular sandwich plates with the nonlinear elastic core material
%J Matematičeskoe modelirovanie
%D 2017
%P 63-78
%V 29
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2017_29_2_a4/
%G ru
%F MM_2017_29_2_a4
A. V. Kudin; S. V. Choporov; S. V. Gomenyuk. Axisymmetric bending of circular and annular sandwich plates with the nonlinear elastic core material. Matematičeskoe modelirovanie, Tome 29 (2017) no. 2, pp. 63-78. http://geodesic.mathdoc.fr/item/MM_2017_29_2_a4/

[1] A. K. Noor, S. W. Burton, C. W. Bert, “Computational Models for Sandwich Panels and Shells”, Applied Mechanics Reviews, 49:3 (1996), 155–199 | DOI

[2] L. M. Kurshin, “Obzor rabot po raschetu trekhslojnykh plastin i obolochek”, Raschet prostranstvennykh konstruktsii, 1962, no. 2, 163–192

[3] E. Carrera, “Historical review of zig-zag theories for multilayered plates and shells”, Appl. Mech. Rev., 56 (2003), 287–308 | DOI | MR

[4] E. Magnucka-Blandzi, L. Wittenbeck, “Approximate solutions of equilibrium equations of sandwich circular plate”, AIP Conference Proceedings, 1558, 2013, 2352–2355 | DOI

[5] K. A. Magnucki, P. A. Jasion, E. B. Magnucka-Blandzi, P. A. Wasilewicz, “Theoretical and experimental study of a sandwich circular plate under pure bending”, Thin-Walled Structures, 79 (2014), 1–7 | DOI

[6] I. A. Tsurpal, Raschet elementov konstruktsii iz nelineino-uprugikh materialov, «Tekhnika», K., 1976, 176 pp.

[7] Iu. N. Tamurov, “Variant obobshchennoi teorii trekhsloinykh pologih obolochek s uchetom obzhatiia fizicheski nelineinogo zapolnitelia”, Prikl. mekhanika, 26:12 (1990), 39–45 | Zbl

[8] A. Riahi, J. H. Curran, “Full 3D finite element Cosserat formulation with application in layered structures”, Applied Mathematical Modelling, 33 (2009), 3450–3464 | DOI | MR | Zbl

[9] M. M. MacLaughlin, D. M. Doolin, “Review of validation of the discontinuous deformation analysis (DDA) method”, International Journal for Numerical and Analytical Methods in Geomechanics, 30:4 (2006), 271–305 | DOI | Zbl

[10] G. N. Pande, G. Beer, J. R. Williams, Numerical methods in rock mechanics, Wiley, Chichester–New York, 1990, 327 pp. | MR | Zbl

[11] J. R. Williams, R. O'Connor, “Discrete element simulation and the contact problem”, Archives of Computational Methods in Engineering, 6:4 (1999), 279–304 | DOI | MR

[12] G. Kauderer, Nichtlineare Mechanik, Springer-Verlag, Berlin–Heidelberg, 1958, 684 pp. | MR | Zbl

[13] A. G. Gorshkov, E. I. Starovojtov, A. V. Iarovaya, Mekhanika sloistykh viazkouprugoplasticheskikh elementov konstruktsii, Fizmatlit, M., 2005, 576 pp.

[14] I. P. Mikhajlov, “Nekotorye zadachi osesimmetrichnogo izgiba kruglykh trekhsloinykh plastin s zhestkim zapolnitelem”, Trudy Leningradskogo korablestroitelnogo instituta, 66 (1969), 125–131

[15] A. P. Prusakov, “Nekotorye zadachi izgiba kruglykh trekhsloinykh plastin s legkim zapolnitelem”, Tr. konf. po teor. plastin i obolochek, v. 1, 1961, 293–297

[16] S. A. Ambartsumyan, Teoriia anizotropnykh plastin: Prochnost, ustoichivost i kolebaniia, Nauka, M., 1987, 360 pp.

[17] Liu Renhuai, “Nonlinear Bending of Circular Sandwich Plates”, Applied Mathematics and Mechanics, English Edition, 2:2 (1981), 189–208 | DOI | Zbl

[18] A. V. Kudin, “Primenenie metoda malogo parametra pri modelirovanii izgiba simmetrichnykh trekhsloinykh plastin s nelinejno-uprugim zapolnitelem”, Visnik Skhidnoukrainskogo nacionalnogo universitetuimeni Volodimira Dalya, 11:165 (2011), 32–40 | Zbl

[19] A. V. Kudin, “Reshenie zadachi osesimmetrichnogo izgiba kruglykh trekhsloinykh plastin s nelineino-uprugim zapolnitelem”, Estestvennye i matematicheskie nauki v sovremennom mire, 3:15, Sb. st. po materialam XVI mezhdunar. nauch.-prakt. konf. (2014), 80–98

[20] M. S. Kornishin, Nelineinye zadachi teorii plastin i pologikh obolochek i metody ikh resheniia, Nauka, M., 1964, 192 pp.