Analytical and Numerical Modelling of the Axisymmetric Bending of Circular Sandwich Plates with the Nonlinear Elastic Core Material

Subject Areas : Engineering

A Kudin ¹ , S Choporov ² , Yu Tamurov ³ , M.A.V Al Omari ⁴

1 - Department of Mathematics, Zaporizhzhya National University, Zhukovsky street 66, Zaporizhzhya 69600, Ukraine
2 - Department of Mathematics, Zaporizhzhya National University, Zhukovsky street 66, Zaporizhzhya 69600, Ukraine
3 - Department of Mathematics, Zaporizhzhya National University, Zhukovsky street 66, Zaporizhzhya 69600, Ukraine
4 - Department of Mathematics, Zaporizhzhya National University, Zhukovsky street 66, Zaporizhzhya 69600, Ukraine

Received: 2016-06-23 Accepted : 2016-08-19 Published : 2016-09-20

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References:

[1] Carrera E., 2003, Historical review of zig-zag theories for multilayered plates and shells, Applied Mechanics Reviews 56:287-308.
[2] Gorshkov A.G., Starovoitov E.I., Yarovaya A.V., 2005, Mechanics of Layer Viscoelastoplastic Construction Elements, Fizmatlit, Moscow.
[3] Kudin A.V., Tamurov Yu.N., 2011, Modeling of bending symmetric sandwich plates with nonlinear elastic core using the small parameter method, Vsnik Sxdnoukrans’kogo Naconal’nogo Unversitetu Men Volodimira Dalya 165(11):32-40.
[4] Magnucka-Blandzi E., Wittenbeck L., 2013, Approximate solutions of equilibrium equations of sandwich circular plate, AIP Conference Proceedings 1558: 2352-2355.
[5] Magnucki K.A., Jasion P.A., Magnucka-Blandzi E.B., Wasilewicz P.A., 2014, Theoretical and experimental study of a sandwich circular plate under pure bending, Thin-Walled Structures 79:1-7.
[6] Mixajlov I.P., 1969, Some problems of axisymmetric bending circular sandwich plates with rigid core, Trudy Leningradskogo Korablestroitel’Nogo Instituta 66: 125-131.
[7] Noor A.K., Scott Burton W., Bert Ch. W., 1996, Computational models for sandwich panels and shells, Applied Mechanics Reviews 49(3): 155-199.
[8] Prusakov A.P., 1961, Some problems bending circular sandwich plates with lightweight filler, Tr. konf. po teor. plastin i obolochek 1:293-297.
[9] Ren-huai L., 1981, Nonlinear bending of circular sandwich plates, Applied Mathematics and Mechanics 2(2): 189-208.
[10] Tamurov Yu.N., 1991, Vibrational processes in a three-layer shell with nonuniform compression of a physically nonlinear filler, International Applied Mechanics 27(7): 698-703.
[11] Vinson J., Sierakowski R.,2002, The Behaviour of Streuctures Composed of Composite Materials, Martinus Nijhoff Publishers , Dordrecht , The Netherlands.
[12] Kauderer G., 1961, Nonlinear Mechanics, Russian Translation Available.
[13] Riahi A., Curran J.H., 2009, Full 3D finite element Cosserat formulation with application in layered structures, Applied Mathematical Modelling 33:3450-3464.
[14] MacLaughlin M.M., Doolin D.M., 2006, Review of validation of the discontinuous deformation analysis (DDA) method, International Journal for Numerical and Analytical Methods in Geomechanics 30(4):271-305.
[15] Pande G.N., Beer G., Williams J.R., 1990, Numerical Methods in Rock Mechanics, Wiley, Chichester.
[16] Williams J.R., O’Connor R., 1999, Discrete element simulation and the contact problem, Archives of Computational Methods in Engineering 6(4): 279-304.
[17] Ambartsumian S., 1970, Theory of Anisotropic Plates, Technomic Stanford Fizmargiz, Moskva.
[18] Timoshenko S.P., Woinowsky-Krieger S., 1959,Theory of Plates and Shells, McGraw-Hill, New York.
[19] Hinch E.J., 1995, Perturbation Methods, Cambridge University Press.