Abstract
This paper compares the analytical model of the axisymmetric bending of a circular sandwich plate with the finite element method (FEM) based numerical model. The differential equations of the bending of circular symmetrical sandwich plates with isotropic face sheets and a nonlinear elastic core material are obtained. The perturbation method of a small parameter is used to represent the nonlinear differential equations as a sequence of linear equations specifying each other. The linear differential equations are solved by reducing them to the Bessel equation. The results of the calculations with the use of the analytical and FEM models are compared with the results obtained by other authors by the example of the following problems: (1) axisymmetric transverse bending of a circular sandwich plate; (2) axisymmetric transverse bending of an annular sandwich plate. The effect of the nonlinear elasticity of the core material on the strained state of the sandwich plate is described.
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References
A. K. Noor, S. W. Burton, and C. W. Bert, “Computational models for sandwich panels and shells,” Appl. Mech. Rev. 49, 155–199 (1996).
L. M. Kurshin, “Review of articles on calculation of three-layer plates and shells,” Raschet Prostr. Konstrukts., No. 2, 163–192 (1962).
E. Carrera, “Historical review of zigzag theories for multilayered plates and shells,” Appl. Mech. Rev. 56, 287–308 (2003).
E. Magnucka-Blandzi and L. Wittenbeck, “Approximate solutions of equilibrium equations of sandwich circular plate,” AIP Conf. Proc. 1558, 2352–2355 (2013).
K. A. Magnucki, P. A. Jasion, E. B. Magnucka-Blandzi, and P. A. Wasilewicz, “Theoretical and experimental study of a sandwich circular plate under pure bending,” Thin-Walled Struct. 79, 1–7 (2014).
I. A. Tsurpal, Calculation of Construction Elements from Nonlinear Elastic Materials (Tekhnika, Kiev, 1976) [in Russian].
Iu. N. Tamurov, “A variant of the generalized theory of three-layered shallow shells taking into account the compression of a physically nonlinear core,” Prikl. Mekh. 26 (12), 39–45 (1990).
A. Riahi and J. H. Curran, “Full 3D finite element Cosserat formulation with application in layered structures,” Appl. Math. Model. 33, 3450–3464 (2009).
M. M. MacLaughlin and D. M. Doolin, “Review of validation of the discontinuous deformation analysis (DDA) method,” Int. J. Numer. Anal. Methods Geomech. 30, 271–305 (2006).
G. N. Pande, G. Beer, and J. R. Williams, Numerical Methods in Rock Mechanics (Wiley, Chichester, New York, 1990).
J. R. Williams and R. O’Connor, “Discrete element simulation and the contact problem,” Arch. Comput. Methods Eng. 6, 279–304 (1999).
G. Kauderer, Nichtlineare Mechanik (Springer, Berlin, Heidelberg, 1958).
A. G. Gorshkov, E. I. Starovoitov, and A. V. Yarovaya, Mechanics of Laminated Viscous Elastoplastic Constructional Elements (Fizmatlit, Moscow, 2005) [in Russian].
I. P. Mikhajlov, “Some problems of axisymmertic bending of circular sandwich plates with rigid core,” Tr. Leningr. Korablestroit. Inst. 66, 125–131 (1969).
A. P. Prusakov, “Some problems of bending of circular sandwich plates with ligh core,” in Proceedings of the Conference on the Theory of Plates and Shells, 1961, Vol. 1, pp. 293–297.
S. A. Ambartsumyan, Theory of Anisotropic Plates: Strength, Stability, and Vibrations (Nauka, Moscow, 1987; CRC, Boca Raton, FL, 1991).
Liu Renhuai, “Nonlinear bending of circular sandwich plates,” Appl. Math. Mech. 2, 189–208 (1981).
A. V. Kudin, “Application of small parameter method during bending simulation of symmetric sandwich plates with nonlinear-elastic core,” Visn. Skhidnoukr. Nac. Univ. im. V. Dalya 11 (165), 32–40 (2011).
A. V. Kudin, “Solution for axisymmertic bending of circular sandwich plates with nonlinear-elastic core,” in Proceedings of the 16th International Conference on Natural and Mathematic Sciences in Modern World, 2014, Vol. 3, No. 15, pp. 80–98.
M. S. Kornishin, Nonlinear Problems of the Theory of Plates and Shallow Shells and Methods of Their Solutions (Nauka, Moscow, 1964) [in Russian].
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Original Russian Text © A.V. Kudin, S.V. Choporov, S.I. Gomenyuk, 2017, published in Matematicheskoe Modelirovanie, 2017, Vol. 29, No. 2, pp. 63–78
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Kudin, A.V., Choporov, S.V. & Gomenyuk, S.I. Axisymmetric bending of circular and annular sandwich plates with nonlinear elastic core material. Math Models Comput Simul 9, 601–612 (2017). https://doi.org/10.1134/S2070048217050076
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DOI: https://doi.org/10.1134/S2070048217050076