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Journal of Applied Mechanics and Technical Physics

, Volume 59, Issue 6, pp 1058–1066 | Cite as

Elastic–Plastic Deformation of Flexible Plates With Spatial Reinforcement Structures

  • A. P. YankovskiiEmail author
Article
  • 3 Downloads

Abstract

A mathematical model for the elastic–plastic bending deformation of spatially reinforced plates is constructed based on a leap-frog numerical scheme. The elastic–plastic behavior of the component materials of the composition is described by the theory of flow with isotropic hardening. The low resistance of the composite plates to transverse shear is taken into account using Reddy’s theory and the geometric nonlinearity of the problem using the von K´arm´an approximation. The dynamic elastic–plastic bending deformation of flat and spatially reinforced metal composite and fiberglass rectangular plates exposed to an air blast wave is investigated. It is shown that for relatively thick plates, replacing a flat leap-frog reinforcement structure by a spatial one leads to a decrease (of a few tens of percent for metal composite structures and a few hundred percent for fiberglass structures) in strain intensity in the binder and to a decrease (insignificant for metal composite structures and a factor of almost 1.5 for fiberglass) in the compliance of the plate in the transverse direction. It has been found that for relatively thin plates, replacing the flat reinforcement structure by a spatial one leads to a slight decrease in its compliance.

Keywords

flexible plates flat reinforcement spatial reinforcement Reddy theory dynamic bending elastic–plastic deformation leap-frog scheme 

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References

  1. 1.
    Yu. M. Tarnopol’skii, I. G. Zhigun, and V. A. Polyakov, Spatially Reinforced Composite Materials: A Reference Book (Mashinostroenie, Moscow, 1987) [in Russian].Google Scholar
  2. 2.
    M. H. Mohamed, A. E. Bogdanovich, L. C. Dickinson, et al., “A New Generation of 3D Woven Fabric Performs and Composites,” SAMPE J. 37 (3), 3–17 (2001).Google Scholar
  3. 3.
    J. Schuster, D. Heider, K. Sharp, and M. Glowania, “Measuring and Modeling the Thermal Conductivities of Three-Dimensionally Woven Fabric Composites,” Mekh. Kompoz. Mater. 45 (2), 241–254 (2009).Google Scholar
  4. 4.
    Yu. M. Tarnopol’skii, V. A. Polyakov, and I. G. Zhigun, “Composite Materials Reinforced by a System of Mutually Orthogonal Straight Fibers. 1. Calculation of Elastic Characteristics,” Mekh. Polimer., No. 5, 853–860 (1973).Google Scholar
  5. 5.
    A. F. Kregers and G. A. Teters, “Structural Model of Deformation of Anisotropic Three-Dimensionally Reinforced Composites,” Mekh. Kompoz. Mater., No. 1, 14–22 (1982).Google Scholar
  6. 6.
    A. P. Yankovskii, “Determination of the Thermoelastic Characteristics of Spatially Reinforced Fibrous Media in the Case of General Anisotropy of Their Components. 1. Structural Model,” Mekh. Kompoz. Mater. 46 (5), 663–678 (2010).Google Scholar
  7. 7.
    A. P. Yankovskii, “Applying the Explicit Time Central Difference Method for Numerical Simulation of the Dynamic Behavior of Elastoplastic Flexible Reinforced Plates,” Vychisl. Mekh. Sploshn. Sred 9 (3), 279–297 (2016).Google Scholar
  8. 8.
    J. N. Reddy, Mechanics of Laminated Composite Plates and Shells: Theory and Analysis (CRC Press, Boca Raton, 2004).CrossRefzbMATHGoogle Scholar
  9. 9.
    A. K. Malmeister, V. P. Tamuz, and G. A. Teters, Strength of Polymers (Zinatne, Riga, 1972) [in Russian].Google Scholar
  10. 10.
    G. V. Ivanov, Yu. M. Volchkov, I. O. Bogul’skii, S. A. Anisimov, and V. D. Kurguzov, Numerical Solution of Dynamic Problemsof Elastic–Plastic Deformation of Solids (Sib. Univ. Izd., Novosibirsk, 2002) [in Russian].Google Scholar
  11. 11.
    A. E. Bogdanovich, Nonlinear Problems of the Dynamics of Cylindrical Composite Shells (Zinatne, Riga, 1987) [in Russian].zbMATHGoogle Scholar
  12. 12.
    R. Houlston and C. G. Des Rochers, “Nonlinear Structural Response of Ship Panels Subjected to Air Blast Loading,” Comput. Struct. 26 (1/2), 1–15 (1987).CrossRefGoogle Scholar
  13. 13.
    Composite Materials: A Reference Book, Ed. by D. M. Karpinos (Naukova Dumka, Kiev, 1985) [in Russian].Google Scholar
  14. 14.
    Handbook of Composite Materials, Book. 1, Ed. by G. Lubin (Mashinostroenie, Moscow, 1988) [Russian translation].Google Scholar
  15. 15.
    I. G. Zhigun, M. I. Dushin, V. A. Polyakov, and V. A. Yakushin, “Composite Materials Reinforced by a System of Mutually Orthogonal Straight Fibers. 2. Experimental Study,” Mekh. Polimer., No. 6, 1011–1018 (1973).Google Scholar

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© Pleiades Publishing, Inc. 2018

Authors and Affiliations

  1. 1.Khristianovich Institute of Theoretical and Applied Mechanics, Siberian BranchRussian Academy of SciencesNovosibirskRussia

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