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Composites: Mechanics, Computations, Applications: An International Journal

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ISSN Imprimer: 2152-2057

ISSN En ligne: 2152-2073

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A MODEL OF A LINEAR VISCOELASTIC ANISOTROPIC PLATE, CONSIDERING AN ARBITRARY INHOMOGENEITY OF THE MATERIAL

Volume 12, Numéro 3, 2021, pp. 77-96
DOI: 10.1615/CompMechComputApplIntJ.2021039253
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RÉSUMÉ

The paper derives a model of an arbitrary inhomogeneous, anisotropic thin plate with linear viscoelastic components under a slowly varying in time loading; the components of a plate are also supposed anisotropic. The displacements of an inhomogeneous plate are developed following the integral formula approach of composite mechanics, by establishing an interrelation between Laplace transformants of displacement fields of the inhomogeneous plate and a homogeneous one with the corresponding type of anisotropy, so-called concomitant. The interrelation comes from an integral formula approximation by the structural functions technique; in this paper, the first-order approximation of the integral formula is considered. A system of partial differential equations for the first-order structural functions is adjusted for the case of linear viscoelastic components, both in the Laplace and time domain. For a concomitant body, Timoshenko plate equations are generalized onto the anisotropic case. An explicit form of displacements and strains of an inhomogeneous plate is obtained. An example−an instantly applied bending of a simply supported plate, composed of isotropic, asymmetrically laid layers−is considered.

RÉFÉRENCES
  1. Aghalovyan, L.A., Asymptotic Theory of Anisotropic Plates and Shells, Singapore: World Scientific, 2015.

  2. Allam, M.N.M., Zenkour, A.M., and El-Mekawy, H.F., Bending Response of Inhomogeneous Fiber- Reinforced Viscoelastic Sandwich Plates, Acta Mech., vol. 209, no. 3, pp. 231-248, 2010.

  3. Altenbach, H. and Eremeyev, V.A., On the Bending of Viscoelastic Plates Made of Polymer Foams, Acta Mech., vol. 204, no. 3, pp. 137-154, 2010.

  4. Ashton, J.E. and Waddoups, M.E., Analysis of Anisotropic Plates, J. Compos. Mater., vol. 3, no. 1, pp. 148-165, 1969.

  5. Bakhvalov, N.S. and Panasenko, G.P., Homogenization: Averaging Processes in Periodic Media, Moscow, Nauka, 1984.

  6. Cai, W., Tu, S., and Tao, G., Thermal Conductivity of PTFE Composites with Three-Dimensional Randomly Distributed Fillers, J. Thermoplastic Comp. Mat, vol. 18, pp. 241-253, 2005.

  7. Carrera, E., An Assessment of Mixed and Classical Theories on Global and Local Response ofMultilayered Orthotropic Plates, Compos. Struct., vol. 50, no. 2, pp. 183-198, 2000.

  8. Cristensen, R.M., Theory of Viscoelasticity. An Introduction, New York, Academic Press, 1971.

  9. Ghinet, S. and Atalla, N., Modeling Thick Composite Laminate and Sandwich Structures with Linear Viscoelastic Damping, Comp. Struct., vol. 89, nos. 15-16, pp. 1547-1561, 2011.

  10. Gorbachev, V.I., Green Tensor Method for Solving Boundary Value Problems of the Theory of Elasticity for Inhomogeneous Media, Computat. Mech. Deformable Rigid Body, vol. 2, pp. 61-76, 1991.

  11. Gorbachev, V.I., Engineering Theory of Inhomogeneous Rods Resistance from Composite Materials, VestnikMGTU, Natural Sciences, vol. 6, pp. 56-72, 2016. DOI: 10.18698/1812-3368-2016-6-56-72.

  12. Gorbachev, V.I., Averaging Equations of Mathematical Physics with Coefficients Dependent on Coordinates and Time, Nanosci. Technol, vol. 8, no. 4, pp. 345-353, 2017.

  13. Gorbachev, V.I. and Kabanova, L.A., Formulation of Problems in the General Kirchhoff-Love Theory of Inhomogeneous Anisotropic Plates, Moscow Univ. Mech. Bull., vol. 73, no. 3, pp. 60-66, 2018.

  14. Ilyushin, A.A. and Pobedria, B.E., Foundations of Mathematical Theory of Thermo Viscoelasticity, Moscow: Nauka, 1970.

  15. Kabanova, L.A., An Approach to Experimental Computation of an Anisotropic Viscoelastic Plate Stiffnesses, Lobachevskii J. Math., vol. 41, no. 10, pp. 2010-2017, 2020.

  16. Kil'chevskiy, N.A., Fundamentals of the Analytical Mechanics of Shells, National Aeronautics and Space Administration, 1965.

  17. Kirchhoff, G., Vorlesungen uber Mathematische Physik: Mechanik, Leipzig, Germany: Taubner, 1876.

  18. Lakes, R.S., Viscoelastic Materials, Cambridge, UK: Cambridge University Press, 2009.

  19. Lekhnitskii, S.G., Anisotropic Plates, Foreign Technology Division Wright-Patterson AFB OH, Rep. AD 0683218, 1968.

  20. Mindlin, R.D. and Medick, M.A., Extensional Vibrations of Elastic Plates, Columbia University New York, Tech. Rep. 28, 1958.

  21. Morozov, N.F., Tovstik, P.E., and Tovstik, T.P., Generalized Timoshenko-Reissner Model for a Multilayer Plate, Mech. Solids, vol. 51, no. 5, pp. 527-537, 2016.

  22. Nowatski, V., Theory of Elasticity, Moscow: Mir, 1975. (in Russian).

  23. Pobedrya, B.E., Mechanics of Composite Materials, Moscow, Izdatelstvo MGU, 1984. (in Russian).

  24. Reissner, E., On Bending of Elastic Plates, Q. ofAppl. Math, vol. 5, no. 1, pp. 55-68, 1947.

  25. Schneider, P. and Kienzler, R., Comparison of Various Linear Plate Theories in the Light of a Consistent Second-Order Approximation, Math. Mech. Solids, vol. 20, no. 7, pp. 871-882, 2015.

  26. Timoshenko, S.P. and Woinowsky-Krieger, S., Theory of Plates and Shells, New York: McGraw-Hill, 1959.

  27. Vlasov, V.Z., The Method of Initial Function in Problems of Theory of Thick Plates and Shells, Proc. of 9th Int. Congr. Appl. Mech, vol. 6, pp. 321-330, 1956.

  28. Wang, Y.Z. and Tsai, T.J., Static and Dynamic Analysis of a Viscoelastic Plate by the Finite Element Method, Appl. Acoust., vol. 25, no. 2, pp. 77-94, 1988.

  29. Zenkour, A.M. and El-Mekawy, H.F., Bending of Inhomogeneous Sandwich Plates with Viscoelastic Cores, J. Vibroengi., vol. 16, no. 7, pp. 3260-3272, 2014.

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