Abstract
The bending response for exponentially graded composite (EGC) sandwich plates is investigated. The three-layer elastic/viscoelastic/elastic sandwich plate is studied by using the sinusoidal shear deformation plate theory as well as other familiar theories. Four types of sandwich plates are considered taking into account the symmetry of the plate and the thickness of each layer. The effective moduli and Illyushin’s approximation methods are used to solve the equations governing the bending of simply-supported EGC fiber-reinforced viscoelastic sandwich plates. Then numerical results for deflections and stresses are presented and the effects due to time parameter, aspect ratio, side-to-thickness ratio and constitutive parameter are investigated.
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References
Plantema, F.J., Sandwich Construction: The Bending and Buckling of Sandwich Beam, Plates and Shells. New York: Wiley, 1966.
Allen, H.G., Analysis and Design of Structural Sandwich Panels. Oxford: Pergamon Press, 1969.
Zenkert, D., An Introduction to Sandwich Construction. Chameleon Press Ltd: London, 1995.
Whitney, J.M., Structural Analysis of Laminated Anisotropic Plates. Lancaster, PA: Technomic, 1987.
Vinson, J.R., The Behavior of Sandwich Structures of Isotropic and Composite Materials. Lancaster, PA: Technomic, 1999.
Pagano, N.J., Exact solutions for rectangular bidirectional composite and sandwich plates. Journal of Composite Materials, 1970, 4(1): 20–34.
Zenkour, A.M., Three-dimensional elasticity solution for uniformly loaded cross-ply laminates and sandwich plates. Journal of Sandwich Structures and Materials, 2007, 9(3): 213–238.
Zenkour, A.M., A comprehensive analysis of functionally graded sandwich plates: Part 1—deflection and stresses. International Journal of Solids and Structures, 2005, 42(18–19): 5224–5242.
Zenkour, A.M., A comprehensive analysis of functionally graded sandwich plates: Part 2—buckling and free vibration. International Journal of Solids and Structures, 2005, 42(18–19): 5243–5258.
Zenkour, A.M. and Alghamdi, N.A., Thermoelastic bending analysis of functionally graded sandwich plates. Journal of Material Sciences, 2008, 43(8): 2574–2589.
Nelson, R.B. and Lorch, D.R., A refined theory for laminated orthotropic plates. ASME Journal Applied Mechanics, 1974, 41: 177–83.
Librescu, L., Elastostatics and Kinematics of Anisotropic and Heterogeneous Shell Type Structures. The Netherlands: Noordhoff, 1975.
Lo, K.H., Christensen, R.M. and Wu, E.M., A high order theory of plate deformation, Part 1: homogeneous plates. ASME J Applied Mechanics, 1977, 44(4): 663–668.
Christensen, R.M., Lo, K.H. and Wu, E.M., A high order theory of plate deformation, Part 2: laminated plates. ASME J Applied Mechanics, 1977, 44(4): 669–676.
Murthy, M.V., An improved transverse shear deformation theory for laminated anisotropic plates. NASA Technical, 1981: 1903.
Reddy, J.N., A simple higher-order theory for laminated composite plates. Journal Applied Mechanics, 1984, 51: 745–752.
Khdeir, A.A. and Reddy, J.N., Exact solutions for the transient response of symmetric cross ply laminates using a higher order plate theory. Composite Science and Technology, 1989, 34(3): 205–24.
Reddy, J.N., Barbero, E.J. and Teply, J.L., A plate bending element based on a generalized laminate plate theory. International Journal for Numerical Mechanics in Engineering, 1989, 28: 2275–2292.
Reddy, J.N. and Khdeir, A.A., Buckling and vibration of laminated composite plates using various plate theories. AIAA Journal, 1989, 27(12): 1808–1817.
Wilson, D.W. and Vinson, J.R., Viscoelastic analysis of laminated plate buckling. AIAA Journal, 1984, 22(7): 982–988.
Kim, C.G. and Hong, C.S., Viscoelastic sandwich plates with cross-ply faces. Journal Structure Engineering, 1988, 114(1): 150–164.
Huang, N.N., Viscoelastic buckling and post buckling of circular cylindrical laminated shells in hydrothermal environment. Journal of Marine Science and Technology, 1994, 2: 9–16.
Pan, H., Vibrations of viscoelastic plates. Journal de Mécanique, 1966, 5: 355–374.
Librescu, L. and Chandiramani, N.K., Dynamic stability of transversely isotropic viscoelastic plates. Journal of Sound and Vibrations, 1989, 130(33): 467–486.
Zenkour, A.M., Buckling of fiber-reinforced viscoelastic composite plates using various plate theories. Journal of Engineering Mathematics, 2004, 50(1): 75–93.
Zenkour, A.M., Thermal effects on the bending response of fiber-reinforced viscoelastic composite plates using a sinusoidal shear deformation theory. Acta Mechanica, 2004, 171(3–4): 171–187.
Allam, M.N.M., Zenkour, A.M. and El-Mekaw, H.F., Bending response of inhomogeneous fiber-reinforced viscoelastic sandwich plates. Acta Mechanica, 2010, 209: 231–248.
Pobedrya, E., Structural anisotropy in viscoelasticity. Polymer Mechanics, 1976, 12(4): 557–61.
Illyushin, A. and Pobedria, B.E., Foundations of Mathematical Theory of Thermo Viscoelasticity. Moscow: Nauka, 1970(in Russian).
Soldatos, K.P. and Timarci, T., A unified formulation of laminated composite, shear deformable, five-degrees-of-freedom cylindrical shell theories. Composite Structures, 1993, 25(1–4): 165–171.
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Zenkour, A.M. Bending responses of an exponentially graded simply-supported elastic/viscoelastic/elastic sandwich plate. Acta Mech. Solida Sin. 24, 250–261 (2011). https://doi.org/10.1016/S0894-9166(11)60026-8
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DOI: https://doi.org/10.1016/S0894-9166(11)60026-8