Abstract
This paper studies the quasi-static stability analysis of fiber-reinforced viscoelastic composite plates subjected to in-plane edge load systems. The study is based on a unified shear-deformable plate theory. This theory enables the trial and testing of different through-thickness transverse shear-strain distributions and, among them, strain distributions that do not involve the undesirable implications of the transverse shear correction factors. Using the method of effective moduli solves the equations governing the stability of simply supported fiber-reinforced viscoelastic composite plates. The solution concerns the determination of the critical in-plane edge loads associated with the asymptotic instability of plates. In a study of this problem the general quasi-static stability solutions are compared with those based on the classical, first-order and sinusoidal transverse shear-deformation theories. Numerical applications using higher-order shear-deformation theory are presented and comparisons with the results of other theories are formulated.
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1._ Z. Hashin, The elastic moduli of heterogeneous materials. J. Appl. Mech. Trans. ASME 84E (1962) 143–150.
Z. Hashin and S. Shtrikman, A variational approach to the theory of the elastic behavior of multiphase materials. J. Mech. Phys. Solids 11 (1963) 127–140.
Z. Hashin, On elastic behavior of fiber reinforced materials of arbitrary transverse phase geometry. J. Mech. Phys. Solids 13 (1965) 119–134.
Z. Hashin, Viscoelastic behavior of heterogeneous media. J. Appl. Mech. Trans. ASME 32E (1965) 630–636.
S. Ahmed and F. R. Jones, A review of particulate reinforcement theories for polymer composites. J. Mater. Sci. 25 (1990) 4933–4942.
D.W. Wilson and J. R. Vinson, Viscoelastic analysis of laminated plate buckling. AIAA J. 22 (1984) 982–988.
C. G. Kim and C. S. Hong, Viscoelastic sandwich plates with cross-ply faces. J. Struct. Engng. 114 (1988) 150–164.
N. N. Huang, Viscoelastic buckling and postbuckling of circular cylindrical laminated shells in hygrothermal environment. J. Marine Sci. Tech. 2 (1994) 9–16.
H. H. Pan, Vibrations of viscoelastic plates. J. de Mécanique 5 (1966) 355–374.
L. Librescu and N. K. Chandiramani, Dynamic stability of transversely isotropic viscoelastic plates. J. Sound Vibr. 130 (1989) 467–486.
A. M. Zenkour, Analytical solution for bending of cross-ply laminated plates under thermo-mechanical loading. Comp. Struct. 65 (2004) 367–379.
K. P. Soldatos and T. Timarci, A unified formulation of laminated composite, shear deformable, five-degrees-of-freedom cylindrical shell theories. Comp. Struct. 25 (1993) 165–171.
B. E. Pobedrya, Structural anisotropy in viscoelasticity. Polymer Mech. 12 (1976) 557–561.
E. Reissner and Y. Stavsky, Bending and stretching of certain types of heterogeneous aelotropic elastic plates. J. Appl. Mech. 28 (1961) 402–408.
J. M. Whitney, Structural Analysis of Laminated Anisotropic Plates. Lancaster, PA: Technomic, (1987) 356 pp.
A. M. Zenkour, Exact mixed-classical solutions for the bending analysis of shear deformable rectangular plates. Appl. Math. Modelling 27 (2003) 515–534.
K. H. Lo, R. M. Christensen and E. M. Wu, A high-order theory of plate deformation: Part 1, homogeneous plates; Part 2, laminated plates. J. Appl. Mech. 44 (1977) 663–676.
M. Levinson, An accurate, simple theory of the statics and dynamics of elastic plates. Mech. Res. Comm. 7 (1980) 343–350.
J. N. Reddy, A simple higher-order theory of laminated composite plates. J. Appl. Mech. 51 (1984) 745–752.
J. N. Reddy, Theory and Analysis of Elastic Plates. Philadelphia: Taylor & Francis (1999) 576 pp.
M. E. Fares and A. M. Zenkour, Buckling and free vibration of non-homogeneous composite cross-ply laminated plates with various plate theories. Compos. Struct. 44 (1999) 279–287.
A. M. Zenkour, Natural vibration analysis of symmetrical cross-ply laminated plates using a mixed variational formulation. Eur. J. Mech. A/Solids 19 (2000) 469–485.
A. M. Zenkour, Buckling and free vibration of elastic plates using simple and mixed shear deformation theories. Acta Mech. 146 (2001) 183–197.
S. P. Timoshenko and J. M. Gere, Theory of Elastic Stability. New York: McGraw-Hill (1961) 541 pp.
M. N. M. Allam and A. M. Zenkour, Bending response of a fiber-reinforced viscoelastic arched bridge model. Appl. Math. Modelling 27 (2003) 233–248.
M. N. M. Allam and A. M. Zenkour, Stress concentration factor of structurally anisotropic composite plates weakened by an oval opening. Compos. Struct. 61 (2003) 199–211.
K. Y. Lam, C. M. Wang and X. Q. He, Canonical exact solutions for Levy-plates on two-parameter foundation using Green's functions. Engng. Struct. 22 (2000) 364–378.
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Zenkour, A. Buckling of fiber-reinforced viscoelastic composite plates using various plate theories. Journal of Engineering Mathematics 50, 75–93 (2004). https://doi.org/10.1023/B:ENGI.0000042123.94111.35
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DOI: https://doi.org/10.1023/B:ENGI.0000042123.94111.35