Keywords: dynamic relaxation, viscoelastic composite, post-buckling, rectilinear orthotropic, sector plates, creep.

A large number of studies on nonlinear structural analysis have been done especially on large deflection and buckling analysis of plates using different analytical and numerical methods. Dumir et al. [1] presents a polynomial series solution for moderately large postbuckling deflection of thick laminated circular and annular plates. The plates were geometrically nonlinear, axisymmetric and had polar orthotropic layers in which the governing equations were solved iteratively by using the Newton-Raphson method. Dynamic relaxation (DR) was used for postbuckling analysis of structures. Turvey and Drinali [2] used DR to solve the nonlinear problem of postbuckling analysis with a finite difference discritization for rectangular and circular plates, respectively. For creep buckling behaviour of plates, Deleeuw [3] studied linear viscoelastic sector plates using spring-damper models and an analytical solution for the governing equations was presented. Huang [4] examined the creep responses of viscoelastic FRP laminates with various imperfections based on the geometrically nonlinear von Karman assumption under in-plane compression.

In the present work the DR method is used for post-buckling analysis of laminated annular sector plate. A linear viscoelastic orthotropic composite is used for the composite system and the viscoelastic composite is employed for the unidirectional fibre reinforced composite sector plate. The governing equations of the annular sector composite plate with simply supported edges which are derived by assuming the FSDT are solved by the finite difference version of the DR method. The DR technique with a central finite difference discretization is used to study the behaviour of the Mindlin plate. The linear viscoelastic orthotropic material is expressed using a Boltzmann superposition integral in conjunction with a recursive-iterative formulation for the hereditary integral of the material. Under uniform in-plane pressure and clamped and hinged edged constraints, the symmetrical laminated sector plate deformation is predicted through time. The present results are compared with the elastic finite element generated numerical results. The correlations are very satisfactory. The load-centre deflections for linear viscoelastic material plate along the radial line of symmetrical for elastic and viscoelastic plates are illustrated. The dimensionless deflection results for up to 50 hours are predicted to show the creep behavior of the material. Finally, the dimensionless stress couple results are obtained after an 8 hour creep time for a graphite-epoxy composite plate.

1

P.C. Dumir, P.G. Dube, A. Mallick, "Axisymmetric postbuckling of moderately thick laminated annular plate using FSDT", Composite Structures, 51, 311-318, 2001. doi:10.1016/S0263-8223(00)00147-1

2

G.J. Turvey, H. Drinali, "Elastic Postbuckling of Orthotropic Circular and Annular Plates with Imperfections", In: The Third Conference of Composite Structures, 315-335, Paisley, Scotland, Elsevier Applied Science, London, England, 1985.

3

S.L. Deleeuw, "Circular viscoelastic plates subjected to in- plane loads", AIAA Journal, 7(5), 931-937, 1971. doi:10.2514/3.6298

4

N.N. Huang, "Viscoelastic analysis of von karman laminated plates under in-plane compression with initial deflection", International Journal of Non-Linear Mechanics, 32(6), 1065-1075, 1997. doi:10.1016/S0020-7462(96)00133-3

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