Dynamic Relaxation Nonlinear Viscoelastic Analysis of Annular Sector Composite Plate

Abstract

The geometrically nonlinear laminated annular plate structure with nonlinear viscoelastic orthotropic composite is considered using the dynamic relaxation (DR) method for the first time in the present study. The DR technique in conjunction with the finite difference discretization is used to study the behavior of a Mindlin plate. The plate is made of nonlinear viscoelastic orthotropic material expressed by the Schapery single integral model. A recursive-iterative formulation is implemented for the hereditary integral of the material. Under uniform lateral pressure and clamped and hinged edged constraints, the unsymmetrical laminated sector plate deformation is predicted in different times. The present results are compared with the elastic finite element (FE) generated numerical results. The correlations are very satisfactory. The load-center deflections for linear and nonlinear viscoelastic material plate along the symmetrical radial line for elastic and viscoelastic plate are illustrated. The dimensionless deflection results for up to 480 min are predicted to show the creep behavior of the material. Finally, the dimensionless stress couple results are obtained after 8 h creep time for a graphite/epoxy composite plate.

Nonlinear Viscoelastic Response of Unidirectional Polymeric Laminated Composite Plates Under Bending Loads

“…The unsymmetrical laminated plate constitutive equations in general form and the detail of the matrices for the determination force and moments, including elastic and viscoelastic terms, can be found elsewhere [17].…”

“…The mentioned relations, together with the boundary conditions, in their finite difference form, establish the set of equations suitable for the DR method. A Detailed description of stability, convergence and damping factors of the DR algorithm can be found elsewhere [17,24].…”

“…Also the bending analysis of linear viscoelastic sector plate with the assumption of higher order displacements was implemented by DR method [16]. Recently, the bending of nonlinear viscoelastic composite sector plate was investigated using DR method by Falahatgar and Salehi [17]. In this work, the governing equations were obtained with the assumption of the first-order shear deformation theory (FSDT) for displacements.…”

A Comparison of Large Deflection Analysis of Bending Plates by Dynamic Relaxation

“…They analyzed higher-order shear deformations by utilizing a finite difference form of the dynamic relaxation technique [25]. Moreover, they studied geometrically nonlinear viscoelastic analysis of annular sector composite plates [26]. Golmakani and Kadkhodayan investigated the nonlinear bending of FGM annular sector plates [27].…”

Thermoviscoelastic dynamic response for a composite material thin narrow strip

“…Pradeep and Ganesan [15] provide a decoupled thermo-mechanical analysis by using finite element method to deal with the thermal buckling and vibration behavior of multi-layer rectangular viscoelastic sandwich plates. In 2009, Falahatgar and Salehi [16] considered the geometrically nonlinear laminated annular plate structure with nonlinear viscoelastic orthotropic composite using the dynamic relaxation method for the first time and the DR technique in conjunction with the finite difference discretization was used to study the behavior of a Mindlin plate; Based on the von Karman's nonlinear geometry and using the methods of multiple scales and finite difference, the nonlinear vibration of an isotropic cantilever plate with viscoelastic laminate was investigated by Firooz and Morad [17]. Gupta and Kumar [18] presented an analysis and numerical results for free transverse vibrations of non-homogeneous visco-elastic elliptic plate whose temperature and thickness spatial variations both are parabolic along a line through plate centre.…”