Simplified Variational Approach for Analysis of Thick Orthotropic Laminated Plates: 1- Cylindrical Bending

Abstract

Reissner's, stress-based, shear deformation plate theory is chosen to approximate the stress field for balanced symmetric laminates. The longitudinal stresses are assumed to vary linearly along the plate thickness. In fact, we may view the purpose of this work as an examination of effectiveness of mathematical laminate models in which the response is defined in terms of force and moment resultants. Average stiffness moduli are considered to characterize the laminate properties. The accuracy and the range of application of the present approach are proved for laminated plate:1-in cylindrical bending and 2-simplly-supported with different thickness, for which elasticity solutions exist. The paper presents the first step of validation of the developed theory. The cylindrical bending of symmetric cross-ply laminated plates subjected to sinusoidal loading is investigated. Results from the present theory are compared with those from exact solutions and other known theories as well.

Simplified Variational Approach for Analysis of Thick Orthotropic Laminated

“…A simplified approach, stress-based, was examined by the authors for laminated plate in cylindrical bending [3] has been extended for simply supported cross-ply symmetric laminates. Average stiffness moduli are considered to characterize the laminate properties, ESL.…”

“…A stress-based approach developed by the authors in a previous work [3] was tested by the bench-mark problem for the plate in a cylindrical bending solved exactly by Pagano. The presented simplified approach gave good results for out-of-plane displacement and the transverse stresses.…”

“…Specifically, the problem of a symmetrically bidirectional laminate with pinned edges under static bending forces is considered. For the sake of brevity, the details of the derivation of equilibrium equations, variational analysis and continuity conditions are omitted, see [3]. For the sake of continuity, only relevant equations are provided.…”