An analytical solution for buckling and vibration analysis of functionally graded sandwich beams using a quasi-3D shear deformation theory

Abstract

Citation: Nguyen, Trung-Kien, Vo, Thuc, Nguyen, Ba-Duy and Lee, Jaehong (2016) An analytical solution for buckling and vibration analysis of functionally graded sandwich beams using a quasi-3D shear deformation theory. Composite Structures, Northumbria University has developed Northumbria Research Link (NRL) to enable users to access the University's research output. Copyright © and moral rights for items on NRL are retained by the individual author(s) and/or other copyright owners. Single copies of full items can be reproduced, displayed or performed, and given to third parties in any format or medium for personal research or study, educational, or not-for-profit purposes without prior permission or charge, provided the authors, title and full bibliographic details are given, as well as a hyperlink and/or URL to the original metadata page. The content must not be changed in any way. Full items must not be sold commercially in any format or medium without formal permission of the copyright holder. The full policy is available online: http://nrl.northumbria.ac.uk/policies.html This document may differ from the final, published version of the research and has been made available online in accordance with publisher policies. To read and/or cite from the published version of the research, please visit the publisher's website (a subscription may be required.)An analytical solution for buckling and vibration analysis of functionally graded sandwich beams using a quasi-3D shear deformation theory AbstractThis paper presents a Ritz-type analytical solution for buckling and free vibration analysis of functionally graded (FG) sandwich beams with various boundary conditions using a quasi-3D beam theory.It accounts a hyperbolic distribution of both axial and transverse displacements. Equations of motion are derived from Lagrange's equations. Two types of FG sandwich beams namely FG-faces ceramic-core (type A) and FG-core homogeneous-faces (type B) are considered. Numerical results are compared with earlier works and investigated effects of the power-law index, thickness ratio of layers, span-to-depth ratio and boundary conditions on the critical buckling loads and natural frequencies.

Bending and Elastic Vibration of a Novel Functionally Graded Polymer Nanocomposite Beam Reinforced by Graphene Nanoplatelets

“…The H-H and C-C boundary conditions are used, and various power-law indices (p) are considered. The results are compared with the available ones obtained by the first-order shear deformation theory (FSDT), third-order shear deformation theory (TSDT) and quasi-3D beam theory from the literature [60,61]. The present results well match the published results.…”

Trigonometric-series solution for analysis of laminated composite beams

“…It is noted that the inappropriate shape functions may cause slow convergence rates and numerical instabilities [21,22]. In addition, for shape functions which do not satisfy boundary conditions, Lagrangian multipliers method can be used to impose boundary conditions [24,33,34].…”

Hygro-thermal effects on vibration and thermal buckling behaviours of functionally graded beams

“…Moreover, it is known that Ritz method is efficient to deal with composite and FG beams with arbitrary boundary conditions. The accuracy and efficiency of this approach can be found in some representative earlier works [24,26,[40][41][42][43][44].…”