A unified formulation to assess theories of multilayered plates for various bending problems Erasmo Carrera * , Angelo Ciuffreda Department of Aeronautics and Aerospace Engineering, Politecnico di Torino, Torino, Italy Available online 11 August 2004 Abstract This work uses a unified formulation to compare about 40 theories for multilayered, composites and sandwich plates which are loadedbytransversepressurewithvariousin-planedistributions(harmonic,constant,triangularandtent-like).So-calledequivalent single layer models (ESLMs), which preserve the number of the unknown variables to be independent by the number of layers, as wellaslayer-wisemodels(LWMs)areconsideredinbothframeworkofprincipleofvirtualdisplacement(PVD)andReissnerMixed Variational Theorem (RMVT). MurakamiÕs Zig-Zag Function is used to introduce zig-zag (ZZ) effects while independent assump- tionsfortransversestresses(bothshearandnormalcomponents)areusedtoenforceinterlaminarcontinuity(IC)betweentwoadja- cent layers. Linear and higher order expansions (fourth-order) are introduced for displacements and stresses in the thickness plate directions. The fundamental effects of transverse strain is evaluated for most of the considered analyses. The whole modeling has beenhereinwrittenbyemployingaunifiedformulationrecentlyproposedbythefirstauthor.Asaresultsalargenumberofclassical and advanced theories for laminated structures are formulated and the related governing equations are written in terms of so-called fundamental nuclei with only nine terms each. Navier-type, closed form solutions of these equations are presented for orthotropic platesbyexpandingtheappliedpressureloadinginFourierseries.Anumberofconclusionshavebeentracedasfarasperformance andlimitationsofcomparedtheoriesisconcerned.Quotedresultscouldbeusedasbenchmarkstoassessavailabletheoriesnotcon- sidered in this paper as well as approximated solution techniques, such as finite element applications. Ó 2004 Elsevier Ltd. All rights reserved. Keywords: Multilayered plates; Classical theories; Advanced theories; Benchmarks; Distributed loadings; Localized loadings; Numerical assessment 1. Introduction Layeredstructuresareincreasinglyusedinaerospace, automotive and ship vehicles. The most common and best known examples of multilayered structures are sandwich panels as well as panels made by advanced composite materials. Nowadays there are examples of fighter and commercial aircraft, helicopter and gliders whose structures are entirely made of composite materi- als. Other examples of layered structures are: thermal protected structures in which layers with high thermal properties are used as thermal skins; biomedical retina; advanced optical mirrors; and semiconductor technolo- gies. A more recent example of layered structures is that of intelligent structures that embed piezo-layers and which are used as sensors and/or actuators to build a closed loop controlled ÔsmartÕ system. The analysis, design and construction of layered structures is of a cumbersome subject. So many differ- ent,complicatedandnewproblemsarisetoaddtothose that are already known for traditional one layered, iso- tropic structures. Processing and manufacturing, char- acterization and properties, mechanical behavior, joints, damage and repair, fatigue etc, are some exam- ples of these topics. A review on these topics with 0263-8223/$ - see front matter Ó 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.compstruct.2004.07.003 * Corresponding author. Tel.: +39 11 546 6836; fax: +39 11 564 6899. E-mail address: erasmo.carrera@polito.it (E. Carrera). Composite Structures 69 (2005) 271–293 www.elsevier.com/locate/compstruct