Nonlinear Behavior And Dynamic Response Of Advanced Composite Plate Structures

Functionally graded materials (FGMs) are microscopically inhomogeneouscomposites usually made from a mixture of metals and ceramics. Carbonnanotube reinforced composites (CNTRCs) are one of the advanced compositematerials reinforced by carbon nanotubes (CNTs). These two advancedcomposite materials are a new generation of composite materials in which themicro-structural details are spatially varied through nonuniform distribution ofthe reinforcement phase. Investigation on the nonlinear behavior and dynamicresponse of FGM and CNTRC plates subjected to mechanical, thermal loads ortheir combinations is a matter of considerable importance in the design of platestructures in aeronautical, mechanical, civil, petrochemical and marineindustries.In the present study we investigated the nonlinear bending behavior andnonlinear vibration characteristics of FGM and CNTRC plate structures restingon an elastic foundation in thermal environments. The main contents and novelcontributions of this thesis are:(1) Two kinds of micromechanics models areadopted to obtain the effective material properties of FGM plate and CNTRCplate, respectively. The effective material properties of FGM plate are assumedto obey the Mori-Tanaka micromechanics model, and the effective materialproperties of CNTRC plate are assumed to obey the extended Voigt model aswell.(2) The governing equations are based on Reddy’s higher-order sheardeformation plate theory and general von Kármán-type equations, whichinclude the plate-foundation interaction and thermal effects. The motion equations are solved by a two-step perturbation technique and a set of higherorder asymptotic solutions is obtained.(3) The effects of material propertygradient, volume fraction, temperature change, foundation stiffness,core-to-face sheet thickness ratio, initial in-plane load as well as the in-planeboundary conditions on the nonlinear bending behavior and vibrationcharacteristics of FGM and CNTRC plate structures are discussed in detailthrough a parametric study.A set of computer programs was developed for this purpose and manyexamples were solved numerically for the first time. These numerical resultsare useful for numerical benchmarking by others in the future. The mainresults achieved in this article are:The FGM volume fraction index has a significant effect on the mechanicalbehavior of both single-layer and sandwich FGM plates. The static deflections,nonlinear to linear frequency ratios and dynamic deflections decrease but thenatural frequencies increase with increases in FGM volume fraction index.The elastic foundation has a significant effect on the nonlinear bending andvibration of both single-layer and sandwich FGM plates. The static/dynamicdeflections and bending moments are decreased when the foundation becomesstiffer. In contrast, the natural frequencies increase when the foundationbecomes stiffer.Functionally graded CNT reinforcement has a significant effect on themechanical behavior of CNTRC plates. CNTRC plate with symmetricaldistribution of CNTS has higher natural frequencies but lower nonlinear tolinear frequency ratios and less dynamic deflections than those of plates withuniform or unsymmetrical distribution of CNTs.The foundation stiffness and initial in-plane load have a significant effecton the nonlinear bending, vibration and dynamic response of both single-layerand sandwich CNTRC plates. The CNT volume fraction and temperaturechange have a moderate effect on the free and forced vibration of CNTRCplates, nonlinear bending and natural frequency as well. The core-to-face sheetthickness ratio has a significant effect on the bending moments-loads curves, natural frequencies and dynamic response of CNTRC sandwich plates.The results presented explore the important issue of FGM and CNTRCplate structures, and thus are greatly helpful to understanding for engineeringdesign.