Nonlinear behaviour and imperfection sensitivity of functionally graded nanocomposite structures

Abstract

Functionally graded nanocomposites in which carbon nanotube (CNT) or graphene reinforcements are dispersed nonuniformly in the matrix have been considered as the new generation materials with great application potentials in various engineering areas such as aerospace, automobile, energy, biomedical and electronic industries. The mechanical analysis of structural elements made from such nanocomposites have therefore attracted increasing attention from both research and engineering communities due to their great importance in both theoretical and practical aspects.This thesis deals with the nonlinear behaviour and imperfection sensitivity of functionally graded nanocomposite structures reinforced with either CNTs or graphene platelets (GPLs). Their material properties are assumed to be functionally graded along the thickness direction, among which the effective material properties of functionally graded CNT-reinforced composites (FG-CNTRCs) are predicted by the extended rule of mixture, while that of functionally graded GPL-reinforced composites (FG-GPLRCs) are estimated by the modified Halpin-Tsai model. The research content of this thesis includes several aspects: 1) buckling and free vibration analysis of sandwich beams with FG-CNTRC face sheets, 2) imperfection sensitive analysis of FG-CNTRC beams, 3) thermo-electro-mechanical analysis of piezoelectric FG-CNTRC beams with geometric imperfections, 4) mechanical analysis of FG-GPLRC beam and plate structures under thermo-mechanical loading.Linear governing equations of sandwich beams with FG-CNTRC facesheets are derived within the framework of first-order shear deformation theory (FSDT). By using the differential quadrature (DQ) method, the buckling and free vibration behaviours of FG-CNTRC sandwich beams are investigated. A parametric study is conducted to show the effects of CNT volume fraction, core-to-facesheet thickness ratio, slenderness ratio, and end supports on the critical buckling load and natural frequencies. Numerical results for sandwich beams with uniformly distributed CNTRC (UD-CNTRC) face sheets are also provided for comparison. The results demonstrate that the sandwich beam with FG-CNTRC facesheets outperforms the beam with UD-CNTRC facesheets in terms of the buckling and vibration performances.For the imperfection sensitivity analysis, nonlinear governing equations and their dimensionless forms are deduced by using the principle of virtual displacements. A generic imperfection model in the form of the product of trigonometric and hyperbolic functions are used to describe the various possible geometric imperfections such as sine type, global, and localized imperfections. The imperfection sensitivity analysis covers several subjects for FG-CNTRC beams under different loading conditions. Among those, the compressive and thermal postbuckling are studied by means of the DQ-based Newton-Raphson technique, the nonlinear free vibration is analysed by using the Ritz method together with a standard iteration procedure. Comprehensive numerical results are presented for geometrically imperfect FG-CNTRC beams, with a particular focus on the influences of imperfection parameters such as half-wave number, location, and amplitude. The results indicate that geometric imperfections have important effects on the nonlinear postbuckling and free vibration behaviours.In the thermo-electro-mechanical analysis, the FG-CNTRC beams are integrated with surface-bonded piezoelectric layers and subjected to a combined action of a uniform temperature rise, a constant actuator voltage and an in-plane force. The effects of shear deformation and geometric imperfection are taken into consideration in theoretical formulations. The thermo-electro-mechanical postbuckling equilibrium path is traced by using the DQ method in conjunction with Newton-Raphson technique. The obtained postbuckling displacements are then included in the free vibration analysis of thermo-electro-mechanically postbuckled FG-CNTRC beams. Free vibration results of postbuckled FG-CNTRC beams with and without geometric imperfections are given and compared to highlight the influence of geometric imperfections. The effects of CNT distribution pattern and volume fraction, temperature rise, actuator voltage, in-plane force, and boundary condition are also discussed in detail.Based on the FSDT and von Karman geometric nonlinearity, the nonlinear dynamic governing equations are established for shear deformable FG-GPLRC beams and plates that are subjected to a uniform temperature rise and a periodic uniaxial in-plane force. By using the DQ method, the thermo-mechanical buckling and postbuckling, as well as free vibration are studied. Subsequently, the parametric instability of FG-GPLRC beams and plates under thermo-mechanical loading are investigated, and the principal unstable region is determined by employing the Bolotin’s method. Special attention is given to the effects of GPL distribution pattern, weight fraction, and geometry so as to best explore the potentials of GPLs towards the development of advanced lightweight composite structures. Numerical results indicate that the addition of a low content of GPLs significantly improves the mechanical properties and structural performances of polymer nanocompositestructures. Symmetric distribution with more GPLs near the surface layers and few GPLs close to the neutral plane is most desirable in terms of the reinforcing effect.As the result of extensive theoretical and numerical analysis by using the computer program packages developed in MATLAB, the present thesis makes valuable contributions to the knowledge base in the subject area by providing comprehensive first-ever-known results, which are helpful in better understanding the mechanical behaviour of such functionally graded nanocomposite structures.