Nonlinear Behavior And Dynamics Of Functionally Graded Composite Plate Structures

Functionally graded materials (FGMs), usually made from a mixture of metals and ceramics,have been regarded as one of the advanced inhomogeneous composite materials with greatapplication potential in many engineering sectors such as aerospace vehicles, nuclear reactors,power generators, automobile industries and so on. Investigations on the mechanical response ofFGM structures under various combinations of mechanical and thermal loading conditions havebeen, therefore, receiving considerably more attention in recent years due to their primeimportance in both theoretical and practical aspects.This paper consists of three parts: (1) development of semi-analytical approaches on the basisof one-dimensional DQ approximation; (2) comprehensive theoretical and numerical studies onthe geometrically nonlinear behavior and dynamics of functionally graded plate structures; (3)investigations of the local deformation of foam-filled sandwich plates induced by localizedtransverse patch loads.Based on the one-dimensional differential quadrature approximation rule, a semi-analyticalDQ method is proposed in the first place to reduce the order of the original system by taking theadvantages of existing analytical solutions and Galerkin procedure. A semi-analytical perturbationDQ approach, which makes use of the perturbation technique combined with the newly developedsemi-analytical DQ method, is then designed as an efficient and reliable way in the nonlinearanalysis of FGM structures.Present research is mainly focused on the nonlinear mechanical response and structuraldynamics of functionally graded rectangular thin plates, shear-deformable plates and cylindricalpanels under different boundary constraints and subjected to combined thermo-mechanical loading.Material properties are assumed to be both position and temperature dependent with materialcomposition varying along thickness direction according to a power law distribution. Theoreticalformulations are presented in terms of displacement components and stress function so that effectsof in-plane loads and boundary conditions can be handled easily. The geometrically nonlinear dynamic governing equations of functionally graded thin platesare derived in the framework of classical plate theory. By using the proposed semi-analyticalapproaches, linear bending, free vibration, transient response, large deflection and postbucklingbehavior of rectangular FGM thin plates under general boundary conditions and combinedtransverse and inplane loads have been investigated extensively. Extensive parametric studies havealso been carried out to reveal the effects of various factors on the mechanical response of theFGM thin plates. For functionally graded plates with moderate thickness, nonlinear dynamic governingequations and their dimensionless forms are derived by using the Reddy's higher order sheardeformable plate theory to account for the parabolic distribution of the transverse shear strains andthe rotary inertia. Thermal effects due to a steady temperature distribution are taken intoconsideration in theoretical formulations. The present work covers a wide range of subjects for theFGM shear deformable rectangular plates with different boundary conditions and in-planeconstraints, and under uniform temperature change. Among those, static bending due tothermo-mechanical loads and free vibration of initially stressed FGM plates are analyzed by usingthe semi-analytical DQ method, the transient response due to impulsive loading is determined bythe mode superposition method, and the thermo-mechanical nonlinear bending solutions areobtained by means of multi-parameter perturbation technique together with the semi-analyticalDQ method. The conditions for the critical buckling to occur for a general functionally gradedplate are also discussed, and the buckling loads and critical temperatures are determined forclamped rectangular plates. Using the Donnell's shell theory and Reddy's higher order shear deformation theory, lineardynamic governing equations are established for the shear deformable functionally gradedcylindrical shell panels with moderate thickness and subjected to thermo-mechanical loading.After the vibrational characteristics of initially stressed FGM cylindrical panels being fullyinvestigated, attention is given to the parametric resonance of FGM cylindrical panels subjected toperiodic dynamic excitation force in the axial direction. Bolotin's method is then employed todetermine the principal instability regions. In the nonlinear analysis of composite laminated thin plates with general boundary supportsand resting on elastic foundations, both large deflection and postbuckling behavior ofanti-symmetric angle-ply and symmetrically cross-ply laminated rectangular plates are examined...