Liner And Nonlinear Analysis Of Functionally Graded Circular Plates

Functionally graded material (FGM) is a kind of composite materials that are microscopically inhomogeneous,taking advantage of the merits of constituent materials adequately.By gradually varying the volume fraction of the constituent materials,FGM possesses the gradient in properties,i.e. the thermal and mechanical properties vary smoothly and continuously from one surface to the other,which eliminates the mismatch of mechanical properties induced by the interface.Such that,FGM is considered as a potential structural material for the future high-speed spacecraft,nuclear reactor and chemical plants duo to its excellent performance in high temperature environments.In this thesis, bending, buckling, post buckling and vibration of FGM circular plates are studied.The material properties of plates are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents, and to be temperature dependent.The governing equations derived for the problem are based on higher-order shear deformation plate theory.It involved the following two parts. 1. Linear analysis on the FGM plates:The small deflection bending and buckling problems of the FGM plates and the plates made of homogeneous materials were studied using differential quadrature method.Effects of the gradients in material properties,the temperature-dependent properties and loading on bending and buckling behavior of the plates are discussed.The results obtained show that gradient properties of the materials have significant effect on the response of the FGM plates,the center deflection of the plates with material properties between those of the ceramic and metal is intermediate to the deflection of the ceramic and metal plates;and when the temperature-dependent properties are taken into account,all the plates with intermediate properties undergo corresponding intermediate values of the critical buckling thermal load when the plates are subjected to uniform thermal load, but this is not true while nonuniform thermal load is applied.Considering the mathematical similarity of the governing equations between the classical and the third-order theories,we obtain the solutions of FGM circular plates based on the third-order plate theory in terms of those of isotropic plates based on the classical plate theory.With the relationships one can obtain the exact solutions for critical buckling loads and natural frequencies of FGM plates for the third-order plate theory just by knowing the corresponding solutions of the isotropic plates for the classical plate theory.2. Nonlinear analysis on the FGM plates:(1) Based on Von Kaman's classical plate theory, the nonlinear motion equations are derived,and then a shooting method is employed to solve the resulting equations for the large amplitude vibration problem.The results obtained show that the fundamental frequency of FGM plate is greater than that of the homogenous plate.The material constant n,amplitude A and thermal load parameterλhave significant effects on the fundamental frequency of the FGM plate.The increase of material constant n and amplitude A results in the increase of fundamental frequency of the plate, but the increase of thermal load results in the decrease of fundamental frequency of the plates.(2) Existence of harmonic vibration is assumed in analysis and the motion equations are separated into two sets. The first set is for the thermal post-buckling and the other is for small amplitude vibration near the post-buckling configuration. The differential quadrature method is used to numerically solve the resulting equations. we used Hadmart and SJT Products to decoupling.(3) Based on higher-order shear deformation plate theory, governing equations for the large deflection bending of the FGM plates,and for axisymmetric small amplitude vibration of the thermally post-buckled FGM plates near the thermal post-buckling configurations are derived.The results obtained by using differential quadrature method show that the stability deformation of FGM plates in temperature fields manifest furcation properties of post-buckling configuration,the natural frequencies vs. temperature also showed furcation properties.The gradient properties have significant effect on the post-buckling configuration and the relation between the natural frequencies and the temperature.The natural frequencies of FGM circular plates is intermediate to that of the metal and ceramic plates.The rising temperature also has significant effect on the natural frequencies of FGM circular plates.The natural frequencies decrease with the increase of the temperature before buckling load,while they increase after the load, and at the point of the buckling load, the natural frequencies approach zero.With the increase of the order of the natural frequencies, the effect of temperature becoming smaller.