Vibration And Buckling Analysis Of Multi-directional Functionally Graded Plates Using The Weak Form Quadrature Element Method

Functionally graded materials(FGMs)are a kind of new composite material fabricated by two or more different material ingredients.The material composition and structure of FGMs are in accordance with continuous variation of the specified gradient in spatial directions such that the materials can satisfy the requirement of the material performance for different parts of the component.Therefore,FGMs have been widely used in a variety of engineering applications,such as optoelectronics,aerospace,nuclear reaction and so on.With the expansion of engineering applications and the development of manufacture technology for FGMs,the uni-directional FGMs become more and more difficult to satisfy the requirement of complex application situations.It has become imperative for researchers to study the manufacturing and mechanical properties of multi-directional FGMs.The weak form quadrature element method(QEM)is an efficient and versatile numerical method.It is based on the weak form description of a problem or the relevant variational principle,making the QEM overcome the drawbacks of the commonly used differential quadrature method(DQM)by avoiding the direct solution to the differential equations.A same set of points are used for numerical integrals and numerical differential in the QEM.The advantages of high order approximation of the DQM are reserved and the information of material parameters is discretized to the integral points.The QEM has shown prominent advantages when dealing with problems with complex geometric shapes,loading conditions or non-homogeneous materials.The vibration and buckling characteristics of multi-directional functionally graded plates are analyzed in this thesis based on the refined plate theory of C1 continuity using the QEM,and Pasternak foundation has been taken into account.The material properties are continuous functions of the coordinates and are assumed to follow power-law and exponent-law distributions.The position of neutral surface is modified considering the inhomogeneous distribution of material properties.Results of numerical examples with different geometric shapes and boundary conditions are compared with available data and good agreement has been reached.The influences of various parameters are investigated,which may provide reference for further research and engineering applications.In addition,geometrically nonlinear vibration characteristics of multi-directional functionally graded plates are studied.The nonlinear strain energy is calculated based on von Karman theory,and nonlinear generalized characteristic equations are obtained from Hamilton's principle.An iterative technique is used to solve the nonlinear generalized characteristic equations,and the influences of maximum amplitude ratio and material gradient coefficient to nonlinear frequency are discussed by numerical examples.