Static Mechanical Response Of Functionally Graded Material Beam And Shell Structures

In this thesis, geometrically nonlinear static responses of a functionally graded Timoshenko beam and a shallow conical shell, subjected to thermal loadings, are studied. The main contents of it are as follows:1. Firstly, the characteristics of functionally graded materials (FGMs) and the applications of FGMs in modern engineering, science and technology are briefly introduced. And then, according to my survey of the corresponding literatures, an outline about the research results and advances in the structural mechanical behaviors of FGM structures is summarized, especially about the macroscopical mechanical responses of FGM beams and plates (shells), subjected to thermal and mechanical loadings, are also presented in details.2. Based on the geometrically nonlinear theory for axially extensible and transversely shearable beams, the thermal buckling and post-buckling of the FGM Timoshenko beams, subjected to transversely non-uniform temperature rise, are investigated. Accurately considering the axial extension and transverse shearing of the beams, the governing equations for FGM Timoshenko beams, subjected to thermal and mechanical loadings with large elastic deformations, were formulated. In the analysis, the material properties of the functionally graded Timoshenko beam are assumed to vary continuously through the thickness of the beam, according to a power law distribution of the volume fraction of the constituents. By using shooting method to numerically solve the above mentioned strongly nonlinear boundary value problems of ordinary differential equations. The results of thermal buckling and post-buckling of transversely non-uniformly heated Timoshenko beams with pinned-pinned edges are obtained. The deformation parameters of the FGM beams versus thermal loading and material gradient constant are plotted. The effects of material gradient properties and thermal loading on deformations of beam are discussed in details. The results show that there exist tension-bend coupling in the deformation because of the transversely non-uniform characteristic of materials.3. Geometrically nonlinear large deformation problem of ceramic/metal FGM thin shallow conical shell is examined. Firstly, by assuming the mechanical properties of the functionally graded conical shells varying continuously through the thickness of the shells and obeying a power law distribution of the fraction of the graded shells and on the basis of the Kirchhoff straight normal assumption together with von Karman's geometrically nonlinear theory, the governing equations for axi-symmetrical large deformation of functionally graded shallow conical shell subjected to non-uniformtemperature rise are derived. Numerical results of bending of the statically thermal loaded shell with large deflection are obtained through solving the boundary value problem for nonlinear ordinary differential equations by using shooting method. The characteristic curves of the deformation parameter versus the shape parameter, thermal loadings and material gradient constant of the FGM shells are illustrated and also the effects of material gradient property, shape parameters and temperature parameters on deformations of shells are discussed in details.