Nonlinear Mechanical Analysis Of A FGM Circular Plate

In this thesis, bending, post-buckling and vibration response of a FGM circular plate are investigated. It is assumed that the properties of functionally graded materials vary continuously through the thickness of the structures and obey a simple power law related to the volume fraction of the constituents. Based on the classical plate theory, the basic equations of a FGM circular plate are derived using the physical neutral surface concept. A shooting method is employed to numerically solve the resulted equations. The main contents are as following:1. We briefly introduced the basic conception, research status of FGM. And numerical method used in this paper named shooting method is simply introduced.2. Static mechanical behavior of a FGM circular plate is studied. The effects of temperature dependence of the material, the material gradient parameter and thermal loads on bending of a simply supported FGM circular plate and post-buckling of a clamped FGM circular plate are discussed. Numerical results obtained here showed that transverse displacements occur no matter how small the in-plane loads; therefore, there is no bifurcation buckling for a simply supported FGM circular plate subjected to in-plane thermal loads; under an in-plane thermal loading, clamped FGM circular plates exhibit typical thermal post-buckling behaviors.3. Dynamic mechanical behavior of FGM circular plate is studied. The effects of temperature dependence of the material, the material gradient parameter and thermal loads on vibration responses near the nonlinear static bending equilibrium configurations for a simply supported FGM circular plate are discussed. Numerical results showed that for the vibration in the vicinity of bended configurations of a simply supported FGM circular plate, the natural frequency decreases initially with an increase in the thermal load and reaches its minimum value; thereafter, it increases; but for the vibration in the vicinity of postbuckled configurations of a clamped FGM circular plate, the natural frequency increases monotonously with an increase in thermal load.4. Small amplitude vibration of a clamped FGM circular plate in the pre-buckling domain is studied. The effects of temperature dependence of the material, the material gradient parameter and thermal loads on vibration responses of the clamped FGM circular plate are discussed. Numerical results showed that for linear vibration of a clamped FGM circular plate in the pre-buckling domain, the natural frequency decreases as the thermal load increases until it reaches zero at the onset of buckling.