Nonlinear Mechanical Behavior Of FGM Circular Plates And Beams Under Thermal Loading

FGM (Functionally graded material) is a new kind of composite materials, 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, which eliminates the mismatch of mechanical properties induced by the interface. So, FGM structures can be used in various special environments and can bear complex loads.In this thesis, nonlinear bending and post-bucking of FGM beams and circular plates subjected to thermal loads are investigated. It is assumed that the properties of FGM 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 beam and plate theory, the basic equations of FGM beams and circular plates are derived using the physical neutral surface concept. An exact solution is obtained for the nonlinear static responses of beams. A shooting method is employed to numerically solve the equations of plates. The main contents are as following:1. The basic definition and development as well as research status of FGM are introduced.2. The nonlinear static responses of FGM beams under an in-plane thermal loading are studied. Effects of material constant and thermal loads are discussed in details on bending and post-buckling of a FGM beam. For a FGM beam clamped at both ends, the equation and the corresponding boundary conditions lead to a differential eigenvalue problem, while for a FGM beam simply supported at both ends, an eigenvalue problem does not arise due to the inhomogeneous boundary conditions, which result in quite different behaviors between clamped and simply supported FGM beams. Under an uniform thermal load, FGM beams clamped at both ends exhibit typical thermal post-buckling behavior. Bifurcation buckling does not occur for FGM beams simply supported at both ends. Load-deflection curve for the simply supported beams have many different branches corresponding to different value intervals of the parameter, k. When subjected to a non uniform in-plane thermal load, with increase of the gradient index n, the thermal buckling load for FGM beams clamped at both ends decreases first and then increases. Deflection of all the beams with material properties between those of the ceramic and metal are not intermediate to the deflection of the ceramic and metal beams.3. The nonlinear static responses of FGM circular plates under an in-plane thermal load are studied. Numerical results obtained herein showed that FGM circular plates clamped at edge under an uniform thermal load exhibit typical thermal post-buckling behavior. The transverse deflection of simply supported FGM circular plates is initiated, regardless of the magnitude of the load. Load-deflection curves have many different branches and with increase of the gradient index n, the dimensionless thermal load increases first and then decreases. When subjected to a non uniform in-plane thermal load, with increase of the gradient index n, the thermal buckling load for FGM circular plates clamped at edge decreases first and then increases. Deflection of all the plates with material properties between those of the ceramic and metal are not intermediate to the deflection of the ceramic and metal plates. For FGM circular plates simply supported at edge, with increase of the gradient index n, the dimensionless thermal load decreases first and then increases when the deflection is small. Load-deflection curves will reversed at different gradient index n lead to different thermal bending configurations. The behavior characteristics of different temperature are considered.