Effect Of Pre-buckling Coupling Deformation On Stability Of A Functionally Graded Plate

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 eliminates the mismatch of mechanical properties induced by the interface. So, FGM can be applied in various special environments and can bear complex loads. More importantly, we can use materials with different capability compose new type material according to our desire, that will bring material design into higher levels. FGM have many advantages which homogeneous material and composite materials do not have. In the case of functionally graded plates the subject is particularly complicated for bending and stretching are coupled. In many of these cases, bifurcation buckling is impossible; that is, transverse deflection is initiated, regardless of the magnitude of the loading. Based on the classical nonlinear plate theory, stability of a functionally graded circular plate under uniform radial compression or thermal load with allowance for pre-buckling deformation was investigated and pointed a method to identify when true bifurcation buckling can occur. The governing equations were derived, and then a shooting method was employed to numerically solve the resulted differential equations. This study shows the important influences of including the pre-buckling deformation on the plate stability. The main contents are as following:1. We briefly introduced the basic principle, definition and development as well as research status of FGM. At the same time, numerical solution used in this paper named shooting method was simply introduced.2. We also introduced coupling mechanism, stability theory and plate theory.3. Based on the classical nonlinear plate theory, the nonlinear governing equations and boundary conditions as well as initial condtions were derived. Stability of a functionally graded circular plate under uniform radial compression or thermal load with allowance for pre-buckling deformation was investigated. The main conditions are as following:(1) Stability of a simply supported or clamped functionally graded circular plate under uniform radial compression with allowance for pre-buckling deformation was investigated. (2) When the temperature dependence was not considered, stability of a simply supported or clamped functionally graded circular plate under thermal load with allowance for pre-buckling deformation was investigated.(3) When the temperature dependence was not considered, stability of a simply supported or clamped functionally graded circular plate under thermal load with allowance for pre-buckling deformation was investigated.