本論文提出三種不同半解析/全解析方法，分析功能性梯度材料(Functionally Graded Material, FGM)和奈米碳管加勁複合材料(Carbon Nanotube-Reinforced Composite, CNTRC)中空圓柱殼之三維撓曲、挫屈以及自由振動問題。各FGM或CNTRC材料層之材料特性為沿著厚度座標方向改變的函數型態，而非常數。本文首先提出改良Pagano方法分析具完全簡支承FGM/CNTRC中空圓柱殼之三維挫屈與自由振動問題；接著提出狀態空間無網格微分再生核(Differential Reproducing Kernel, DRK)方法和漸近無網格DRK方法，並將該二半解析方法應用於具不同邊界組合之FGM/CNTRC中空圓柱殼之三維撓曲、挫屈和自由振動問題分析。上述三方法之系統方程式均基於Reissner混合變分原理(Reissner's mixed variational theorem, RMVT)推導而得，其中各場量變數在環向座標之變化假設為傅立葉函數，在軸向和徑向座標之變化則彼此解法各有不同。文中探討各重要效應對該圓柱殼之應力、位移、最低振頻以及臨界載重參數之影響，諸如：材料性質梯度指數、幾何參數和不同邊界條件。

This dissertation proposed three semi-analytical/fully-analytical methods for the three-dimensional (3D) bending, buckling and free vibration analyses of functionally graded material (FGM) circular hollow cylinders and functionally graded (FG) carbon nanotube-reinforced composite (CNTRC) ones with various boundary conditions. The material properties of each FGM layer are assumed to vary through the thickness coordinate. A modified Pagano method was first developed for the exact 3D buckling and free vibration analyses of simply-supported, FGM and FG CNTRC cylinders under axial compression. Subsequently, two semi-analytical meshless methods using the differential reproducing kernel interpolation were developed, which are the state space DRK and asymptotic DRK methods, and these were also applied to investigate the mechanical behaviors of FGM/FG CNTRC cylinders with combinations of simply-supported and clamped edges. The sets of system equations of the above three methods were derived by Reissner’s mixed variational theorem (RMVT), in which the circumferential distributions of each variable were assumed to be the Fourier series, while the solution process for determinations of the axial and thickness distributions of this differs from one another. The influence with regard to some crucial effects on the stress and displacement components, the lowest frequency parameters, and the critical load parameters of the cylinder is undertaken, such as the material property gradient index, aspect ratio and different boundary conditions.

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