本文以彈性力學的理論推導CCCC-FGM平板的解析解，平板受到不同的外力作用，即均勻分佈負載與集中力。平板為雙層板，上半層為FGM材料，蒲松比為常數，楊氏係數在厚度方向呈S型函數變化(簡稱S-FGM)，下半層則為均質材料。使用疊加法，CCCC-FGM平板受到均勻分佈負載或集中力的解析解可由三個子問題疊加而成，他們分別為SSSS-FGM平板受到相同的負載作用與SSSS-FGM平板各別在相反對邊承受未知彎矩。在每一個子問題中，使用Levy’s method (單傅立葉級數展開)與Navier’s method (雙傅立葉級數展開)兩個方法來求得解析解。
在有限元素分析中，使用20節點的固體元素，並且獲得平板的位移與應力的數值解。在研究中改變的參數有二，包括楊氏係數比值與施加之外力條件，此二參數對於平板力學行為的影響將會詳細地討論。研究結果顯示，雖然解析解在平板中心處的位移與有限元素數值解非常符合，應力在FGM材料楊氏係數變化較劇烈的區域仍不準確，需要更多的元素來模擬使其準確度提高。
本文的第二部份探討FGM平板與FGM樑的相似性。考慮一平板，其一對邊為簡支撐，另一對邊為自由端，研究結果顯示當蒲松比為零，無論平板長寬比為多少，平板均可視為樑；對於蒲松比不為零的情況，例：ν = 0.3，長寬比越大，平板的力學行為越接近樑 (當長寬比大於15時。)

Based on the elasticity theory, the analytical solutions of the thin functionally graded plate with four-edge clamped (CCCC FGM plate) are obtained in this thesis. The plate is subjected to uniformly distributed pressure and concentrated load applied at the plate center, respectively. The FGM plate contains two equal-thickness layers, i.e. FGM and homogeneous material. For the FGM layer, the Poisson’s ratio is assumed to be a constant and the Young’s Modulus varies along the thickness direction in Sigmoid function form (called S-FGM). By using the superposition principle, the closed form of the CCCC FGM plate under uniformly distributed pressure or concentrated load can be obtained from three sub-problems. They are the simply-supported-edge FGM plate (SSSS FGM plate) under same load, and two SSSS FGM plates subjected to a pair of unknown bending moment at opposite edges, respectively. In each sub-problem, the Navier’s method and Levy’s method are employed to obtain the analytical solution. The finite element analysis is performed to get the displacements and normal stress fields in the whole plate. The results show that the displacement obtained from the analytical formulation at the center point of the plate is well compared with that from FEM calculation. However, the accuracy of the numerical bending stresses near the region where material changed abruptly is doubtful. The second part of this thesis is to discuss the mechanical similarity of a FGM beam and a FGM plate. Consider a FGM plate with opposite edges free and simply-supported, respectively. It shows that the FGM plate with zero Poisson’s ratio can be treated as the beam for all a/b ratio. For non-zero Poisson’s ratio (say, 0.3), the FGM plate and beam are similar only when a/b ratio getting larger enough (e.g. more than 15.)

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