本論文主要以等效均質法(EHM)來分析FGM板，原先FGM板內部材料分佈較為複雜，首先透過等效均質法將FGM板等效均質化成楊氏模數為E之均質板，再找出均質板與FGM板之間的關係，其為等效位移比、等效應變比、等效應力比，最後利用等效轉換比能將均質板之力學結果轉換成FGM板之力學結果。此法不僅能用在理論分析，也能應用於有限元素分析。本文使用三種材料分佈形式，分別為S型函數(S-FGM)、S型函數濺鍍板(S-FGM coating)、S型函數介面塗層板(S-FGM undercoating)，並考慮兩種形狀的板，分別為矩形及圓形。文中考慮兩種邊界條件:(1)板周圍為簡支端；(2)x向對邊為簡支端，y向對邊為自由端，且皆受均佈載重作用。並在第五章單獨加入溫度載重進行討論。為了驗證等效均質法的正確性，以有限元素軟體分析板之位移、應變、應力，再跟FGM的結果進行比較。
研究結果顯示，與文獻中的理論解相比，在有限元素運算中，EHM的誤差小於FGM的誤差。此外，在有限元素運算中，使用EHM可以減少因為FGM材料分布所造成的誤差。

The main purpose of this thesis is to develop the equivalent homogenization method (EHM) to easily and effectively investigate the mechanical behaviors of the rectangular or circular FGM plates, in which the material distribution is more complicated, subjected to transverse load or thermal load. First, the equivalent homogeneousYoung's modulus of the FGM plate is defined and determined. Then the expressions of the equivalent ratios which are the equivalent displacement ratio, the equivalent strain ratio, and the equivalent stress ratio are estimated. Finally, the displacement, strain, and stress of the FGM plate can be easily determined by multiplying the results of the homogenous plates by the equivalent ratios. It is noted that the EHM can not only be used in the theoretical analysis but also in finite element analysis. In this study, three kinds of material distributions, S-FGM, S-FGM coating, and S-FGM undercoating are under consideration. Two kinds of boundary conditions are considered. One is the simply supported at all edges, and the other is simply supported along two opposite edges and free along other edges. The correctness of the equivalent homogenization method is verified by comparing the results obtained by proposal method with those of the finite element calculations.
The result shows that the error using the EHM is much smaller than that utilizing the FGM plate theory in finite element calculation when comparing with the theoretical solutions in the literature. In addition, the use of the EHM can reduce the error attributed to the material distribution of the FGM plates in finite element calculation.

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