本研究主要是在分析圓形功能梯度板在簡支端之束制下受不同側向載重作用之力學分析。首先推導FGM圓板受到一環狀載重的理論解，以此作為基礎解。再利用此基礎解透過積分得到另外三種載重形式下的理論解，分別為三角形均變載重、二次函數載重及局部均佈載重，最後，理論解與有限元素軟體MARC之分析結果相互比較，以驗證理論推導之正確性。
依照理論解中所要求之圓板尺寸建立有限元素之模型，並且考慮三種材料性質，分別為幕次方函數型、S型函數與指數函數型之FGM板、FGM濺鍍板及FGM界面塗層板，隨著板之勁度的改變，探討在各種不同載重形式下板之位移、應力及應變關係。
結果顯示，受到相同之外力作用時，勁度越小之板其位移和應力就越大，且其理論解與數值解之誤差皆小於5%，因此，本篇論文之理論解將可適用於邊界條件與本論文所提出之相同條件下的情形。

The main purpose of this research is to analyze the mechanical behavior of circular Functionally Graded Materials (FGM) plate with simply supported subjected to different loads young’s modulus of plate changes along the thickness direction.
First, we derive the fundamental solution with the plate subjected ring load. Second, by integrating the fundamental solution, the other three different kinds of loads including triangular load, quadratic function load and partial uniform load are obtained. Finally, the analytical solution is compared with the numerical solution obtained by MARC software of finite element mothod.
The study is concentrated to thee kinds of composites which are FGM plates, FGM coating plates, and FGM undercoated plates. The displacement, stress and strain subjected to different types of loads are discussed.
Finally, the results show that the deflections and the stresses are influenced by the stiffness coefficient . The deflection decreases with the increase stiffness. And
the results reveal that the theoretical solutions are available for case whose
conditions are the same as those in this thesis.

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