本研究主要以傅立葉級數展開方式推導功能梯度材料板於兩對邊為簡支端、另兩對邊為自由端受溫度載重之理論級數解，且運用MARC有限元素軟體，驗證所推導之理論公式之正確性，並進一步探討其力學分析。
在分析過程中，探討楊氏模數、熱膨脹係數在 方向呈冪次函數、S型函數及指數型函數分佈之功能梯度材料板受線性溫度與等溫度之作用其內部的撓度、應變、應力。
分析結果顯示，板頂與板底之楊氏模數比、熱膨脹係數比、溫度載重比或冪次方在特定比值時，可控制撓度變形為零，或不為零之等撓度變形。

The main purpose of thesis is to analyze Functionally Graded Material plates with two opposite edges simply supported and the other two edges free by Fourier series expansion. The numerical solutions by MARC software of finite element method are obtained and compared with analytical solutions.

In analysis process, the Functionally Graded Material (FGM) plates with Young’s modulus, and the coefficients of thermal expansion obeying the power-law, sigmoid, or exponential functions along thickness direction are under investigated. In addition, the internal deflection, strain and stress will be considered under constant thermal distribution or liner thermal distribution in the z direction.

Results reveal that the deflection is zero or nonzero constant, when the ratio of Young’s modulus ratio, coefficients of thermal expansion ratio, and temperatures at the top and bottom of the FGM plates, and the exponential parameter of material property are certain values.

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