本論文主要目的在於分析探討功能梯度中空圓盤或圓柱的應力場。假設楊氏係數與密度沿徑向方向呈冪次方函數變化，且視蒲松比為常數，根據彈性力學的小位移理論，分別推導出單層與雙層中空圓盤在同時承受內壓、外壓與旋轉時的應力解析解，並以圖表的方式探討材料非均質性對於應力場的影響。就單層中空圓盤而言，探討圓盤分別在承受內壓、外壓或旋轉時，應力場在不同非均質材料參數下的變化；就雙層中空圓盤而言，著重於探討圓盤之應力場與干涉量間的相互關係，並考慮不同材料分佈下，若圓盤間接觸壓或干涉量保持相同時，兩圓盤不發生鬆脫的臨界角速度；除此之外，本文推導所得之應力場，可以退化至數個文獻上已經發表之案例，藉此證明本論文結果之正確性。

The purpose of this thesis is to investigate the stress field of functionally graded hollow disks or cylinders. The Young’s modulus and density are assumed to vary along the radial direction in a power law and Poisson’s ratio is assumed as a constant. The exact solutions for stresses in single-layered and double-layered functionally graded hollow disks or cylinders under internal pressure, external pressure and rotation are obtained by using the infinitesimal theory of elasticity. The effects of material inhomogeneity on stress field will be discussed graphically. As to a single-layered hollow disk, the stress field with different nonhomogeneous material parameter subjected to internal pressure, external pressure or rotation, respectively, will be discussed. For double-layered hollow disks, the dependency of stress field on the interference will then be emphasized. The critical rotating speed of the compound hollow disk can be determined when the contact pressure or interference between the disks is kept constant and the material distribution is varied. In additions, the derived stress field solutions can be reduced to several simple problems and compared well with the results previous studies.

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