本文基於Reissner混合變分原理(Reissner’s mixed variational theorem，RMVT)，發展半解析有限環形柱體法(semi-analytical finite annular prism method，FAPM)作為雙向功能性梯度(functionally graded，FG)圓錐殼，於變化邊界條件下承受正弦分佈或均佈載重時的三維(three-dimensional，3D)應力與變形分析。在此理論中，FG圓錐殼的斷面被分割為一定數量的有限環形柱體元素，其中利用傅立葉函數以及拉格朗日多項式，分別對圓錐殼的環向及每一環形元素中作為場量主變數的子午線-厚度面之場量變數進行內插。假設FG圓錐殼的材料成份體積分量於子午線-厚度面遵循雙向冪次函數分佈，其有效材料性質則利用兩相材料混合定律推估。本文FAPM的分析結果證明其解收斂迅速，且其收斂解與文獻中的3D分析解高度契合。

Based on the Reissner’s mixed variational theorem (RMVT), a semi-analytical finite annular prism method (FAPM) is developed for three-dimensional (3D) static analyses of bi-directional functionally graded (FG) truncated conical shells. The material properties of the FG truncated conical shell are assumed to obey a bi-directional power-law distribution of the volume fractions of the constituents through the meridian-thickness surface, the effective material properties of which are estimated using the rule of mixtures. Implementation of the current FAPMs shows their solutions converge rapidly and that the convergent solutions are in excellent agreement with the 3D solutions available in the literature.

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