本文基於Reissner之混合變分理論(Reissner’s mixed variational theorem，RMVT)發展弱形式有限環形柱體元素法(finite annular prism methods，FAPMs)，進行雙向功能性梯度(functionally graded，FG)材料圓板於不同邊界條件以及彈性載重下之靜力分析。文中將圓板分割成數個環型柱體元素，各別元素將以三角函數以及拉格朗日多項式函數對其環向與徑向-厚度方向表面內插基本量場之變化。假設圓板之材料性質遵循沿徑向-厚度表面體積分量之組成之雙向性冪次函數分佈或雙重指數變化之指數函數分佈。簡支承與固定端邊界之受載FG圓板以FAPM求出之解與文獻中以三維彈性力學理論和二維進階板理論比較下皆有良好表現。

A weak-form formulation of finite annular prism methods (FAPM) based on the Reissner’s mixed variational theorem (RMVT), is developed for the quasi three-dimensional (3D) static analysis of two-directional functionally graded (FG) circular plates. The material properties of the circular plate are assumed to obey either a two-directional power-law distribution of the volume fractions of the constituents through the radial-thickness surface or an exponential function distribution varying doubly exponentially through it. These FAPM solutions of FG circular plates are in excellent agreement with the solutions obtained available in the literature.

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