本文發展基於Reissner混合變分原理（Reissner’s mixed variational theorem，RMVT）的有限圓柱層殼法（finite cylindrical layer methods，FCLMs）歸一理論，探討應用於具簡支承邊界條件，單層、雙層及多層功能性壓電材料（functionally graded piezoelectric material，FGPM）組成的中空圓柱殼，在表面開放和封閉迴路條件下，殼承受電彈耦合荷載之靜態分析。文中考慮四種不同形式的電彈荷載，分別作用於中空圓柱殼的內、外表面。分析時，將中空圓柱殼切割成有限數量的圓柱殼層，並假設中空圓柱殼的材料性質沿著厚度方向呈指數變化。三角函數及Lagrange多項式函數分別用來內插各主變數在面內(in-plane)及厚度方向之變化。此外，沿著厚度方向展開的變數，其階數可以自由選擇，可以為線性(linear)、二次(quadratic)及三次(cubic)。文中亦將進行多層FGPM中空圓柱殼承受電彈荷載作用下之靜態電彈耦合行為之參數分析與綜合比較。

A unified formulation of Reissner’s mixed variational theorem-based finite cylindrical layer methods is developed for the static analysis of simply-supported, multilayered functionally graded piezoelectric material (FGPM) circular hollow cylinders. The material properties of the cylinder are assumed to obey an exponent-law exponentially varying through the thickness coordinate of this. The trigonometric functions and Lagrange polynomials are used to interpolate the in-surface and thickness variations of the primary variables of each individual layer, respectively. The coupled electro-elastic effects on the static behaviors of multilayered FGPM cylinders are closely examined.

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