摘 要
本文根據三維電彈性力學理論，藉由微擾法，進行含壓電材料之開放型圓柱層殼受力場或電場作用下的静定撓曲問題之解析。首先，透過圓柱座標系將三維電彈性力學之22條基本方程式重新組合，消去曲面應力場量，並以彈性位移、橫向應力、電位差與電位移等8個場量為主要變數，將22條基本方程式化簡為8條微分方程式；再經由適當的無因次化處理，使用漸近展開法，將各場量展開成與一微小參數相關之冪級數型式，則原三維基本方程式可分離成不同階數、層次分明且具遞迴特性之微分方程組。依序將各階微分方程式沿厚度方向進行連續積分，並透過雙傅立葉級數展開，可導出由低階至高階遞迴型式之二維控制方程式，其中，古典殼理論即為此近似理論之首階近似解。根據低階場量解得高階修正場量，有系統地逐階循環修正，可求得收斂之精確解。文中應用推得之含壓電材料開放型複合圓柱層殼之三維漸近理論，解析四邊皆為簡支承且受正弦型式分佈外力場、或電場作用下之數值範例，其數值顯示，無論在收斂性和精確度上均有理想之結果。

ABSTRACT
An asymptotic theory of laminated piezoelectric cylindrical shells is developed on the basis of three-dimensional (3D) linear piezoelectricity. The twenty-two basic equations of 3D piezoelectricity are firstly reduced to eight differential equations in terms of eight primary variables of elastic and electric fields. With mathematical means such as nondimensionalization, asymptotic expansion and successive integration, recurrent sets of governing equations for various order problems can be obtained. The two-dimensional equations in the classical laminated piezoelectric shell theory (CST) are identical to those of first-order approximation to the 3D piezoelectricity. The first-order solutions can be determined by solving these equations of which expanded with Double Fourier Series，and the present corrections may amend the value of the higher-order field. Finally, 3D piezoelectricity solutions could be approached in a systematic and recursive way. There are several benchmark solutions for various laminated piezoelectric cylindrical shells given to demonstrate the performance of the theory.

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