基於Reissner混合變分原理（Reissner’s mixed variational theorem, RMVT）有限圓柱層殼法（finite cylindrical layer methods, FCLMs）之歸一理論，發展具簡支承之疊層壓電中空圓柱殼嵌入功能性梯度彈性材料(functionally graded elastic material, FGEM)核心層之擬三維(quasi-three-dimensional, quasi-3D)挫屈分析。這類圓柱殼承受軸向壓力並在內、外表面上具有開放或封閉迴路邊界條件。使用三維線性挫屈理論，其中一組薄膜應力是由挫屈前狀態預先定義的三維位移場推衍求得。FGEM核心層則依兩相材料之體積分率的冪級數函數組合而成，其有效材料性質將以兩相材料混合原理(the rule of mixtures)和Mori-Tanaka微觀定理來估計。數值範例中使用不同階數在厚度方向擴展彈性場和電場變數的FCLM解，藉由比較它們的解與文獻提供的三維精確解來評估FCLM之精度和收斂率。文中亦綜合探討材料性質梯度指標、不同表面條件和長-厚比對圓柱殼臨界挫屈載重之影響。

A unified formulation of Reissner’s mixed variational theorem-based finite cylindrical layer methods (FCLMs) is developed for the quasi-three-dimensional (3D) buckling analysis of simply-supported, sandwich piezoelectric circular hollow cylinders embedded with a functionally graded elastic material (FGEM) core. These cylinders are subjected to axial compression and with open-/closed-circuit boundary conditions on the lateral surfaces. A 3D linear buckling theory is used, in which a set of membrane stresses is determined using a set of predefined 3D deformations for the pre-buckling state. The material properties of the FGEM core are assumed to obey the power-law distributions varying through the thickness coordinate of this according to the volume fractions of constituents, and their effective material properties are estimated using the rule of mixtures and Mori-Tanaka’s micromechanics scheme. The accuracy and convergence rate of the FCLMs with various orders used for expanding the elastic and electric variables in the thickness direction are assessed by comparing their solutions with the exact 3D ones available in the literature. A parametric study with regard to the effects of material-property gradient index, different surface conditions and aspect ratios on the critical loads of the cylinder are undertaken.

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