本文致力於以Reissner混合變分原理(the Reissner mixed variational theorem, RMVT)為起源，發展有限層殼元素法(finite cylindrical layer methods, FCLMs)，並將其應用於多層疊合功能性材料簡支承中空圓柱殼受純軸壓、純圍壓、或軸圍壓組合載重作用下之三維線性挫屈分析。本文定義功能性梯度材料的材料性質在厚度方向呈冪級數變化。理論推演中，將圓柱殼分割為一系列的有限層殼元素，使用傅立葉函數與Lagrange多項式函數對各層內外表面之主要變數進行內插，且在階數的選用上各變數是獨立的，可選用線性、二階或三階函數分布來做厚度方向的參數模擬。本RMVT有限圓柱層殼元素法所求得之數值解，將與既有文獻中之二維或三維理論解進行精度與收斂率之檢核。此外，亦進一步探討材料性質、載重強度、正交比、圓柱殼長度與半徑比和半徑與厚度比等效應對臨界挫屈載重值之影響。

The unified formulations of finite cylindrical layer methods (FCLMs) based on the Reissner mixed variational theorem (RMVT) are developed for the three-dimensional (3D) linear buckling analysis of simply-supported, multilayered functionally graded material (FGM) circular hollow cylinders and laminated composite ones under pure axial compression, external pressure, and combined axial compression with external pressure. The material properties of the FGM layer are assumed to obey the power-law distributions of the volume fraction of the constituents through the thickness coordinate. In these formulations, the cylinder is divided into a number of finite cylindrical layers, in which the trigonometric functions and Lagrange polynomials are used to interpolate the in- and out-of-surface variations of the primary variables of each individual layer, respectively, as well as the related order of each primary variable can be freely chosen, such as the layerwise linear, quadratic or cubic function distribution through the thickness coordinate. The accuracy and convergence of the RMVT-based FCLMs developed in this article are assessed by comparing their solutions with both the exact 3D and accurate two-dimensional (2D) solutions available in the literature. A parametric study for variations of the lowest critical load parameters with the material-property gradient index, and the load intensity, orthotropic, length-to-radius ratio, and radius-to-thickness ratios is carried out.

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