本文提出以Reissner混合變分原理(Reissner’s mixed variational theorem, RMVT)為基礎的有限層殼方法(finite cylindrical layer methods, FCLMs)歸一理論，應用於具簡支承多層複合材料空心圓柱殼以及功能性梯度材料空心圓柱殼受外力作用之三維靜力分析。文中假設功能性梯度材料的材料參數沿厚度方向以指數函數型態分佈。本文中將圓柱殼細分為數個有限圓柱層，其中以三角函數與Lagrange多項式函數對每一離散層各面內與面外變數進行內插，利用h-refinement代替p-refinemen來對求得之數值解進行收斂性探討，在形狀函數厚度方向上的假設可以分成線性、二次與三次多項式函數分布，在有限圓柱層殼方法解的精度上是以文獻中三維彈性力學之的正確解來做比較。此外，文中亦探討本有限層殼方法求得解的收斂率與數值不穩定的情形。

A unified formulation of finite cylindrical layer methods (FCLMs) based on the Reissner mixed variational theorem (RMVT) is developed for the quasi-three-dimensional (3D) analysis of simply-supported, multilayered composite cylinders and sandwich circular hollow cylinders with an embedded functionally graded material (FGM) cylindrical layer, subject to mechanical loads. The material properties of the FGM layer are assumed to obey an exponent-law varying exponentially with the thickness coordinate. In this formulation, the circular hollow 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 field variables of each individual layer, respectively. Because an h-refinement instead of a p-refinement process is adopted to yield the convergent solutions in this work, the layerwise linear, quadratic or cubic function distribution through the thickness coordinate is assumed for the related field variables. The accuracy of the FCLMs developed in this article is assessed by comparing their solutions with the exact 3D ones available in the literature, and the convergence rate and possibility of numerical instability of these FCLMs are also investigated.

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