本文以改良Pagano 方法探討兩邊簡支承之多層疊合功能性梯度材料(或三明治板)和纖維增強複合材料(the fiber-reinforced composit material,FRCM)中空圓柱殼在受軸壓狀態下的挫屈行為分析。假設功能性梯度材料(the functional graded material, FGM)的每層材料參數隨著厚度座標呈現二相材料體積比的冪級數變化。Pagano 方法是基於虛位移原理(the principle of virtual displacement, PVD)，傳統上是用來分析纖維增強複合層板之結構行為，本文則將其改良成可以分析多層疊合的功能性材料圓柱殼，其中改良的部分如下:(a)以Reissner 混合變分原理(Reissner’s mixed variational theorem, RMVT)代替以位移為基礎的虛位移原理進行解析;(b)利用Euler 公式將系統方程式之解由複數解型態轉換為實數解型態;(c)應用連續近似法，將功能性梯度材料圓柱殼切割成多個離散層結構，且各單層之厚度相較於圓心至中曲面的半徑長度微小;(d)使用傳遞矩陣法，可逐層求解系統方程式，提升計算效能。藉由以上改良，便可拓展Pagano 方法應用在解析功能性材料圓柱殼之挫屈問題，並可減少原Pagano 方法耗費之計算時間。文中亦將改良Pagano 法求得之解與既有文獻中之三維彈性力學解進行驗證，結果顯示本改良pagano 解收斂快速且精確。此外，本文亦進行多層疊合功能性梯度材料圓柱殼的長度-半徑比、半徑-厚度比、各層厚度比、材料參數梯度指標對臨界挫屈載重影響之參數分析研究。

The three-dimensional (3D) linear buckling analysis of simply-supported,multilayered (or sandwiched) functionally graded material (FGM) and fiber-reinforced composite material (FRCM) circular hollow cylinders under axial compressive loads is presented. The material properties of each FGM layer in this work are assumed to obey a power-law distribution of the volume fractions of the constituents through the thickness coordinate. The Pagano method, which is based on the principle of virtual displacement (PVD) and is conventionally used for the analysis of laminated FRCM structures, is modified to be feasible for this study for multilayered FGM cylinders, in which Reissner’s mixed variational theorem (RMVT), the successive approximation and thetransfer matrix methods, and the transformed real-valued solutions of the system equations are used. Implementing the modified Pagano method in this subject
shows that the computation of determining the critical loads becomes less time-consuming than is usually the case, and is independent of the total number of layers constituting the cylinders. In addition, the modified Pagano solutions of critical loads of multilayered FRCM cylinders are in excellent agreement with the exact 3D ones available in the literature, and these for sandwiched FGM cylinders may provide as the benchmark solutions to assess the ones obtained using various two-dimensional FGM theories and numerical models.

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