本文提出基於Reissner 混合變分原理(Reissner mixed variational theorem,RMVT)之有限層狀元素法(finite rectangular layer methods, FRLMs)應用於具簡支承正交性複合材料矩形板以及功能性材料三明治矩形板受雙軸壓作用之三維線性挫屈分析。文中假設功能性梯度材料的材料參數沿厚度方向以冪級數型態分布。文中將平板細分為數個有限層板，並利用傅立葉函數與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 程序進行收斂性分析。此外，本文將沿著厚度方向改變形狀函數的次數來提高精度，並探討次數的高低對收斂性以及準確性造成的影響，其中本有限層狀法求得的解亦與文獻中三維彈性力學正解以及精準二維數值解進行綜合比較。

Based on the Reissner mixed variational theorem (RMVT), finite rectangular
layer methods (FRLMs) are developed for the three-dimensional (3D) linear
buckling analysis of simply-supported, fiber-reinforced composite material (FRCM)
and functionally graded material (FGM) sandwich plates subjected to bi-axial
compressive loads. In this work, the material properties of the FGM layers are
assumed to obey the power-law distributions of the volume fractions of the
constituents through the thickness, and the plate is divided into a number of finite
rectangular layers, in which the trigonometric functions and Lagrange polynomials
are used to interpolate the in- and out-of-plane variations of the field variables of
each individual layer, respectively, and an h-refinement process is adopted to yield
the convergent solutions. The accuracy and convergence of the RMVT-based
FRLMs with various orders used for expansions of each field variables through the
thickness are assessed by comparing their solutions with the exact 3D and accurate
two-dimensional ones available in the literature.

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