本文以Reissner混合變分原理為基礎，發展有限層狀元素法的歸一理論推衍，並用於具簡支撐功能性壓電材料三明治板在熱荷載作用下的三維熱挫屈及焦電彈耦合分析。該功能性材料核心層的材料性質假設沿厚度方向遵循組分體積分數的冪函數分佈，熱挫屈分析中核心層和表面層的材料性質均考慮為溫度之函數。核心層的有效材料性質由二相混合法則或Mori-Tanaka法則計算。在熱傳分析中則考慮固定溫度和熱對流兩種表面條件。文中將不同階數的有限層狀元素法解與文獻中的三維精確解進行比較，驗證其精確度與收斂性。此外，在上述分析的基礎上，本文還發展了一種結合複合形法的混合基因演算法，用於探求功能性材料板在穩態熱荷載作用下之最佳化材料組分最佳化，期使最小化板內的熱應力。此分析中板被人為劃分為Nl層，材料組分沿厚度的分佈假設為特定函數或非特定函數，並比較兩者的結果。

Based on Reissner’s mixed variational theorem (RMVT), a unified formulation of finite layer methods (FLMs) is developed for the quasi-three-dimensional (3D) thermal buckling and coupled thermo-electro-mechanical analysis of simply-supported, sandwich piezoelectric plates embedded with a functionally graded elastic material (FGEM) core, the material properties of which are considered to be thickness-dependent. In addition, a hybrid genetic algorithm with the complex method is developed for the optimization of the material composition of a multi-layered functionally graded material plate with temperature-dependent material properties in order to minimize the thermal stresses induced in the plate when it is subjected to steady-state thermal loads.

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