本文主要在研究具隨機材料性質之功能梯度板(FGM, functionally graded plate)在熱溫度環境中之隨機響應，假設材料性質為隨機變數且隨厚度方向逐漸改變，文中根據板的一階剪變形理論(first-order shear deformation) ，可得功能梯度板的本構方程式(constitutive equations)，以描述功能梯度板之位移及應變與應力的關係，本文並以虛功原理及有限元素法(FEM, finite element method)得到板之統御方程式及近似解，再導入一階擾動法得到功能梯度板響應的平均值及變異數。數值結果顯示，體積指數及溫度場變化對功能梯度板位移響應及應力有顯著的影響，其結果將用蒙地卡羅模擬法驗證之。

The main purpose of the thesis is to study the random responses of functionally graded plates with random material properties in thermal environment. The material properties are assumed to be random variables and graded in the thickness direction. Based on the first order shear deformation theory of plate, the constitutive equations are formulated to describe the relationship among the displacement, strain, and stress of functionally graded plate. The governing equations of plate are derived by using the virtual work principle and solved by using the finite element method. The static response and stress of the functionally graded plates are investigated by varying the volume function of the ceramic and metallic constituents using a simple law distribution. At last a perturbation technique is employed to obtain the first-order response statistics-mean and variance of the flexural deflection of plate. The results show that the volume fraction and the temperature field distribution have significant effect on both the static displacement response and stress of the functionally graded plate. The results are also verified by using the Monte Carlo simulation.

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