論 文 摘 要

本論文研究功能梯度材料板於兩對邊簡支端、另兩對邊為梁，承受均佈橫向載重之力學分析，將問題拆解成五個小題，根據疊加原理，求解出板邊緣撓度、邊緣旋轉角，以傅立葉級數(Fourier Series)展開求出於包森比 為常數、楊氏模數沿著板的厚度方向變化之FGM板連接梁之理論級數解，並與有限元素軟體MARC分析數值解，以驗證理論解之正確性。而分析之楊氏模數分佈形狀有冪次方函數(P-type)、S型函數(S- type)及指數函數型(E- type)等三種體積分佈函數，板之型態有FGM板、FGM濺鍍板及FGM界面塗層板，比對其於FGM板中點沿著 方向之應力、應變以及在 平面上沿著 方向之撓度變化；在理論解部份，探討FGM板邊緣與梁間的邊緣撓度、旋轉角與邊緣反力、邊緣彎矩之間的關係，考慮改變梁剛度大小知情況下，梁剛度對FGM板撓度之影響。

ABSTRACT

The main purpose of this research is to analyze the mechanical analysis of FGM plates with two opposite edges simply supported and two other edge beams subjected to uniform load by Fourier series expansion. It is assumed that the Poisson’s ratio of the FGM plates remains constant, however the Young's modulus of the FGM plates vary along the thickness direction. The study is concentrated to three kinds of distributions of Young's modulus, which are power-law function (P-FGM), sigmoid function (S-FGM), and exponential function (E-FGM). And three type of plates which are FGM plates, FGM coated plates, and FGM undercoated plates are under considered.

To obtain the analytical solution, the problem is divided into five topics first, and then according to the principle of superposition, the edge deflections and edge rotations of the plate are solved. The analytical solutions are compared with the numerical solutions obtained by MARC software of finite element method. Results show that the analytical solutions of the stresses in the center of the FGM plate, the strains along the z-direction, and the deflections along the y-axies agree very well with the numerical solutions. Moreover, the study is also focused on the effects of the stiffness of the edge beams on the deflections of the FGM plates.

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