本文主要以Levy-solution理論建立x向對邊為簡支端，y向對邊為任意支承的均佈彈性支承之功能梯度材料(FGM)板受橫向軸壓的平衡方程式與諧和方程式，進而代入y向的邊界條件而解出其挫屈載重。研究結果顯示，楊氏模數比與材料指標相同下，改變材料分佈模式對於其挫屈載重的影響劇烈，在邊界條件的改變下支承對板的束制能力越強，對於挫屈的束制較為強烈，增加彈性支承的勁度對於抵抗挫屈有明顯之效果。

The main purpose of this thesis is to establish the equilibrium and compatibility equations for FGM rectangular plate subjected simple-support at both x side and arbitrary support at the other side , uniform elastic support on the bottom plate, by using the Levy-solution. The buckling equation obtained after giving the boundary condition of y side and analyze the critical load after giving the parameter of material property. Two kinds of boundary conditions are considered. One is to subjected simple-support at both x side with free end at both y side and another is simple-support at both x side with fixed end at both y side. It is assumed that the Poisson’s ratio of the plate remains constant and the Young’s modulus vary along the thickness direction. The research is concentrated to three kind of distribution of Young’s modulus, which are power-law (P-FGM), sigmoid function (S-FGM), and exponential function (E-FGM). Moreover, extending the research to FGM coated plate and FGM undercoated plate to complete this article. To prove the accuracy of analytical solution, the numerical solutions by MARC software of finite element method are obtained and compare with the analytical solution. Results show that the variation of Young's modulus distribution affects the buckling behaviors of the FGM plates seriously. When the plate resist buckling fixed end better than free end. Increase elastic support’s stiffness can Improve the buckling load.

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