本文應用 Reissner 混合變分原理，配合既定之整體三階位移場和局部二階應力場假設，忽略側向正向應力之效應，推衍二維剪力變形理論，並將本理論應用於功能性異相非均質材料板之靜態問題解析。本理論對於各全域與局部域變數之假設，可滿足層間界面應力與位移的連續條件。在功能性材料的性質假設上，本文不僅討論冪次型態的材料參數，更加入級數型態的材料參數範例。根據Reissner 混合變分原理可得到一組Euler_Lagrange方程式與邊界條件，基於分離變數法將各變數以傅立葉級數展開後，本理論可應用於功能性異相非均質材料板之靜態問題解析，並進一步討論材料參數之冪次與範例板之寬厚比對於本理論適用範圍的影響。

A Reissner mixed variational theorem (RMVT)-based third-order shear deformation theory (TSDT) is developed for the static analysis of simply-supported, multilayered functionally graded material (FGM) plates subjected to mechanical loads. The material properties of the FGM layers are assumed to obey either the exponent-law distributions through the thickness coordinate or the power-law distributions of the volume fractions of the constituents. In the present theory, Reddy’s third-order displacement model and the layerwise parabolic function distributions of transverse shear stresses are assumed in the kinematic and kinetic fields, respectively, a priori, where the effect of transverse normal stress is regarded as minor and thus ignored. The continuity conditions of both transverse shear stresses and elastic displacements at the interfaces between adjacent layers are then exactly satisfied in the present RMVT-based TSDT. On the basis of RMVT, a set of Euler_Lagrange equations associated with the possible boundary conditions is derived. In conjunction with the method of variable separation and Fourier series expansion, the present theory is successfully applied to the static analysis of simply-supported, multilayered FGM plates subjected to mechanical loads. A parametric study of the effects of the material-property gradient index and the span-thickness ratio on the displacement and stress components induced in the plates is undertaken.

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