本文提出無網格配點法中，微分再生核內插法(Differential Reproducing Kernel, DRK)配合狀態空間法(State Space Methods)，用於求解功能性梯度材料(Functionally Graded Materials, FGMs)之梁結構及圓板結構，探討三維撓曲及自由振動等相關物理問題。
首先探討微分再生核內插法中，核函數中的改善函數及原始函數之選取，討論使用正規化高斯函數、三次曲線函數、四次曲線函數及八次曲線函數的搭配下，形狀函數之差異，並求解均向性材料古典梁受均勻載重下的撓曲分析，並搭配微分擬合法(Differential Quadrature Method, DQM)及解析解，相互驗證其函數搭配之優劣。
再將所挑選出較準確的改善函數及原始函數，使用微分再生核內插法來求解功能性材料基於Reissner 能量泛函數之穩值原理推導混合Timoshenko梁理論之Euler-Lagrange方程式，並設定端點為不同邊界，如：簡支承、固定端及自由端之組合邊界條件，研究其靜態方程式下的各種物理量及精確程度。再運用Hamilton 原理來推導基於Reissner混合變分原理之Timoshenko梁理論之運動方程式，探討其結構於不同組合邊界條件下之自然振動頻率及主變數之模態。
進而使用微分再生核內插法配合狀態空間法來求解軸對稱功能性梯度材料之疊層圓板，將圓板沿厚度切為數個薄層之方式，配合傳遞矩陣法計算其厚度方向之主要變數，與文獻對照及討論其切層數及微分再生核法中階數與點數多寡影響之精確度。

A state space differential reproducing kernel (DRK) method is developed for the three-dimensional (3D) analysis of functionally graded material (FGM) axisymmetric circular plates with simply-supported and clamped edges. The strong formulation of this 3D elasticity axisymmetric problem is derived on the basis of the Reissner mixed variational theorem (RMVT), which consists of the Euler-Lagrange equations of this problem and its associated boundary conditions. The primary field variables are naturally independent of the circumferential coordinate, then interpolated in the radial coordinate using the early proposed DRK interpolation functions, and finally the state space equations of this problem are obtained, which represent a system of ordinary differential equations in the thickness coordinate. The state space DRK solutions can then be obtained by means of the transfer matrix method. The accuracy and convergence of this method are examined by comparing their solutions with the accurate ones available in the literature.

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