摘要
　　本文以三維漸近展開的解析模式來分析複合層板的力學行為。基本作法是視疊層板沿厚度方向為異向性材料所組成的構件，先從三維彈性方程式出發，不對位移場及應力場先預作假設，將其重新組合，利用無因次化，推導出三維彈性力學基本方程式及各場量，並將位移與應力分量對一個與板厚相關之微小參數作漸進展開，可得漸進展開模式中的各階層控制方程式。接著再搭配「微分再生核近似法」原理，來做數值模擬。和一般數值方法不同的是，微分再生核近似法在求解形狀函數之高階導數時具有高度的效率及精確性，很適合分析漸進展開後具有高階微分狀態的各階層控制方程式。

　　本文最後選取了一橢圓正交複合層板來分別用三種不同疊層形式的順序及夾緣邊界支承。而所得之結果和解析解相比較後，都證明我們可以得到合理準確的數據。故漸進展開解析理論搭配再生核近似法作數值分析，實為一良好的選擇。

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