臺灣博碩士論文加值系統

　　本論文提出以微分值積法(Differential Quadrature Method)來分析複合層板之脫層挫曲行為。層板的控制方程式以古典積層板理論為基礎，先經過座標轉換後，再以微分值積法則將層板控制方程式轉換成代數方程，最後求解其特徵值，即為脫層層板的挫曲應變。求解挫曲應變的過程中，將脫層之橢圓形層板透過座標轉換轉成正方形後，利用Jacobian轉換關係式可得到一組新的權值矩陣。本研究的結果與文獻上所提供的結果比較都相當吻合，驗證了微分值積法的準確性。本文並探討脫層區域之半軸長度變化及不同纖維角度對脫層層板之挫曲應變的影響。結果顯示微分值積法於複合層板脫層挫曲應變的分析非常方便及快速，並且具有良好的準確性。

　　In this thesis, the delamination buckling of laminated plates based on the classical laminated plate theory is investigated by using the differential quadrature method (DQM). By using the quadrature rule, the governing equations of laminated plate in the differential form are transformed into algebraic equations, from which we solve for the eigenvalues, the buckling strains. In the solution process, we use coordinate transformation to transform the elliptical laminate into a square, then we use the Jacobian transformation to obtain a new weighting matrix. To evaluate the accuracy of the DQM, numerical results obtained by the DQM are compared with the solutions in the literature. Furthermore, effects of the length of semi-axis and the fiber angle on the buckling strain are studied. Numerical results show the high accuracy, efficiency, and convenience of the DQM.

摘要............................................i
英文摘要.......................................ii
致謝..........................................iii
表目錄.........................................vi
圖目錄........................................vii

第一章 緒論....................................1
1-1 研究動機..............................1
1-2 文獻回顧..............................2
1-3 本文研究..............................5

第二章 複合層板之控制方程式....................6
2-1 位移場................................6
2-2 應變-位移與應力-應變關係式............6
2-3 控制方程式...........................10
2-4 邊界條件.............................13

第三章 微分值積法.............................14
3-1 微分值積法的原理.....................14
3-2 取樣點...............................16
3-3 新的權值矩陣.........................17
3-4 微分值積法的應用.....................23
3-5 邊界修正矩陣之調整...................26

第四章 數值模擬結果與討論.....................27
4-1 收斂性與準確性分析...................27
4-2 鋁板.................................28
4-3 [0/90]不對稱纖維排列複材層板.........28
4-4 不同纖維角度之複材單層層板...........29

第五章 結論...................................31

參考文獻.......................................32
自述...........................................43

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