本文探討非對稱複合材料疊層板的修復問題，利用針對非對稱疊層板之拉伸彎矩耦合現象所提出的邊界積分式[38]，將其擴展至外部修補情況。分別在含有橢圓孔洞的疊層板(Laminated plat)和疊層板補片(Patch)之間的重疊區域加入因相互作用力而產生的內力之面積分項到各自的邊界積分式中，並透過推導力平衡方程式以及位移連續條件使得兩者在接合處上完美結合。接著利用類史磋公式(Stroh-like formalism)對非對稱複材疊層板的拉伸彎矩耦合現象所得到通解[9]，用以分析以上兩個不同的邊界積分式。
為了驗證本文所提出的外部修補問題分析方法，我們將邊界積分式與其基本解融入由本師門開發的AEPH (Anisotropic Elastic Plates_Hwu) 結構分析程式中進行數值分析。接著透過商用軟體ANSYS中的殼元素來比較本文所提出的邊界元素法和有限元素法兩種方法之結果和差異。最終的實驗結果顯示，本文所提出的邊界元素法計算外部修補問題的分析方法在位移場具有良好的準確性和可靠性。然而，在疊層板中的應力場未能提供出合理之解答，造成此現象的原因以及後續探討將會在本文4.5節討論。

This paper investigates the repair issues associated with composite laminates, specifically focusing on the phenomenon of coupled stretching-bending in asymmetric laminates. To address this problem, we extend the boundary integral equation by incorporating the area terms that account for the internal forces generated between two plies overlapping in laminates. By employing the equilibrium equations and displacement continuity equations, we achieve a seamless integration of the boundary integral equation for laminates with elliptical holes and laminate patches. Additionally, we employ the Stroh-like formalism to obtain a general solution for the coupled stretching-bending phenomenon in asymmetric composite laminates, which is then utilized to analyze the two aforementioned boundary integral equations.

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