藉由類史磋公式(Stroh-like formalism)，能夠找出針對非對稱複材疊層板之拉伸彎矩偶合分析的通解。由於類史磋公式的通解及材料特徵關係之數學形式與應用於二維異向性彈性力學的史磋公式(Stroh formalism)相同，許多在二維問題使用的尋解方法可直接應用於拉伸彎矩偶合分析。倘若相對應二維問題之場域解已被推導，在通解與邊界條件之數學形式相同的條件下，某些拉伸彎矩偶合之特定問題的解析解能夠簡易地導出。運用以上之優勢，在本文中，將推導含彈性異質之疊層板受均佈負載與集中負載的解析解。其中集中負載的答案一般稱為格林函數(Green’s function)，由此能計算出邊界元素分析所需的基本解，並帶入針對拉伸彎矩偶合分析的邊界積分式，即可發展出含彈性異質複材疊層板之特殊邊界元素分析。
將以上異質問題之解析解與格林函數融入本師門研發之結構分析程式AEPH (Anisotropic Elastic Plates_Hwu)進行數值分析，並透過商業軟體ANSYS內的殼元素，比較解析解、特殊邊界元素法與有限元素法之間的結果與差異，藉此驗證本文提出的關於異質問題之分析方法。另外透過調整彈性異質之幾何尺寸與材料性質，上述解析解與特殊邊界元素法亦可應用在含孔洞/裂縫/直線異質/剛性異質疊層板之拉伸彎矩偶合分析。

Through Stroh-like formalism, whose mathematical form is identical to Stroh formalism for two-dimensional linear anisotropic elasticity, the general solutions for unsymmetric composite laminates with bending extension coupling have been derived. Due to such analogous form, most of the mathematical techniques developed for two-dimensional problems can be transferred to the coupled stretching-bending problems. With such advantage, in this thesis the field solutions for laminates with elastic inclusions subjected to uniform loading at infinity or to concentrated loading will be derived. With the solutions for concentrated loading, generally called “Green’s functions”, the fundamental solutions in the boundary element method can be calculated, and the special boundary element analysis for composite laminates with elastic inclusions will be presented. After comparing the results among the analytical solutions, special boundary element method, and shell element of finite element method, we verified our analyses presented in this thesis with the demonstration of the advantage for our analytical solutions and special boundary element method.

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