複材疊層板不僅僅利用在航空領域上，也運用在許多的工程應用上。複材疊層板的偶合效應更是在世界上被廣泛探討的。基於複材疊層板的可設計性，許多工程設計者常常利用其偶合效應來完成一些金屬材料或對稱性複材疊層板所沒有的特性，其中常見的偶合效應有：拉伸-彎曲偶合效應、磁場-電場-機械偶合效應及其在溼熱環境下的效應等等。因為孔洞/裂縫的存在對材料與結構強度的影響一直是大家所關心的問題，為了要有效且有系統的解決此類的問題，最近我們建立了複材疊層板拉伸-彎曲偶合分析之類史磋公式，更利用此套公式進一步發展出複材疊層板在溼熱環境下及其磁場-電場-機械偶合效應分析。在此類史蹉公式中，我們刻意將所有相關數學列式寫成和二維問題一模一樣之型式，因此，含孔洞/裂縫的複材疊層板之各種偶合分析之相關問題必可迎刃而解。利用此類史蹉公式，一些以前對於含壓電磁效應及在溼熱環境的複材疊層板所不能解決的問題之解析解，如今都可以利用此公式得出。除此之外，我們也可得出含孔洞之複材疊層板其孔洞邊緣之合力的解析式及含裂縫的複材疊層板之應力集中函數。為了要展示及驗證我們的成果，數個含孔洞/裂縫之複材疊層板的各種偶合效應分析的實用案例將在此論文中被探討，並利用商業有限元素分析軟體－ANSYS佐證，以顯示我們結果的正確性、簡單性及一般性。

　Since the composite laminates are now in widespread use, not only in traditional areas like aerospace, but also in many engineering applications. Many coupling phenomena within the composite laminates are widely focused in the world. Due to the designable characteristics of composite laminates, the engineering designers always want to utilize the coupling effects to do something that cannot be achieved by using metallic or symmetric laminates. Some of these coupling effects are stretching-bending and magneto-electrical-mechanical couplings in hygrothermal environment. Because of the stress concentration, the understanding of these coupling effects on holes/cracks in laminates becomes important for the practical engineering design. In order to establish a systematic analytical approach for these problems, recently we developed a Stroh-like formalism for coupled stretching-bending analysis for composite laminates. Based upon this formalism, an extended Stroh-like formalism for coupled stretching-bending analysis under hygrothermal environment and for magneto-electro-elastic composite laminates can be constructed in this thesis. In the newly developed Stroh-like formalism for various coupling conditions, most of the relations are purposely organized into the forms of Stroh formalism for two-dimensional problems. Thus, many unsolved problems of composite laminates in various coupling conditions may be solved directly from their corresponding two-dimensional problems. By using the Stroh-like formalism introduced in this thesis, the explicit solutions for an unbounded laminate, symmetric or unsymmetric, disturbed by an elliptical hole and/or a crack under hygrothermal and/or magnetoelectrical environment or not, are now obtained. Moreover, through the use of some identities derived in this thesis, the resultants around the hole boundary are obtained explicitly in real form. The stress intensity factors of cracks in composite laminates are also given in this thesis. To illustrate the generality of our analytical solutions, several numerical examples are presented to discuss the coupling effects of laminates, the shape effects of holes and stress intensity factors of laminates. The ANSYS finite element software package is also used to compare our results, which shows that our solutions are exact, simple and general.

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