當結構由多個不同部件組成，且每個部件由不同材料製成時，在結構的某些局部區域可能會出現許多界面角。由於材料性質的不一致，應力奇異性可能會在這些地方發生，從而引發結構失效。因此，設計適當的接頭以防止失效的發生和擴展是非常重要的。應力的奇異階次及其相關的應力強度因子是理解失效開始的兩個重要參數。由於一般界面角的奇異階次可能是實數或複數，相異或重複，為描述不同類型的界面，已經推出了多種不同的應力強度因子的定義。為了在所有種類的界面角（包括裂縫和界面裂縫）之間建立直接的聯繫，先前的研究提出了一種統一的應力強度因子定義。為了準確且高效地計算這一統一定義的應力強度因子，本研究使用滿足界面連續性條件的基本解建立了一種特殊的邊界元素法。相關的邊界積分方程中涉及的奇異積分，通過設置適當的剛體運動和內插附近非奇異解來近似解決。為了避免在角落附近出現不穩定和不準確的區域，採用了路徑獨立的H積分進行計算，並推導出H積分與應力強度因子之間的關係。此外，本研究為不同的積分路徑提供了H積分所需的位移和曳引力的輔助解。多個數值範例，如界面裂縫、界面邊緣缺口、單搭接接頭和含有脫層的疊層複合材料，展示了本文方法的準確性及正確性。

When a structure is composed of many different parts and each part is made by different materials, it is very possible that many interface corners appear in several local fields of the structure. Due to the mismatch of elastic properties, stress singularity may occur at the interface corners, which will initiate structural failure. Thus, designing a proper joint to prevent the failure initiation and propagation is important. The singular orders of stresses and their associated stress intensity factors are two important parameters for understanding failure initiation. Since the singular orders of general interface corners may be real or complex, distinct or repeated, several different definitions of stress intensity factors have been proposed for different types of interfaces. In order to build a direct connection among all general interface corners (including cracks and interface cracks), a unified definition of stress intensity factors was proposed in our previous studies. To calculate this uni-defined stress intensity factors accurately and efficiently, a special boundary element using the fundamental solution satisfying the interface continuity conditions was established. The singular integrals involved in the associated boundary integral equations are then solved by the setting of proper rigid body motions and the approximation through interpolation of nearby non-singular solutions. To avoid the unstable and inaccurate region near the corners, a path-independent H-integral was suggested, and the relations between H-integral and stress intensity factors are derived. Moreover, the auxiliary solutions of displacements and tractions required in H-integral are provided in this thesis for different integral paths. Several numerical examples, such as interface crack, interface corner, single lap joint, and laminated composites containing delamination, are presented to demonstrate the methodology employed in this thesis.

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