結構健康監測對於工程安全性以及效率上具有極大影響力，逆有限元素法也常被應用，然而傳統模型在位移不連續以及應力集中之區域富有挑戰，因此本研究引進逆擴展有限元素法，其優勢在於不需重新劃分網格且可分配均勻網格，且在逆有限元素法架構中加入水平集方法以及強化形狀函數，試圖解決上述問題。此外，本研究也聚焦在近場動力學，利用鍵結的概念，善於處理結構損傷之位移不連續面會出現應力奇異性等破壞力學挑戰，並將其運用於疲勞壽命預測上。最後，本研究結合運算效率上有優勢之逆擴展有限元素法以及近場動力學對局部區域之敏感度，對於不同開孔之平板進行分析，且展現其運用於結構健康監測之高度潛力。

Structural health monitoring (SHM) plays a pivotal role in ensuring the safety and operational efficiency of engineering structures. While the inverse finite element method (iFEM) has been widely adopted for SHM, conventional models encounter significant challenges when resolving displacement discontinuities and stress concentrations. To overcome these limitations, this study introduces the inverse extended finite element method (iXFEM).By incorporating the level set method and enriched shape functions into the traditional iFEM framework, the proposed iXFEM accurately captures geometric interfaces without the need for remeshing, thereby allowing the deployment of uniform background meshes. Furthermore, this research investigates Ordinary State-Based Peridynamics (OSPD). Leveraging its non-local interaction formulation, OSPD intrinsically overcomes fracture mechanics challenges—such as stress singularities at damage-induced discontinuity surfaces—and is comprehensively applied to fatigue prediction.Ultimately, by coupling the computational efficiency of iXFEM with the localized sensitivity of OSPD, this study successfully analyzes plates containing various macroscopic cutouts, demonstrating the tremendous potential of this integrated framework for advanced SHM applications.

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