結構健康監測 (Structural Health Monitoring, SHM) 在確保工程結構之安全性與耐久性方面扮演關鍵角色。近年來，逆有限元素法 (Inverse Finite Element Method, iFEM) 已廣泛應用於各類SHM領域。然而，傳統iFEM模型在監測應力集中與結構奇異行為時仍面臨顯著挑戰。為此，本研究提出一種創新的逆擴展有限元素法 (Inverse Extended Finite Element Method, iXFEM)，以應用於含強不連續與弱不連續損傷結構之健康監測。所提出的iXFEM方法將水平集方法 (Level set method) 與增強形狀函數 (Enriched shape functions) 引入iFEM架構中，藉以提升其對幾何與材料不連續性之解析能力。此外，本研究亦探討於在iXFEM架構下引入h-與p-局部網格加密技術，以提升應力集中區域之解析精度。透過多個裂縫、挖孔、夾雜物以及雙重材料平板的數值分析，驗證iXFEM能在使用有限數量應變感測器的情況下，有效監測結構與破壞響應，顯示iXFEM在SHM應用中的高度潛力。

Structural Health Monitoring (SHM) plays a critical role in ensuring the safety and durability of engineering structures. In recent years, the Inverse Finite Element Method (iFEM) has been widely applied across various SHM domains. However, conventional iFEM models still face significant challenges in capturing stress concentrations and singular behaviors. To address these limitations, this study proposes a novel Inverse Extended Finite Element Method (iXFEM) tailored for monitoring structural health in systems exhibiting strong and weak discontinuities. The proposed iXFEM framework integrates the level set method and enriched shape functions into the standard iFEM formulation, thereby enhancing its capability to model geometric and material discontinuities. Furthermore, this study explores the incorporation of local h- and p-refinement strategies within the iXFEM architecture to improve the resolution of stress fields in regions of high gradient or discontinuity. Through a series of numerical simulations involving cracked plate, hole, inclusion, and bi-material interface, the effectiveness of the iXFEM approach is validated. The results demonstrate that accurate reconstruction of structural and failure responses can be achieved using a limited number of strain sensors, emphasizing the significant potential of iXFEM for structural health monitoring.

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