Structural health monitoring of shell structures with preexisting cracks

Plate and shell-like structures are widely used in the aerospace, marine, and renewable energy sectors. However, they are susceptible to various defects, especially cracks, during their operational lifespan. Although the inverse Finite Element Method (iFEM) offers significant advantages, such as real-time shape sensing capabilities, its current formulations cannot reconstruct crack mechanics and analyze structures with preexisting cracks. Geometric discontinuities, such as cracks, present unique challenges that require special treatment in fracture mechanics. This study presents a novel inverse crack tip shell element for real-time reconstruction of full-field displacement profiles and computation of Stress Intensity Factors (SIFs), addressing the limitations of current iFEM formulations. The proposed six-node triangular inverse element is flexible in mapping complex geometries and inherently ensures strain singularity at the crack tip by repositioning its mid-side nodes. The proposed inverse formulation is numerically validated against benchmark analytical and high-fidelity Finite Element Method (FEM) reference solutions for varying geometries and crack configurations subjected to different loading and boundary conditions. The study also introduces a variational technique for optimizing sensor locations within the inverse element domain to accurately compute Stress Intensity Factors (SIFs). The proposed inverse shell formulation is computationally efficient and seamlessly integrates within the iFEM framework for real-time shape sensing and Structural Health Monitoring (SHM) of shell structures with preexisting cracks.