A methodology for applying isogeometric inverse finite element method to the shape sensing of stiffened thin-shell structures

The capability of reconstructing the displacement field of a structure based on in-situ strain measurements is referred to as “shape sensing” and constitutes a fundamental unit for the real-time monitoring of critical structural components. The Inverse Finite Element Method (iFEM) is one of the most promising innovative techniques for accomplishing this task. This study explores the application of iFEM in conjunction with Isogeometric Analysis (IGA) for the shape sensing of stiffened thin-shell structures. The use of IGA allows for the exact representation of computational geometry, simplifies mesh refinement, and potentially reduces the number of installed sensors. In the context of IGA, when the geometry of a structure is composed of multiple surfaces, non-conforming interfaces are typically involved. To overcome this issue, we propose an assembly process based on the Lagrange multiplier method to jointly apply iFEM and IGA to shell structures assemblies. The methodology is numerically validated using FEM models both to generate the in-situ strain data and as a comparison for iFEM reconstruction results. The case studies include a T-beam, a reinforced hyperbolic paraboloid, and a wingbox. Convergence analyzes are performed to investigate the shape sensing accuracy as the number of inverse elements increases. Additionally, contour plots of displacement field components are compared with the reference solution, revealing a high degree of agreement.