Shape Sensing of Beam-Like Structures Using the Robust iFEM-iQS4 Inverse Shell Element

The reconstruction of 2-D/3-D deformation and stress fields using a limited number of strain sensors is called "shape sensing" and it plays an important role in structural health monitoring (SHM) methods. The inverse finite element method (iFEM) is one of the best shape sensing algorithms developed based on strain data from a set of on-board/embedded sensors. The iFEM accomplishes this task by minimizing the errors between these collected (experimental/simulated) strains and the calculated (analytical) strains using a weighted least squares function. In the present study, we attempt to verify the applicability of a quadrilateral iFEM plate/shell element, iFEM-iQS4, for shape sensing of 2-D beam-like structures by comparing it with a recently developed inverse beam element iFEM-iBeam3. We also demonstrate the high efficiency and accuracy of iFEM-iQS4 analysis for 3-D shape sensing of beam-like structures with different cross sections. Finally, the accuracy of the numerical examples is validated by an experimental test.