Strain-based shape prediction for flexible: Beam-like structures

This study presents a shape prediction technique for flexible beam-like structures based on measured strains at multiple sensing stations. A deformed beam can be described in terms of the reference line and the reference cross-sectional planes at each point along the reference line. The Kirchhoff’s beam theory denotes the relationship between the deformed configuration of a beam and the curvatures of its reference line. The curvatures are related to measured strains on the beam surface using the concept of Green’s strain tensor. In this way, the structural deformation is recovered from the measured strains. To test the performance of the proposed algorithm, a numerical beam model is firstly designed and studied. Then, a flexible beam model equipped with fiber optic sensors is tested under different load cases. The results show that the proposed algorithm can be applied successfully to flexible beams. The paper discusses the application of this method in monitoring the configuration of the deformed wings, which are often modelled as beams.