Kinematic shape sensing of two-dimensional plates in bending

In engineering, accurate real-time deformation sensing is critical for monitoring structures such as bridges, ship hulls, and aircraft fuselages, to ensure their integrity and safety. Shape sensing technologies, which form the basis of this thesis, offer a way to infer structural deformations through methods such as inertial measurements, optical sensing, and strain gauges, combined with mathematical models for surface deformation reconstruction and analysis.

This research pursues an approach called kinematic shape sensing, which aims to develop algorithms that are capable of deducing real-time structural deformation from discrete strain-based measurements and boundary conditions, bypassing the need for material property knowledge. This has been done previously for one-dimensional spars by incorporating strain measurements into a reconstruction algorithm that relies on beam bending theory to derive lateral deformation. The objectives of this research are to (a) expand current kinematic shape sensing methods to two-dimensional plates in bending, (b) validate newly developed kinematic models against benchmark data derived from finite element analysis, and (c) inform the physical experimental setup in order to apply the kinematic models to real-world applications.

Two kinematic shape sensing methodologies were explored: a linearized beam bending model and a summation of continuous functions approach, evaluated under various loading conditions. This thesis dives into the theory and implementation of each method and conclusive results that meet the success criteria for the objectives identified above. In all, kinematic shape sensing demonstrates precision, promising low cost, and potential to serve as a foundation for intricate sensing needs within the realm of hydrodynamics and fluid-structure interactions.