Kinematic Shape Sensing of a 2D Plate in Bending
What is Shape Sensing?
Shape sensing is a method used to measure deflections of bodies. Previous work has produced accurate, real-time deflection reconstructions on slender beams by utilizing strain measurements and kinematic modeling.
This research aims to extend this method to a 2D plate in bending, which could enable real-time monitoring of fuselage panels and wings.
Creating a Kinematic Model
A kinematic model was derived by fitting polynomials to strains measured at various points on the plate. Solving a linearized beam bending equation (PDE) in the x and y directions with appropriate boundary conditions allows plate-normal deflections to be obtained, as done previously with shape-sensing spars.
This model was then tested in MATLAB against synthetic data obtained from FEA. Various boundary conditions were employed based on different scenarios.
Scenario A: Plate with Two-Fixed Edges
FEA Model
Fine Mesh via Mathematical Model
Coarse Mesh via Mathematical Model