Shape Monitoring of a Beam Structure from Measured Strain or Curvature

This paper presents results of numerical simulations and an experimental investigation of a method to determine shape of a beam from curvature and/or strain measurements. The purpose of this work was to develop an efficient and accurate method that can be used in real time shape monitoring of beam type structures with possible extension to more complex systems. A method based upon solving a set of continuity equations is presented. Numerical simulations were implemented to minimize the number of sensors and to determine the most beneficial sensor locations and sensor/model configuration to capture the shape in a timely and effective manner. Simulations showed that dividing the beam into segments (elements) and placing sensors at the Gauss point locations of each segment gave only 0.14% systematic error while using three elements and two Gauss points per element. An experiment was designed using an aluminum beam combined with a data acquisition system and a shape reconstruction algorithm. The real-time reconstruction of shape from curvature data was accomplished using strain gages for the curvature estimates. The results were compared to a technique based on position only data and point cloud image data. Overall, consistent results were obtained. The percent difference between the experimental and photogrammetry results fluctuated from 1.4 to 3.5% when various magnitudes of concentrated loads were applied to the beam. This methodology may be useful in real-time shape control and shape modification systems with potential applications in structural health monitoring and damage detection.