SSB-iFEM for Beams: Displacement Reconstruction with a Reduced Number of Strain Sensors

This thesis investigates the application of the inverse Finite Element Method (iFEM) to Euler-Bernoulli beam elements, focusing on a Single-Sensor-Based (SSB) iFEM formulation that reconstructs the displacement field from discrete surface-strain measurements without requiring paired sensors on opposite faces. For beam applications, this enables accurate recovery with unpaired layouts that may place sensors on one or both faces, while still keeping the overall sensor count low. The work adapts recent SSB ideas to one-dimensional beam models and implements the formulation in Matlab. The approach treats each strain reading as an independent measurement associated with its physical location on the cross-section or along the span, allowing flexible layouts driven by accessibility and practical instrumentation constraints. The numerical procedure follows a standard finite-element workflow that assembles and solves a least-squares problem at the structural level, with consistent handling of local/global frames and boundary conditions. Validation proceeds from simple beam cases to configurations indicative of more complex geometries. Across these numerical studies, the SSB-based reconstruction achieves accuracy comparable to the conventional beam iFEM when provided with comparable information. In other words, the SSB formulation and the classical formulation are equivalent in terms of displacement reconstruction performance within the tested conditions. Overall, the results support SSB-iFEM for beam-like structures as a practical route to shape sensing with fewer sensors and non-paired layouts, offering an attractive option for structural health monitoring and real-time displacement reconstruction in aerospace and related engineering applications.