Two-Dimensional Deformation Estimation of Beam-Like Structures Using Inverse Finite-Element Method: Theoretical Study and Experimental Validation

The real-time estimation of structural deformations using discrete strain data, known as shape sensing, is critical to the health monitoring of structures such as bridges. An innovative methodology called the inverse finite-element method (iFEM) is proposed to solve this issue. In this paper, a novel two-node inverse beam element, iBeam3, is developed for two-dimensional deformation monitoring of beam type structures. The present iFEM formulation is derived based on the least-squares variational principle involving section strains of Euler-Bernoulli beam theory for stretching and bending. The iBeam3 element is able to reconstruct deformed shapes without any prior material and/or loading information because only the strain-displacement relationship is used in the formulation. Static and dynamic validation cases regarding steel beams with different boundary conditions subjected to transverse force are discussed in detail. In the tests, different discretization strategies are used to perform the iFEM analysis, and the effects of sensor positions, number of sensors, and measurement errors are evaluated with respect to iFEM-predicted accuracy. The experimental results demonstrate that the iBeam3 element is accurate, robust, and highly efficient. The present methodology provides promising potential in the real-time shape sensing of civil infrastructures.