Efficient shape sensing of plate structures using the inverse Finite Element Method aided by strain pre-extrapolation

The inverse problem of reconstructing structural deformations based on measured strain data, known as shape sensing, is addressed in this numerical study for a cantilevered plate undergoing complex bending and twisting deformations. The inverse Finite Element Method (iFEM) is the main computational tool used for solving the inverse problem, and the Smoothing Element Analysis (SEA) is used as a pre-processing step seeding additional strain data into a high-fidelity iFEM discretization. This novel SEA-iFEM approach demonstrates that even with a small number of strain sensors and a judicial choice of strain-sensor layouts, accurate shape-sensing reconstructions for plate structures can be obtained.