The inverse Finite Element Method for shape sensing of aerospace structures

The paper presents recent theoretical developments and numerical results obtained at NASA Langley Research Center, by Dr. Alex Tessler and co-workers, and at Politecnico di Torino, by the AESDO Group, addressing the inverse problem of “shape-sensing”, i.e., reconstruction of structural displacements using surface-measured strains. The theoretical framework of the inverse Finite Element Method (iFEM) is briefly presented. Both the original formulation for built-up shell structures and the recent formulation for truss, beam, and frame structures are described. Several numerical and experimental results for plate- and beam-like structures subjected to static and dynamic loads are presented. It is shown that iFEM is a valid approach for shape sensing due to its computational efficiency, accuracy, and robustness with respect to experimental strain-measurement errors. The iFEM shape-sensing methodology is particularly attractive because it does not require any information regarding applied loading, elastic material constants, inertial properties, or damping characteristics.