A novel multiscale inverse FEM for stiffened panels under sparse sensing

The inverse Finite Element Method (iFEM) is a robust model-based computational technique for reconstructing full-field displacement and strain states from experimental measurements, relying solely on strain data, geometry, and boundary conditions. It has proven highly effective for shell-like structures commonly found in aerospace, marine, and mechanical engineering. However, its application to stiffened panels—one of the most prevalent structural configurations in these domains—remains challenging due to geometric discontinuities, stiffness variations, and limited sensor coverage that hinder accurate full-field reconstruction. This study addresses these challenges by introducing a novel multiscale iFEM–dehomogenization framework designed to extend iFEM applicability to complex stiffened structures under sparse sensing conditions. The proposed methodology operates in two stages. First, iFEM reconstructs the displacement field on a macroscale plate-only model representing the sensorized surface of the structure. Then, a dehomogenization procedure, based on Representative Volume Elements (RVEs), transfers the reconstructed global response to the detailed stiffened geometry, enabling the recovery of local displacements, strain and stresses in non-instrumented regions. The main objectives of this work are to (i) reduce the dependency on dense sensor networks, (ii) maintain high reconstruction accuracy despite geometric and sensing limitations, and (iii) enable efficient multiscale recovery of local fields for Structural Health Monitoring (SHM) applications. The framework has been validated against both experimental and numerical studies on a stiffened aluminum panel. Results show that the proposed approach achieves displacement reconstruction errors below 6% compared with high-fidelity finite element and experimental benchmarks. These findings demonstrate that coupling iFEM with multiscale dehomogenization provides a physically consistent, computationally efficient, and scalable strategy for real-time shape sensing and SHM of complex engineering stiffened structures.