Structural deformation reconstruction using the hybrid shell-beam inverse Finite Element Method: theory & numerical results

This work introduces a robust and computationally efficient method for reconstructing the full-field elastic deformations of thin-walled and stiffened panel structures using discrete strain-sensor measurements. The approach presented is based on the inverse Finite Element Method (iFEM), a variationally-based shape sensing technique that attempts to reconstruct the structural displacements by matching a set of experimental and analytically defined strains in a least-squares sense. The novelty of the present work is the introduction of a hybrid discretisation paradigm for the iFEM whereby both beam and shell inverse finite elements are conjointly used to model the structure and capture its deformations. The theoretical framework for this new method and the kinematic coupling between shell and beam inverse elements, proposed based on the first-order shear deformation theory, is presented. Adoption of such a hybrid discretization scheme reduces the number of inverse elements required for structural modelling, thereby reducing computational time and effort. Additionally, beam elements reduce the number of in-situ strain sensors required compared to a solely shell-based inverse model. The hybrid iFEM approach is demonstrated numerically for the shape sensing of a stiffened panel under different load conditions. The preliminary results are accurate and efficient, demonstrating the capabilities of the hybrid iFEM as a potential monitoring approach, especially for aerospace applications where high strength and low mass requirements have led to the widespread adoption of thin-walled and stiffened structural geometry designs.