Hybrid Shell-Beam Inverse Finite Element Method for the Shape Sensing of Stiffened Thin-Walled Structures: Formulation and Experimental Validation on a Composite Wing-Shaped Panel.

This work presents a novel methodology for the accurate and efficient elastic deformation reconstruction of thin-walled and stiffened structures from discrete strains. It builds on the inverse finite element method (iFEM), a variationally-based shape-sensing approach that reconstructs structural displacements by matching a set of analytical and experimental strains in a least-squares sense. As iFEM employs the finite element framework to discretize the structural domain and as the displacements and strains are approximated using element shape functions, the kind of element used influences the accuracy and efficiency of the iFEM analysis. This problem is addressed in the present work through a novel discretization scheme that combines beam and shell inverse elements to develop an iFEM model of the structure. Such a hybrid discretization paradigm paves the way for more accurate shape-sensing of geometrically complex structures using fewer sensor measurements and lower computational effort than traditional approaches. The hybrid iFEM is experimentally demonstrated in this work for the shape sensing of bending and torsional deformations of a composite stiffened wing panel instrumented with strain rosettes and fiber-optic sensors. The experimental results are accurate, robust, and computationally efficient, demonstrating the potential of this hybrid scheme for developing an efficient digital twin for online structural monitoring and control.

Delamination and Skin-Spar Debond Detection in Composite Structures Using the Inverse Finite Element Method.

This work presents a novel strategy for detecting and localizing intra- or inter-laminar damages in composite structures using surface-instrumented strain sensors. It is based on the real-time reconstruction of structural displacements using the inverse Finite Element Method (iFEM). The iFEM reconstructed displacements or strains are post-processed or 'smoothed' to establish a real-time healthy structural baseline. As damage diagnosis is based on comparing damaged and healthy data obtained using the iFEM, no prior data or information regarding the healthy state of the structure is required. The approach is applied numerically on two carbon fiber-reinforced epoxy composite structures: for delamination detection in a thin plate, and skin-spar debond detection in a wing box. The influence of measurement noise and sensor locations on damage detection is also investigated. The results demonstrate that the proposed approach is reliable and robust but requires strain sensors proximal to the damage site to ensure accurate predictions.

Shape Sensing of Plate Structures Using the Inverse Finite Element Method: Investigation of Efficient Strain-Sensor Patterns.

Methods for real-time reconstruction of structural displacements using measured strain data is an area of active research due to its potential application for Structural Health Monitoring (SHM) and morphing structure control. The inverse Finite Element Method (iFEM) has been shown to be well suited for the full-field reconstruction of displacements, strains, and stresses of structures instrumented with discrete or continuous strain sensors. In practical applications, where the available number of sensors may be limited, the number and sensor positions constitute the key parameters. Understanding changes in the reconstruction quality with respect to sensor position is generally difficult and is the aim of the present work. This paper attempts to supplement the current iFEM modeling knowledge through a rigorous evaluation of several strain-sensor patterns for shape sensing of a rectangular plate. Line plots along various sections of the plate are used to assess the reconstruction quality near and far away from strain sensors, and the nodal displacements are studied as the sensor density increases. The numerical results clearly demonstrate the effectiveness of the strain sensors distributed along the plate boundary for reconstructing relatively simple displacement patterns, and highlight the potential of cross-diagonal strain-sensor patterns to improve the displacement reconstruction of more complex deformation patterns.