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

Abstract

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.

Shape Sensing in Plate Structures through Inverse Finite Element Method Enhanced by Multi-Objective Genetic Optimization of Sensor Placement and Strain Pre-Extrapolation

“…More recently, a novel class of elements [ 24 ] has been introduced, leveraging the refined zig-zag theory [ 25 ], to exploit the iFEM technique in moderately thick sandwich and laminated composite structures. Over the last few years, iFEM has found both numerical and/or experimental applications in shape-sensing analyses across various interesting case studies, including marine vessels [ 26 ], offshore wind turbine towers [ 27 ], and stiffened panels [ 14 , 28 , 29 ].…”

Delamination Detection and Localization in Vibrating Composite Plates and Shells Using the Inverse Finite Element Method

“…The efficient shape-sensing via the iFEM made it an attractive SHM technique, and soon, through introduction of various inverse elements, such as a four-node quadrilateral inverse shell element, known as iQS4 [ 33 ], its range of applications was expanded. In this context, successful implementations of the iFEM can be found in aerospace [ 34 , 35 , 36 , 37 , 38 ], marine [ 39 , 40 ], civil engineering [ 41 ], and machining [ 42 ] applications. More importantly, the theoretical basis of the iFEM has also experienced significant contributions through the works of various researchers [ 43 , 44 ].…”