Abstract
This paper investigated the effect of sensor density and alignment for three-dimensional shape sensing of an airplane-wing-shaped thick panel subjected to three different loading conditions, i.e., bending, torsion, and membrane loads. For shape sensing analysis of the panel, the Inverse Finite Element Method (iFEM) was used together with the Refined Zigzag Theory (RZT), in order to enable accurate predictions for transverse deflection and through-the-thickness variation of interfacial displacements. In this study, the iFEM-RZT algorithm is implemented by utilizing a novel three-node C°-continuous inverse-shell element, known as i3-RZT. The discrete strain data is generated numerically through performing a high-fidelity finite element analysis on the wing-shaped panel. This numerical strain data represents experimental strain readings obtained from surface patched strain gauges or embedded fiber Bragg grating (FBG) sensors. Three different sensor placement configurations with varying density and alignment of strain data were examined and their corresponding displacement contours were compared with those of reference solutions. The results indicate that a sparse distribution of FBG sensors (uniaxial strain measurements), aligned in only the longitudinal direction, is sufficient for predicting accurate full-field membrane and bending responses (deformed shapes) of the panel, including a true zigzag representation of interfacial displacements. On the other hand, a sparse deployment of strain rosettes (triaxial strain measurements) is essentially enough to produce torsion shapes that are as accurate as those of predicted by a dense sensor placement configuration. Hence, the potential applicability and practical aspects of i3-RZT/iFEM methodology is proven for three-dimensional shape-sensing of future aerospace structures.
Highlights
Structural health monitoring (SHM) has become a critical process for composite structures, those used in aeronautical, naval and civil applications [1,2,3]
For an individual i3-Refined Zigzag Theory (RZT) element, the analytical and experimental strains associated with the membrane, bending, zigzag, and transverse-shear deformations can be interrelated based on a weighted-least-squares functional Φe as [43]
In the second case study, the Inverse Finite Element Method (iFEM) analysis was carried out using i3-RZT models, which contained contained the discrete strain measurements obtained from the torsion scenario
Summary
Structural health monitoring (SHM) has become a critical process for composite structures, those used in aeronautical, naval and civil applications [1,2,3]. This formulation is not general enough for complex geometries, due to the inherent assumptions made for a simple cantilever plate Another shape-reconstruction algorithm [23] proposed, based on a weighted-least-squares functional, aimed to enforce the compatibility between the analytical and measured bending curvatures of the Kirchhoff plate theory. An inverse interpolation algorithm, involving least-squares minimization of calculated and measured strains, was proposed for shape sensing of aerospace structures [24] This methodology requires the recovery of the applied loading before the solution of displacements, but the loading conditions may have a non-trivial physical topology in the real environment, causing the main drawback of the proposed formulation. The most efficient and practical sensor network is determined for each loading scenario, by comparing iFEM-RZT displacement results with those of FEM analyses
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