A smoothed iFEM approach for efficient shape-sensing applications: Numerical and experimental validation on composite structures

摘要

A smoothed inverse finite element method (iFEM~(s)) is developed by coupling the inverse finite element method (iFEM) and the smoothing element analysis (SEA) for real-time reconstruction of displacement field utilizing a network of discrete strain-sensor measurements. This reconstruction is commonly referred to as "shape sensing". The shape-sensing capabilities of iFEM~(s) in multilayered composite and sandwich structures are validated using both numerical and experimental strain data. The iFEM~(s) approach first recovers continuous (smoothed, full field) strains from discrete strain measurements and subsequently employs these strains in the least-squares variational principle to obtain the deformed structural shape. To model through-the-thickness displacement distributions accurately, the kinematic relations of the refined zigzag theory (RZT) are incorporated into the mathematical formulation of iFEM~(s). The least-squares functional accommodates the membrane, bending, zigzag, and full transverse-shear section strains. Moreover, simplified forms of this functional are derived for both woven composite and sandwich structures. Subsequently, a four-node quadrilateral inverse-plate element, iRZT4, is implemented for discretization of the geometry and approximation of kinematic variables. The high accuracy of present computational framework is successfully demonstrated by performing shape- and stress-sensing analyses using numerical strain data. Then, the predictive capabilities of iFEM~(s) are also explored on a twill-woven wing-shaped sandwich laminate using experimental strain measurements from surface mounted strain gauges and embedded fiber Bragg grating (FBG) sensors. Finally, the improved shape-sensing predictions of iFEM~(s) for both numerical and experimental cases are compared to the conventional iFEM application.