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

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.