A piecewise inverse finite element method for shape sensing of the morphing wing fishbone

The shape sensing technology plays a significant role in enhancing the structural performance and flight efficiency of the morphing aircraft by providing feedback to actuation and control systems in real time. The inverse finite element method (iFEM) is a fast, accurate, and robust shape-sensing method based on in-situ surface strain measurements. However, the conventional iFEM becomes less effective when applied to real engineering structures. Thus, this paper proposes a piecewise iFEM (P-iFEM) based on a two-node inverse Hermite beam element (iHB2) for the load-bearing structure of the morphing wing. The P-iFEM method discretizes the structure into a combination of rigid and elastic parts, based on the geometry of the structure when assembling the inverse elements. The Hermite polynomial shape function in iHB2 is adopted to increase the reconstruction efficiency, as only one degree of freedom of deflection is required to achieve the C¹-continuity to reconstruct the displacement fields. The high accuracy and efficiency of the proposed method are validated with a numerical fishbone model. Finally, the proposed method is applied to a fishbone structure of a real adaptive deformed wing with high accuracy.