Shape sensing of aerospace structures by coupling of isogeometric analysis and inverse finite element method

This paper presents a novel isogeometric inverse Finite Element Method (iFEM) formulation, which couples the NURBS-based isogeometric analysis (IGA) together with the iFEM methodology for shape sensing of complex/curved thin shell structures. The primary goal is to be geometrically exact regardless of the discretization size and to obtain a smoother shape sensing even with less number of strain sensors. For this purpose, an isogeometric KirchhoffLove inverse-shell element (iKLS) is developed on the basis of a weighted-least-squares functional that uses membrane and bending strain measures consistent with the KirchhoffLove shell theory. The novel iKLS element employs NURBS not only as a geometry discretization technology, but also as a discretization tool for displacement domain. Therefore, this development serves the following beneficial aspects of the IGA for the shape sensing analysis based on iFEM methodology: (1) exact representation of computational geometry, (2) simplified mesh refinement, (3) smooth (high-order continuity) basis functions, and finally (4) integration of design and analysis in only one computational domain. The superior capabilities of iKLS element for shape sensing of curved shells are demonstrated by various case studies including a pinched hemisphere and a partly clamped hyperbolic paraboloid. Finally, the effect of sensor locations, number of sensors, and the discretization of the geometry on solution accuracy is examined.