Isogeometric iFEM Analysis of Thin Shell Structures

Abstract

Shape sensing is one of most crucial components of typical structural health monitoring systems and has become a promising technology for future large-scale engineering structures to achieve significant improvement in their safety, reliability, and affordability. The inverse finite element method (iFEM) is an innovative shape-sensing technique that was introduced to perform three-dimensional displacement reconstruction of structures using in situ surface strain measurements. Moreover, isogeometric analysis (IGA) presents smooth function spaces such as non-uniform rational basis splines (NURBS), to numerically solve a number of engineering problems, and recently received a great deal of attention from both academy and industry. In this study, we propose a novel “isogeometric iFEM approach” for the shape sensing of thin and curved shell structures, through coupling the NURBS-based IGA together with the iFEM methodology. The main aim is to represent exact computational geometry, simplify mesh refinement, use smooth basis/shape functions, and allocate a lower number of strain sensors for shape sensing. For numerical implementation, a rotation-free isogeometric inverse-shell element (isogeometric Kirchhoff–Love inverse-shell element (iKLS)) is developed by utilizing the kinematics of the Kirchhoff–Love shell theory in convected curvilinear coordinates. Therefore, the isogeometric iFEM methodology presented herein minimizes a weighted-least-squares functional that uses membrane and bending section strains, consistent with the classical shell theory. Various validation and demonstration cases are presented, including Scordelis–Lo roof, pinched hemisphere, and partly clamped hyperbolic paraboloid. Finally, the effect of sensor locations, number of sensors, and the discretization of the geometry on solution accuracy is examined and the high accuracy and practical aspects of isogeometric iFEM analysis for linear/nonlinear shape sensing of curved shells are clearly demonstrated.

Advanced Structural Health Monitoring Method by Integrated Isogeometric Analysis and Distributed Fiber Optic Sensing

“…It should be noted that an exact inverse is not possible since the fiber strain calculation using Equation (29) is irreversible. Previous studies have proposed the inverse method using least squares for plates [ 16 ], using inverse FEM (iFEM) for shells and plates [ 17 ] and, recently, using inverse IGA-iFEM for shells with strain gauge rosettes [ 36 ]. However, our formulations of integrated IGA and DFOS presented in Section 2 and the following inverse method are substantially different since our method explicitly considers the geometry of the fiber and does not impose any restriction on the location or resolution of sampling points.…”

Shape Sensing of a Complex Aeronautical Structure with Inverse Finite Element Method

“…These have been recently assessed with each other on a comparative study [ 33 ], demonstrating how the iQS4 is more accurate than the iMIN3 for plane problems, while, in the case of curved structures, the best accuracy is archived by the iCS8. Then, other formulations exploit a combined use of iFEM and the Refined Zig-Zag theory (RZT) to compute the through-the-thickness displacement field on composite structures [ 34 , 35 ], while, the combination of isogeometric analysis and iFEM is beneficial for large non-linear deformations [ 36 ]. Finally, the iFEM was also recently extended to damage identification [ 30 , 37 , 38 , 39 ] by considering that discrepancies between the physical structure and the iFEM model generate wrong displacement and strain field reconstructions.…”

Shape-Sensing of Beam Elements Undergoing Material Nonlinearities

“…The kinematic relations are obtained by combining the kinematics assumptions of Mindlin plate theory and of a solid shell. Most recently, Kefal and Oterkus [ 11 ] presented an isogeometric iFEM methodology for shape-sensing analyses of complex thin plate and shell structures. Zhao et al [ 12 ] proposed a new iFEM formulation for reconstructing the displacement field of variable cross-section beams based on isogeometric analysis.…”