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.
Highlights
Structural health monitoring (SHM) is an interdisciplinary procedure that (1) integrates sensing systems into a structure, (2) processes the data collected from the sensing systems in real time, and (3)Sensors 2020, 20, 2685; doi:10.3390/s20092685 www.mdpi.com/journal/sensorsSensors 2020, 20, 2685 provides decisive real-time information from the structure about its global and/or local structural state.The main objective of SHM is to detect unusual structural behaviors to pinpoint failures or an unhealthy structural condition
Utilizing the non-uniform rational basis splines (NURBS) basis functions, the isogeometric analysis (IGA) serves an exact representation of computational geometry, no matter how coarse the discretization
This study presents a novel “isogeometric inverse finite element method (iFEM) formulation”, which couples the NURBS-based
Summary
Structural health monitoring (SHM) is an interdisciplinary procedure that (1) integrates sensing systems into a structure, (2) processes the data collected from the sensing systems in real time, and (3). Utilizing the non-uniform rational basis splines (NURBS) basis functions, the IGA serves an exact representation of computational geometry, no matter how coarse the discretization It simplifies the mesh refinement by eliminating the need for communication with the computer aided design (CAD) geometry once the initial isogeometric model is constructed. The novel iKLS element presented employs NURBS basis functions, as a geometry discretization technology, and as a discretization tool for displacement domain 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 (4) integration of design and analysis in only one computational geometry.
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