Faculty of Engineering and Natural Sciences, Sabanci University, Tuzla, Istanbul 34956, Turkey.
Integrated Manufacturing Technologies Research and Application Center, Sabanci University, Tuzla, Istanbul 34956, Turkey.
Sensors (Basel). 2020 May 8;20(9):2685. doi: 10.3390/s20092685.
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.
形状传感是典型结构健康监测系统中最重要的组成部分之一，已成为未来大型工程结构实现安全、可靠性和经济适用性显著提高的一项有前途的技术。逆有限元法（iFEM）是一种创新的形状传感技术，用于使用原位表面应变测量进行结构的三维位移重构。此外，等几何分析（IGA）提供了光滑的函数空间，如非均匀有理 B 样条（NURBS），用于数值求解许多工程问题，最近受到学术界和工业界的广泛关注。在这项研究中，我们提出了一种新颖的“等几何 iFEM 方法”，用于薄壳和曲壳结构的形状传感，通过将基于 NURBS 的 IGA 与 iFEM 方法相结合。主要目的是表示精确的计算几何形状，简化网格细化，使用光滑的基/形状函数，并分配较少数量的应变传感器进行形状传感。为了数值实现，通过利用 Kirchhoff-Love 壳理论的运动学，在协变曲线坐标中开发了无旋转的等几何逆壳单元（等几何 Kirchhoff-Love 逆壳单元（iKLS））。因此，本文提出的等几何 iFEM 方法最小化了加权最小二乘泛函，该泛函使用膜和弯曲部分应变，与经典壳理论一致。本文提出了各种验证和演示案例，包括 Scordelis-Lo 屋顶、压扁的半球和部分夹紧的双曲抛物面。最后，检查了传感器位置、传感器数量和几何离散化对解精度的影响，清楚地证明了等几何 iFEM 分析在曲线壳的线性/非线性形状传感中的高精度和实用性。
