Structural Engineering and Mechanics

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Deformation estimation of plane-curved structures using the NURBS-based inverse finite element method

  • Runzhou You (School of Civil Engineering, Dalian University of Technology) ;
  • Liang Ren (School of Civil Engineering, Dalian University of Technology) ;
  • Tinghua Yi (School of Civil Engineering, Dalian University of Technology) ;
  • Hongnan Li (School of Civil Engineering, Dalian University of Technology)
  • Received : 2023.01.29
  • Accepted : 2023.09.04
  • Published : 2023.10.10
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Abstract

An accurate and highly efficient inverse element labelled iPCB is developed based on the inverse finite element method (iFEM) for real-time shape estimation of plane-curved structures (such as arch bridges) utilizing onboard strain data. This inverse problem, named shape sensing, is vital for the design of smart structures and structural health monitoring (SHM) procedures. The iPCB formulation is defined based on a least-squares variational principle that employs curved Timoshenko beam theory as its baseline. The accurate strain-displacement relationship considering tension-bending coupling is used to establish theoretical and measured section strains. The displacement fields of the isoparametric element iPCB are interpolated utilizing nonuniform rational B-spline (NURBS) basis functions, enabling exact geometric modelling even with a very coarse mesh density. The present formulation is completely free from membrane and shear locking. Numerical validation examples for different curved structures subjected to different loading conditions have been performed and have demonstrated the excellent prediction capability of iPCBs. The present formulation has also been shown to be practical and robust since relatively accurate predictions can be obtained even omitting the shear deformation contributions and considering polluted strain measures. The current element offers a promising tool for real-time shape estimation of plane-curved structures.

Keywords

Acknowledgement

This work was supported by the National Natural Science Foundation of China (Grant Nos. 52208303 and 52027811) and the National Postdoctoral Program for Innovative Talents (Grant No. BX20220051). These grants are greatly appreciated.

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