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Structural Engineering and Mechanics Volume 88, Number 1, October10 2023 , pages 83-94 DOI: https://doi.org/10.12989/sem.2023.88.1.083 |
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Deformation estimation of plane-curved structures using the NURBS-based inverse finite element method |
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Runzhou You, Liang Ren, Tinghua Yi and Hongnan Li
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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. | ||
| Key Words | ||
| inverse finite element method; plane-curved structures; shape sensing; strain sensors; Timoshenko beam | ||
| Address | ||
| Runzhou You, Liang Ren, Tinghua Yi and Hongnan Li: School of Civil Engineering, Dalian University of Technology, No.2 Linggong Road, Ganjingzi District, Dalian, Liaoning, PR China | ||