Two-Dimensional Deformation Estimation of Beam-Like Structures Using Inverse Finite-Element Method: Theoretical Study and Experimental Validation
Publication: Journal of Engineering Mechanics
Volume 147, Issue 5
Abstract
The real-time estimation of structural deformations using discrete strain data, known as shape sensing, is critical to the health monitoring of structures such as bridges. An innovative methodology called the inverse finite-element method (iFEM) is proposed to solve this issue. In this paper, a novel two-node inverse beam element, iBeam3, is developed for two-dimensional deformation monitoring of beam type structures. The present iFEM formulation is derived based on the least-squares variational principle involving section strains of Euler-Bernoulli beam theory for stretching and bending. The iBeam3 element is able to reconstruct deformed shapes without any prior material and/or loading information because only the strain-displacement relationship is used in the formulation. Static and dynamic validation cases regarding steel beams with different boundary conditions subjected to transverse force are discussed in detail. In the tests, different discretization strategies are used to perform the iFEM analysis, and the effects of sensor positions, number of sensors, and measurement errors are evaluated with respect to iFEM-predicted accuracy. The experimental results demonstrate that the iBeam3 element is accurate, robust, and highly efficient. The present methodology provides promising potential in the real-time shape sensing of civil infrastructures.
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Data Availability Statement
All data, models, or code that support the findings of this study are available from the corresponding author on reasonable request.
Acknowledgments
This work has been supported by the National Key Research and Development Program of China (Grant No. 2016YFC0701107) and the Fund of the National Natural Science Foundation of China (Grant Nos. 51421064, 51327003, and 51678109). These grants are greatly appreciated.
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Published In
Journal of Engineering Mechanics
Volume 147 • Issue 5 • May 2021
Copyright
© 2021 American Society of Civil Engineers.
History
Received: Jul 6, 2020
Accepted: Dec 7, 2020
Published online: Feb 24, 2021
Published in print: May 1, 2021
Discussion open until: Jul 24, 2021
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