Shape Reconstruction Method for Monitoring Large Deformed Beam Structures
Publication: Journal of Engineering Mechanics
Volume 150, Issue 8
Abstract
Shape sensing refers to the deformation reconstruction of structures using measured surface strain. However, there is currently a lack of research on the shape sensing of large deformations, especially for beam structures. To address this issue, this paper proposes a new method called the rotation angle approximation (RAA) for reconstructing large deformations of beam structures. This method utilizes theoretical and actual curvatures to create a least-squares error functional. By minimizing this functional, the rotation angles of the corresponding beam can be obtained, avoiding the accumulation of errors that occurs when using traditional computation methods. The deformed shapes can be predicted utilizing the boundary conditions and the rotation angles along the beam. This method can reconstruct the large deformation of a beam without requiring prior knowledge about the material properties or external loads. The accuracy and effectiveness of this method were validated through numerical simulations and experiments. The results indicate that this method can accurately predict the different deformations of a beam induced by various loading conditions.
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Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request. The available items include experimental data and numerical models.
Acknowledgments
This research work was jointly supported by the National Natural Science Foundation of China (Grant Nos. 52008236 and 52078284), Guangdong Basic and Applied Basic Research Foundation (2022A1515010812 and 2021A1515011770), and Shantou University Scientific Research Foundation (Grant No. NFT19039). These grants are greatly appreciated.
References
Alioli, M., P. Masarati, M. Morandini, G. L. Ghiringhelli, T. Carpenter, and R. Albertani. 2015. “Nonlinear membrane inverse finite elements.” In Proc., AIP Conf. Proc. Melville, NY: American Institute of Physics.
Bakalyar, J., and C. Jutte. 2012. “Validation tests of fiber optic strain-based operational shape and load measurements.” In Proc., 53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conf. 20th AIAA/ASME/AHS Adaptive Structures Conference 14th AIAA. Reston, VA: American Institute of Aeronautics and Astronautics. https://doi.org/10.2514/6.2012-1904.
Bogert, P., E. Haugse, and R. Gehrki. 2003. “Structural shape identification from experimental strains using a modal transformation technique.” In Proc., 44th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conf., 1626. Bethel, CT: International Society for Optical Engineering. https://doi.org/10.2514/6.2003-1626.
Colombo, L., D. Oboe, C. Sbarufatti, F. Cadini, S. Russo, and M. Giglio. 2021. “Shape sensing and damage identification with iFEM on a composite structure subjected to impact damage and non-trivial boundary conditions.” Mech. Syst. Signal Process. 148 (Apr): 107163. https://doi.org/10.1016/j.ymssp.2020.107163.
Derkevorkian, A., S. F. Masri, J. Alvarenga, H. Boussalis, J. Bakalyar, and W. L. Richards. 2013. “Strain-based deformation shape-estimation algorithm for control and monitoring applications.” AIAA J. 51 (9): 2231–2240. https://doi.org/10.2514/1.J052215.
Ding, G., S. Yue, S. Zhang, and W. Song. 2021. “Strain-deformation reconstruction of CFRP laminates based on Ko displacement theory.” Nondestr. Test. Eval. 36 (2): 145–157. https://doi.org/10.1080/10589759.2019.1707200.
Esposito, M., and M. Gherlone. 2020. “Composite wing box deformed-shape reconstruction based on measured strains: Optimization and comparison of existing approaches.” Aerosp. Sci. Technol. 99 (Feb): 105758. https://doi.org/10.1016/j.ast.2020.105758.
Feng, D. 2020. “Research on structural deformation reconstruction technology based on fiber grating strain sensing.” Master’s thesis, School of Mechanical Engineering, Dalian Univ. of Technology.
Foss, G., and E. Haugse. 1995. “Using modal test results to develop strain to displacement transformations.” In Vol. 2460 of Proc., 13th Int. Modal Analysis Conf., 112. Bethel, CT: International Society for Optical Engineering.
Gherlone, M., P. Cerracchio, and M. Mattone. 2018. “Shape sensing methods: Review and experimental comparison on a wing-shaped plate.” Prog. Aerosp. Sci. 99 (Apr): 14–26. https://doi.org/10.1016/j.paerosci.2018.04.001.
Gherlone, M., P. Cerracchio, M. Mattone, M. Di Sciuva, and A. Tessler. 2014. “An inverse finite element method for beam shape sensing: Theoretical framework and experimental validation.” Smart Mater. Struct. 23 (4): 045027. https://doi.org/10.1088/0964-1726/23/4/045027.
Guan, B. L., Z. L. Su, Q. F. Yu, Z. Li, W. W. Feng, D. Yang, and D. S. Zhang. 2022. “Monitoring the blades of a wind turbine by using videogrammetry.” Opt. Lasers Eng. 152 (Aug): 106901. https://doi.org/10.1016/j.optlaseng.2021.106901.
Jiang, T., J. Zhu, Y. Gao, L. Ren, C. Qu, and D. Li. 2023. “Shape reconstruction of a Timoshenko beam under the geometric nonlinearity condition.” J. Eng. Mech. 149 (6): 04023031. https://doi.org/10.1061/JENMDT.EMENG-7097.
Jiang, T., J. W. Zhu, and Y. Shi. 2021. “Detection of pipeline deformation induced by frost heave using OFDR technology.” Front. Phys. 9 (Jun): 684954. https://doi.org/10.3389/fphy.2021.684954.
Kaloop, M. R., and H. Li. 2009. “Monitoring of bridge deformation using GPS technique.” KSCE J. Civ. Eng. 13 (6): 423–431. https://doi.org/10.1007/s12205-009-0423-y.
Ko, W. L., and V. T. Fleischer. 2011. Extension of Ko straight-beam displacement theory to deformed shape predictions of slender curved structures. Washington, DC: National Aeronautics and Space Administration.
Ko, W. L., W. L. Richards, and V. T. Tran. 2007. Displacement theories for in-flight deformed shape predictions of aerospace structures. Washington, DC: National Aeronautics and Space Administration.
Lively, P. S., M. J. Atalla, and N. W. Hagood. 2001. “Investigation of filtering techniques applied to the dynamic shape estimation problem.” Smart Mater. Struct. 10 (2): 264. https://doi.org/10.1088/0964-1726/10/2/311.
Lung, S.-F., and W. L. Ko. 2016. “Applications of displacement transfer functions to deformed shape predictions of the G-III swept-wing structure.” In Proc., Congress Int. Council of the Aeronautical Sciences (ICAS 2016). Edwards, CA: NASA Dryden Flight Research Center.
Ma, Z., and X. Y. Chen. 2019. “Fiber Bragg gratings sensors for aircraft wing shape measurement: Recent applications and technical analysis.” Sensors 19 (1): 55. https://doi.org/10.3390/s19010055.
Ou, J. P., and H. Li. 2010. “Structural health monitoring in mainland China: Review and future trends.” Struct. Health. Monit. 9 (3): 219–231. https://doi.org/10.1177/1475921710365269.
Paczkowski, K., and H. R. Riggs. 2007. “An inverse finite element strategy to recover full-field, large displacements from strain measurements.” In Proc., 26th Int. Conf. on Offshore Mechanics and Arctic Engineering, 531–537. New York: ASME. https://doi.org/10.1115/OMAE2007-29730.
Palma, P. D., G. Palumbo, M. Della Pietra, V. Canale, M. Alviggi, A. Iadicicco, and S. Campopiano. 2019. “Deflection monitoring of bi-dimensional structures by fiber Bragg gratings strain sensors.” IEEE Sens. J. 19 (11): 4084–4092. https://doi.org/10.1109/JSEN.2019.2896910.
Papa, U., S. Russo, A. Lamboglia, G. Del Core, and G. Iannuzzo. 2017. “Health structure monitoring for the design of an innovative UAS fixed wing through inverse finite element method (iFEM).” Aerosp. Sci. Technol. 69 (Apr): 439–448. https://doi.org/10.1016/j.ast.2017.07.005.
Qiu, Y., P. K. Arunachala, and C. Linder. 2023. “SenseNet: A physics-informed deep learning model for shape sensing.” J. Eng. Mech. 149 (3): 04023002. https://doi.org/10.1061/JENMDT.EMENG-6901.
Rapp, S., L.-H. Kang, J.-H. Han, U. C. Mueller, and H. Baier. 2009. “Displacement field estimation for a two-dimensional structure using fiber Bragg grating sensors.” Smart Mater. Struct. 18 (2): 025006. https://doi.org/10.1088/0964-1726/18/2/025006.
Sun, L., Z. Shang, Y. Xia, S. Bhowmick, and S. Nagarajaiah. 2020. “Review of bridge structural health monitoring aided by big data and artificial intelligence: From condition assessment to damage detection.” J. Struct. Eng. 146 (5): 04020073. https://doi.org/10.1061/(ASCE)ST.1943-541X.0002535.
Tessler, A. 2003. A variational principle for reconstruction of elastic deformations in shear deformable plates and shells. Washington, DC: National Aeronautics and Space Administration.
Tessler, A., R. Roy, M. Esposito, C. Surace, and M. Gherlone. 2018. “Shape sensing of plate and shell structures undergoing large displacements using the inverse finite element method.” Shock Vib. 2018 (Apr): 8076085. https://doi.org/10.1155/2018/8076085.
Wang, Z. C., D. Y. Duan, H. R. Yu, Y. Xin, and F. Li. 2021. “Local bending deformation monitoring of bi-dimensional bridge deck based on the displacement-strain transfer matrix.” J. Civ. Struct. Health Monit. 11 (3): 809–832. https://doi.org/10.1007/s13349-021-00485-w.
Wu, G., F. Qiao, X. Fang, M. Liang, and Y. Song. 2023. “Straightness perception mechanism of scraper conveyor based on the three-dimensional curvature sensing of FBG.” Appl. Sci. 13 (6): 3619. https://doi.org/10.3390/app13063619.
Ye, X. W., T. Jin, P. P. Ang, X. C. Bian, and Y. M. Chen. 2021. “Computer vision-based monitoring of the 3-D structural deformation of an ancient structure induced by shield tunneling construction.” Struct. Control Health 28 (4): e2702. https://doi.org/10.1002/stc.2702.
You, R., L. Ren, C. Yuan, and G. Song. 2021. “Two-dimensional deformation estimation of beam-like structures using inverse finite-element method: Theoretical study and experimental validation.” J. Eng. Mech. 147 (5): 04021019. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001917.
Zhao, F., H. Bao, and F. Zhang. 2023. “Geometrically nonlinear deformation reconstruction of based on Euler–Bernoulli beam theory using a nonlinear iFEM algorithm.” Thin-Walled Struct. 189 (Aug): 110884. https://doi.org/10.1016/j.tws.2023.110884.
Zhao, F., A. Kefal, and H. Bao. 2022. “Nonlinear deformation monitoring of elastic beams based on isogeometric iFEM approach.” Int. J. Non-Linear Mech. 147 (Apr): 104229. https://doi.org/10.1016/j.ijnonlinmec.2022.104229.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 150 • Issue 8 • August 2024
Copyright
© 2024 American Society of Civil Engineers.
History
Received: Aug 24, 2023
Accepted: Mar 19, 2024
Published online: May 30, 2024
Published in print: Aug 1, 2024
Discussion open until: Oct 30, 2024
ASCE Technical Topics:
- Approximation methods
- Beams
- Construction engineering
- Construction management
- Continuum mechanics
- Deformation (mechanics)
- Dynamics (solid mechanics)
- Engineering fundamentals
- Engineering mechanics
- Material mechanics
- Material properties
- Materials engineering
- Measurement (by type)
- Methodology (by type)
- Motion (dynamics)
- Rotation
- Sensors and sensing
- Solid mechanics
- Structural engineering
- Structural mechanics
- Structural members
- Structural systems
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