Structural Engineering and Mechanics

  • 제88권1호
  • /
  • Pages.83-94
  • /
  • 2023
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

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)
  • 투고 : 2023.01.29
  • 심사 : 2023.09.04
  • 발행 : 2023.10.10
⟨ 이전 논문 다음 논문 ⟩

초록

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.

키워드

과제정보

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.

참고문헌

  1. Abdollahzadeh, M.A., Kefal, A. and Yildiz, M. (2020), "A comparative and review study on shape and stress sensing of flat/curved shell geometries using C0-continuous family of iFEM elements", Sensor., 20(14), 3808. https://doi.org/10.3390/s20143808.
  2. Ataei, S., Tajalli, M. and Miri, A. (2016), "Assessment of load carrying capacity and fatigue life expectancy of a monumental Masonry Arch Bridge by field load testing: A case study of veresk", Struct. Eng. Mech., 59(4), 703-718. https://doi.org/10.12989/sem.2016.59.4.703.
  3. Bayat, M., Pakar, I., Ahmadi, H.R., Cao, M. and Alavi, A.H. (2020), "Structural health monitoring through nonlinear frequency-based approaches for conservative vibratory systems", Struct. Eng. Mech., 73(3), 331-337. https://doi.org/10.12989/sem.2020.73.3.331.
  4. Bogert, P., Haugse, E. and Gehrki, R. (2003), "Structural shape identification from experimental strains using a modal transformation technique", 44th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Norfolk, United States, April.
  5. Cazzani, A., Malagu, M. and Turco, E. (2016), "Isogeometric analysis of plane-curved beams", Math. Mech. Solid., 21(5), 562-577. https://doi.org/10.1177/1081286514531265.
  6. Cerracchio, P., Gherlone, M., Di Sciuva, M. and Tessler, A. (2015), "A novel approach for displacement and stress monitoring of sandwich structures based on the inverse finite element method", Compos. Struct., 127, 69-76. https://doi.org/10.1016/j.compstruct.2015.02.081.
  7. Chen, K.Y., Cao, K.T., Gao, G.M. and Bao, H. (2021), "Shape sensing of Timoshenko beam subjected to complex multi-node loads using isogeometric analysis", Measure., 184, 109958. https://doi.org/10.1016/j.measurement.2021.109958.
  8. Chen, Z.X. and Yu, L. (2020), "A novel WOA-based structural damage identification using weighted modal data and flexibility assurance criterion", Struct. Eng. Mech., 75(4), 445-454. https://doi.org/10.12989/sem.2020.75.4.445.
  9. Chung, W., Kim, S., Kim, N.S. and Lee, H.U. (2008), "Deflection estimation of a full scale prestressed concrete girder using long-gauge fiber optic sensors", Constr. Build. Mater., 22(3), 394-401. https://doi.org/10.1016/j.conbuildmat.2006.08.007.
  10. Ciminello, M., Ameduri, S., Concilio, A., Dimino, I. and Bettini, P. (2017), "Fiber optic shape sensor system for a morphing wing trailing edge", Smart. Struct. Syst., 20(4), 441-450. https://doi.org/10.12989/sss.2017.20.4.441.
  11. Deng, L. and Cai, C.S. (2007), "Applications of fiber optic sensors in civil engineering", Struct. Eng. Mech., 25(5), 577-596. https://doi.org/10.12989/sem.2007.25.5.577.
  12. Derkevorkian, A., Masri, S.F., Alvarenga, J., Boussalis, H., Bakalyar, J. and Richards, W.L. (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.
  13. Gherlone, M., Cerracchio, P. and Mattone, M. (2018), "Shape sensing methods: Review and experimental comparison on a wing-shaped plate", Prog. Aerosp. Sci., 99, 14-26. https://doi.org/10.1016/j.paerosci.2018.04.001.
  14. Gherlone, M., Cerracchio, P., Mattone, M., Di Sciuva, M. and Tessler, A. (2012), "Shape sensing of 3D frame structures using an inverse finite element method", Int. J. Solid. Struct., 49(22), 3100-3112. https://doi.org/10.1016/j.ijsolstr.2012.06.009.
  15. Gherlone, M., Cerracchio, P., Mattone, M., Di Sciuva, M. and Tessler, A. (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.
  16. Hong, H.S., Kim, K.H. and Choi, C.K. (2004), "Assumed strain finite strip method using the non-periodic B-spline", Struct. Eng. Mech., 18(5), 671-690. https://doi.org/10.12989/sem.2004.18.5.671.
  17. Hughes, T., Cottrell, J.A. and Bazilevs, Y. (2005), "Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement", Comput. Meth. Appl. Mech. Eng., 194(39-41), 4135-4195. https://doi.org/10.1016/j.cma.2004.10.008.
  18. Ignesti, D., Ferri, G., Auricchio, F., Reali, A. and Marino, E. (2023), "An improved isogeometric collocation formulation for spatial multi-patch shear-deformable beams with arbitrary initial curvature", Comput. Meth. Appl. Mech. Eng., 403, 115722. https://doi.org/10.1016/j.cma.2022.115722.
  19. Kang, L.H., Kim, D.K. and Han, J.H. (2007), "Estimation of dynamic structural displacements using fiber Bragg grating strain sensors", J. Sound Vib., 305(3), 534-542. https://doi.org/10.1016/j.jsv.2007.04.037.
  20. Kefal, A. (2019), "An efficient curved inverse-shell element for shape sensing and structural health monitoring of cylindrical marine structures", Ocean Eng., 188, 106262. https://doi.org/10.1016/j.oceaneng.2019.106262.
  21. Kefal, A., Oterkus, E., Tessler, A. and Spangler, J.L. (2016), "A quadrilateral inverse-shell element with drilling degrees of freedom for shape sensing and structural health monitoring", Eng. Sci. Technol. Int. J., 19(3), 1299-1313. https://doi.org/10.1016/j.jestch.2016.03.006.
  22. Kefal, A., Tessler, A. and Oterkus, E. (2017), "An enhanced inverse finite element method for displacement and stress monitoring of multilayered composite and sandwich structures", Compos. Struct., 179, 514-540. https://doi.org/10.1016/j.compstruct.2017.07.078.
  23. Kim, N.S. and Cho, N.S. (2004), "Estimating deflection of a simple beam model using fiber optic bragg-grating sensors", Exp. Mech., 44(4), 433-439. https://doi.org/10.1177/0014485104045431.
  24. Ko, W.L., Richards, W.L. and Tran, V.t. (2007), "Displacement theories for in-flight deformed shape predictions of aerospace structures", Report No. NASA/TP-2007-214612, NASA Dryden Flight Research Center, Edwards, USA.
  25. Li, L., Zhong, B., Li, W., Sun, W. and Zhu, X. (2017), "Structural shape reconstruction of fiber Bragg grating flexible plate based on strain modes using finite element method", J. Intel. Mater. Syst. Struct., 29(4), 463-478. https://doi.org/10.1177/1045389X17708480.
  26. Lin, S.T.K., Lu, Y., Alamdari, M.M. and Khoa, N.L.D. (2022), "Neural network based numerical model updating and verification for a short span concrete culvert bridge by incorporating Monte Carlo simulations", Struct. Eng. Mech., 81(3), 293-303. https://doi.org/10.12989/sem.2022.81.3.293.
  27. Marino, E. (2016), "Isogeometric collocation for three-dimensional geometrically exact shear-deformable beams", Comput. Meth. Appl. Mech. Eng., 307, 383-410. https://doi.org/10.1016/j.cma.2016.04.016.
  28. Marino, E. (2017), "Locking-free isogeometric collocation formulation for three-dimensional geometrically exact shear-deformable beams with arbitrary initial curvature", Comput. Meth. Appl. Mech. Eng., 324, 546-572. https://doi.org/10.1016/j.cma.2017.06.031.
  29. Ni, P.H., Wang, X.J. and Zhou, H.Y. (2021), "Output-only structural damage detection under multiple unknown white noise excitations", Struct. Eng. Mech., 79(3), 327-336. https://doi.org/10.12989/sem.2021.79.3.327.
  30. Nobahari, M., Ghasemi, M.R. and Shabakhty, N. (2017), "A novel heuristic search algorithm for optimization with application to structural damage identification", Smart. Struct. Syst., 19(4), 449-461. https://doi.org/10.12989/sss.2017.19.4.449.
  31. Pisoni, A.C., Santolini, C., Hauf, D.E., Dubowsky, S. and Soc Exptl, M. (1995), "Displacements in a vibrating body by strain gauge measurements", 13th International Modal Analysis Conference, Nashville, February.
  32. Ren, L., Chen, J., Li, H., Song, G. and Ji, X. (2009), "Design and application of a fiber Bragg grating strain sensor with enhanced sensitivity in the small-scale dam model", Smart Mater. Struct., 18(3), 1973-1978. https://doi.org/10.1088/0964-1726/18/3/035015.
  33. Savino, P., Gherlone, M. and Tondolo, F. (2019), "Shape sensing with inverse finite element method for slender structures", Struct. Eng. Mech., 72(2), 217-227. https://doi.org/10.12989/sem.2019.72.2.217.
  34. Savino, P., Tondolo, F., Gherlone, M. and Tessler, A. (2020), "Application of inverse finite element method to shape sensing of curved beams", Sensor., 20(24), 7012. https://doi.org/10.3390/s20247012.
  35. Song, G.B., Ho, S.C.M. and Kong, Q.Z. (2019), "Structural damage detection and health monitoring", Appl. Sci.-Basel, 9(19), 4027. https://doi.org/10.3390/app9194027. 
  36. Tessler, A. and Spangler, J.L. (2003), "A variational principal for reconstruction of elastic deformation of shear deformable plates and shells", Report No. NASA/TM-2003-212445, NASA Langley Research Center, Hampton, USA.
  37. Tessler, A. and Spangler, J.L. (2004), "Inverse FEM for full-field reconstruction of elastic deformations in shear deformable plates and shells", NASA Langley Research Center, Hampton, USA.
  38. Tessler, A. and Spangler, J.L. (2005), "A least-squares variational method for full-field reconstruction of elastic deformations in shear-deformable plates and shells", Comput. Meth. Appl. Mech. Eng., 194(2-5), 327-339. https://doi.org/10.1016/j.cma.2004.03.015.
  39. Wan, H.P. and Ni, Y.Q. (2018), "Bayesian modeling approach for forecast of structural stress response using structural health monitoring data", J. Struct. Eng., 144(9), 04018130. https://doi.org/10.1061/(asce)st.1943-541x.0002085.
  40. Wang, X., Li, Z.L., Zhuo, Y., Di, H., Wei, J.F., Li, Y.C. and Li, S.L. (2021), "Indirect displacement monitoring of high-speed railway box girders consider bending and torsion coupling effects", Smart. Struct. Syst., 28(6), 827-838. https://doi.org/10.12989/sss.2021.28.6.827.
  41. Wang, Y.J., Wang, Z.P., Xia, Z.H. and Poh, L.H. (2018), "Structural design optimization using isogeometric analysis: A comprehensive review", CMES-Comput. Model. Eng. Sci., 117(3), 455-507. https://doi.org/10.31614/cmes.2018.04603.
  42. Yang, S.Y. and Sin, H.C. (1995), "Curvature-based beam element for the analysis of Timoshenko and shear-deformable curved beams", J. Sound Vib., 187(4), 569-584. https://doi.org/10.1006/jsvi.1995.0545.
  43. Yang, X.M., Yi, T.H., Qu, C.X., Li, H.N. and Liu, H. (2022), "Performance warning of bridges under train actions through equivalent frequency response functions", J. Bridge Eng., 27(10), 04022091. https://doi.org/10.1061/(asce)be.1943-5592.0001925.
  44. Yi, T.H., Li, H.N. and Gu, M. (2013), "Wavelet based multi-step filtering method for bridge health monitoring using GPS and accelerometer", Smart. Struct. Syst., 11(4), 331-348. https://doi.org/10.12989/sss.2013.11.4.331.
  45. You, R.Z. and Ren, L. (2021), "An enhanced inverse beam element for shape estimation of beam-like structures", Measure., 181, 109575. https://doi.org/10.1016/j.measurement.2021.109575.
  46. You, R.Z., Ren, L., Yuan, C.L. and Song, G.B. (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.
  47. Zhao, F.F., Bao, H., Xue, S. and Xu, Q. (2019), "Multi-objective particle swarm optimization of sensor distribution scheme with consideration of the accuracy and the robustness for deformation reconstruction", Sensor., 19(6), 1306. https://doi.org/10.3390/s19061306.
  48. Zhao, F.F., Kefal, A. and Bao, H. (2022), "Nonlinear deformation monitoring of elastic beams based on isogeometric iFEM approach", Int. J. Nonlin. Mech., 147, 104229. https://doi.org/10.1016/j.ijnonlinmec.2022.104229.
  49. Zhao, F.F., Xu, L.B., Bao, H. and Du, J.L. (2020), "Shape sensing of variable cross-section beam using the inverse finite element method and isogeometric analysis", Measure., 158, 107656. https://doi.org/10.1016/j.measurement.2020.107656.
  50. Zhao, Y., Du, J.L., Bao, H. and Xu, Q. (2018), "Optimal sensor placement based on eigenvalues analysis for sensing deformation of wing frame using iFEM", Sensor., 18(8), 2424. https://doi.org/10.3390/s18082424.
  51. Zhong, X. and Yu, L. (2022), "Structural damage identification based on transmissibility assurance criterion and weighted Schatten-p regularization", Struct. Eng. Mech., 82(6), 771-783. https://doi.org/10.12989/sem.2022.82.6.771.