Journal of Applied and Computational Mechanics
Two-node Curved Inverse Finite Element Formulations based on Exact Strain-displacement Solution
Document Type : Research Paper
Authors
Department of Structural, Geotechnical and Building Engineering, Politecnico di Torino, Turin, 10129, Italy
Abstract
The inverse finite element method (iFEM) is an efficient algorithm developed for real-time monitoring of structures equipped by a network of strain sensors. The inverse element for modeling curved beams was previously developed using an approximate solution based on independently interpolated displacement components. In this study, a new formulation is proposed by the development of a least-squares variational principle using the kinematic framework of the curved beam theory. The library of existing iFEM-based elements is expanded by introducing three different inverse curved elements named iCB3, iCB4 and iCB5 respectively. This new formulation has been developed considering the exact solution of the curved beam theory that corresponds to the membrane-bending coupling and the explicit statement of the rigid-body motions. The three inverse elements, which require three, four and five measurement points respectively, extend the practical utility of iFEM for shape sensing analysis of curved structures according to the minimum available quantity of strain sensors. The effectiveness and higher accuracy of the iCB/iFEM methodology compared to other solutions present in literature are demonstrated considering numerical studies on curved beams under static transverse force and distributed loading conditions. For these problems, the effect of strain measurements error, number of sensors and discretization refinement on the solution accuracy is evaluated.
Keywords
Main Subjects
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[1] Tessler, A., Spangler, J.L., A Variational Principle for Reconstruction of Elastic Deformations in Shear Deformable Plates and Shells, NASA/TM-2003-212445, 2003.
[2] Tessler, A., Spangler, J.L., A least-squares variational method for full-field reconstruction of elastic deformations in shear-deformable plates and shells, Computer Methods in Applied Mechanics and Engineering, 194(2-5), 2005, 327-339.
[3] Gherlone, M., Beam inverse finite element formulation, LAQ Rep. Politecnico di Torino, 2008.
[4] Gherlone, M., Cerracchio, P., Mattone, M., Di Sciuva, M., Tessler, A., Dynamic shape reconstruction of three-dimensional frame structures using the inverse finite element method, Proceedings of 3rd ECCOMAS Thematic Conference on Computational Methods in Structural Dynamics and Earthquake Engineering, Corfù, Greece, 2011.
[5] Gherlone, M., Cerracchio, P., Mattone, M., Di Sciuva, M., Tessler, A., Shape Sensing of 3D frame structures using an inverse Finite Element Method, International Journal of Solids and Structures, 49, 2012, 3100-3112.
[6] Cerracchio, P., Gherlone, M., Di Sciuva, M., Tessler, A., A novel approach for displacement and stress monitoring of sandwich structures based on the inverse Finite Element Method, Composite Structures, 127, 2015, 69-76.
[7] Kefal, A., Oterkus, E., Tessler, A., Spangler, J.L., A quadrilateral inverse-shell element with drilling degrees of freedom for shape sensing and structural health monitoring, Engineering Science and Technology, an International Journal, 19, 2016, 1299-1313.
[8] Kefal, A., Tessler, A., Oterkus, E., An enhanced inverse finite element method for displacement and stress monitoring of multilayered composite and sandwich structures, Composite Structures, 179, 2017, 514-540.
[9] Tessler, A., Roy, R., Esposito, E., Surace, C., Gherlone, M., Shape Sensing of Plate and Shell Structures Undergoing Large Displacements Using the Inverse Finite Element Method, Shock and Vibration, 2018, 2018, 8076085.
[10] Kefal, A., An efficient curved inverse-shell element for shape sensing and structural health monitoring of cylindrical marine structures, Ocean Engineering, 188, 2019, 106262.
[11] Savino, P., Gherlone, M., Tondolo, F., Shape sensing with inverse finite element method for slender structures, Structural Engineering & Mechanics, 72(2), 2019, 217-227.
[12] Kefal, A., Tabrizi, I.E., Yildiz, M., Tessler, A., A smoothed iFEM approach for efficient shape-sensing applications: Numerical and experimental validation on composite structures, Mechanical Systems and Signal Processing, 152, 2021, 107486.
[13] Kefal, A., Oterkus, E., Isogeometric iFEM Analysis of Thin Shell Structures, Sensors, 20(9), 2020, 2685.
[14] Savino, P., Tondolo, F., Gherlone, M., Tessler, A., Application of Inverse Finite Element Method to Shape Sensing of Curved Beams, Sensors, 20(24), 2020, 7012.
[15] Colombo, L., Sbarufatti, C., Giglio, M., Definition of a load adaptive baseline by inverse finite element method for structural damage identification, Mechanical Systems and Signal Processing, 120, 2019, 584-607.
[16] Colombo, L., Oboe, D., Sbarufatti, C., Cadini, F., Russo, S., Giglio, M., Shape sensing and damage identification with iFEM on a composite structure subjected to impact damage and non-trivial boundary conditions, Mechanical Systems and Signal Processing, 148, 2021, 107163.
[17] Roy, R., Gherlone, M., Surace, C., Damage Localisation in Thin Plates Using the Inverse Finite Element Method, Proceedings of the 13th International Conference on Damage Assessment of Structures. Lecture Notes in Mechanical Engineering, Springer, Singapore, 2020.
[18] Li, M., Kefal, A., Cerik, B.C., Oterkus, E., Dent damage identification in stiffened cylindrical structures using inverse Finite Element Method, Ocean Engineering, 198, 2020, 106944.
[19] Oboe, D., Colombo, L., Sbarufatti, C., Giglio, M., Comparison of strain pre-extrapolation techniques for shape and strain sensing by iFEM of a composite plate subjected to compression buckling, Composite Structures, 262, 2021, 113587.
[20] Quach, C.C., Vazquez, S.L., Tessler, A., Moore, J.P., Cooper, E.G., Structural Anomaly Detection Using Fiber Optic Sensors and Inverse Finite Element Method, AIAA Guidance, Navigation, and Control Conference and Exhibit, San Francisco, California, 2005.
[21] Gherlone, M., Cerracchio, P., Mattone, M., Di Sciuva, M., Tessler, A., Beam shape sensing using inverse finite element method: theory and experimental validation, Proceeding of 8th International Workshop on Structural Health Monitoring, Stanford, California, 2011.
[22] Gherlone, M., Cerracchio, P., Mattone, M., Di Sciuva, M., Tessler, A., An inverse finite element method for beam shape sensing: theoretical framework and experimental validation, Smart Material and Structures, 23(4), 2014, 045027.
[23] Kefal, A., Oterkus, E., Displacement and stress monitoring of a chemical tanker based on inverse finite element method, Ocean Engineering, 112, 2016, 33-46.
[24] Kefal, A., Oterkus, E., Displacement and stress monitoring of a Panamax containership using inverse finite element method, Ocean Engineering, 119, 2016, 16-29.
[25] Papa, U., Russo S., Lamboglia, A., Del Core, G., Iannuzzo, G., Health structure monitoring for the design of an innovative UAS fixed wing through inverse finite element method (iFEM), Aerospace Science and Technology, 69, 2017, 439-448.
[26] Kefal, A., Yildiz, M., Modeling of Sensor Placement Strategy for Shape Sensing and Structural Health Monitoring of a Wing-Shaped Sandwich Panel Using Inverse Finite Element Method, Sensors, 17(12), 2017, 2775.
[27] Zhao, Y., Bao, H., Duan, X., Fang, H., The Application Research of Inverse Finite Element Method for Frame Deformation Estimation, International Journal of Aerospace Engineering, 2017, 2017, 1326309.
[28] Liu, M., Zhang, X., Song, H., Zhou, S., Zhou, Z., Zhou, W., Inverse Finite Element Method for Reconstruction of Deformation in the Gantry Structure of Heavy-Duty Machine Tool Using FBG Sensors, Sensors, 18(7), 2018, 2173.
[29] Liu, M., Zhang, X., Song, H., Wang, J., Zhou, S., Reconstruction algorithm for obtaining the bending deformation of the base of heavy-duty machine tool using inverse finite element method, Metrology and Measurement System, 25(4), 2018, 727-741.
[30] Liu, M., Zhou, F., Song, H., Yang, X., Wang, J., Deformation Reconstruction for a Heavy-Duty Machine Column Through the Inverse Finite Element Method, IEEE Sensors Journal, 20(16), 2020, 9218-9225.
[31] Zhao, Y., Du, J., Bao, H., Xu, Q., Optimal Sensor Placement Based on Eigenvalues Analysis for Sensing Deformation of Wing Frame Using iFEM, Sensors, 18(8), 2018, 2424.
[32] Zhao, Y., Du, J., Bao, H., Xu, Q., Optimal Sensor Placement for Inverse Finite Element Reconstruction of Three-Dimensional Frame Deformation, International Journal of Aerospace Engineering, 2018, 2018, 6121293.
[33] Kobayashi, M., Murayama, H., Shape sensing for pipe structures by inverse finite element method based on distributed fiber-optic sensors, 26th International Conference on Optical Fiber Sensors, Lausanne, Switzerland, 2018.
[34] Kefal, A., Mayang, J.B., Oterkus, E., Yildiz, M., Three dimensional shape and stress monitoring of bulk carriers based on iFEM methodology, Ocean Engineering, 147, 2018, 256-267.
[35] Niu, S., Li, K., Liu, J., Bao, H., A Refined Shape Sensing Method for Skin Antenna Structure Based on Inverse Finite Element Method, Applied Sciences, 10(21), 2020, 7620.
[36] Li, M., Kefal, A., Oterkus, E., Oterkus, S., Structural health monitoring of an offshore wind turbine tower using iFEM methodology, Ocean Engineering, 204. 2020, 107291.
[37] Dawe, D.J., Rigid-body motions and strain-displacement equations of curved shell finite elements, International Journal of Mechanical Sciences, 14(9), 1972, 569-578.
[38] Dawe, D.J., Curved finite elements for the analysis of shallow and deep arches, Computers & Structures, 4(3), 1974, 559-580.
[39] FEA Ltd, LUSAS Finite Element System V15.1: User’s Manual, FEA Ltd, UK, 1995.
[40] Qatu, M.S., Theories and analyses of thin and moderately thick laminated composite curved beams, International Journal of Solids and Structures, 30(20), 1993, 2743-2756.
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