近年來，逆有限元素法受到日益關注，並被視為結構健康監測領域中的主要方法之一。針對工程應用中常見的加勁薄板結構，本研究提出混合式逆有限元素法，可針對具有多種加強材類型的結構，在感測器數量有限的布局下實現高效監測。然而，複雜結構的即時監測應用須具備快速且穩定的數值計算能力。為應對此挑戰，本研究將模型降階技術整合進混合式逆有限元素法架構中，以提升其計算速率。此外，本研究亦納入熱與機械載荷條件，以進一步驗所提出的方法在不同載荷環境下對結構行為的準確預測能力。研究結果顯示，該方法在解決加勁結構健康監測問題方面展現出高度潛力。

Recently, the inverse finite element method (iFEM) has gained increasing attention and is regarded as one of the primary approaches in the field of structural health monitoring. To evaluate stiffened thin-walled structures, which are commonly used in engineering applications, a Hybrid iFEM is proposed in this study to enable efficient monitoring of structures with various types of stiffeners using a sparse sensor layout. However, the practical implementation of real-time monitoring in complex structures requires rapid and stable computational performance. To address this challenge, a model order reduction technique (MOR) is incorporated into the Hybrid iFEM framework to enhance computational efficiency. Furthermore, this study considers combined thermo-mechanical loading conditions to further demonstrate the capability of the proposed Hybrid iFEM in accurately predicting structural responses under diverse operational environments. The results highlight the strong potential of the method in addressing structural health monitoring of stiffened structures.

[1] International Maritime Organization (IMO). "Recommendations for the Fitting of Hull Stress Monitoring Systems." International Maritime Organization (IMO), UK, 1994.
[2] Det Norske Veritas (DNV-GL). Rules for Classification." Det Norske Veritas (DNV-GL), Norway, 2022.
[3] Bureau Veritas (BV). "Rules for Hull Stress and Motion Monitoring MON-HULL." Bureau Veritas (BV), France, 2022.
[4] American Bureau of Shipping (ABS). "Guide for Hull Condition Monitoring System." American Bureau of Shipping (ABS), USA, 2020.
[5] M. Fujikubo. "A digital twin for ship structures—R&D project in Japan". Data-Centric Engineering." vol. 5, 2024.
[6] A. Silva-Campillo, F. Pérez-Arribas, J.C. Suárez-Bermejo. "Health-Monitoring Systems for Marine Structures: A Review." Sensors, vol. 23, pp. 2099, 2023.
[7] A. Tessler, J.L. Spangler. "A Variational Principal for Reconstruction of Elastic Deformation of Shear Deformable Plates and Shells." NASA Langley Research Center: Hampton, USA, 2003.
[8] A. Tessler, J.L. Spangler. "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, vol. 194, pp. 327-339, 2005.
[9] A. Kefal, E. Oterkus, A. Tessler, J.L. Spangler. "A Quadrilateral Inverse Shell Element with Drilling Degrees of Freedom for Shape Sensing and Structural Health Monitoring." Engineering Science and Technology, an International Journal, vol. 19, pp. 1299-1313, 2016.
[10] A. Kefal. "An Efficient Curved Inverse-Shell Element for Shape Sensing and Structural Health Monitoring of Cylindrical Marine Structures." Ocean Engineering, vol. 188, pp. 106262, 2019.
[11] A. Kefal, E. Oterkus. "Isogeometric iFEM Analysis of Thin Shell Structures." Sensors, vol. 20, pp. 2685, 2020.
[12] A. Kefal, A. Tessler, E. Oterkus. "An Enhanced Inverse Finite Element Method for Displacement and Stress Monitoring of Multilayered Composite and Sandwich Structures." Composite Structures, vol. 179, pp. 514-540, 2017.
[13] A. Kefal, J.B. Mayang, E. Oterkus, M. Yildiz. "Three Dimensional Shape and Stress Monitoring of Bulk Carriers Based on iFEM Methodology." Ocean Engineering, vol. 147, pp. 256-267, 2018.
[14] A. Kefal, E. Oterkus. "Displacement and Stress Monitoring of a Panamax Containership using Inverse Finite Element Method." Ocean Engineering, vol. 119, pp. 16-29, 2016.
[15] A. Kefal, E. Oterkus. "Displacement and Stress Monitoring of a Chemical Tanker Based on Inverse Finite Element Method." Ocean Engneering, vol. 112, pp. 33-46, 2016.
[16] M. Li, A. Kefal, B. Cerik, E. Oterkus. "Structural Health Monitoring of Submarine Pressure Hull using Inverse Finite Element Method." In Trends in the Analysis and Design of Marine Structures, CRC Press, USA, 2019.
[17] M. Li, A. Kefal, E. Oterkus, S. Oterkus. "Structural Health Monitoring of an Offshore Wind Turbine Tower using iFEM Methodology." Ocean Engineering, vol. 204, pp. 107291, 2020.
[18] M. Li, Y. Dirik, E. Oterkus, S. Oterkus. "Shape Sensing of NREL 5 MW Offshore Wind Turbine Blade using iFEM Methodology." Ocean Engineering, vol. 273, pp. 114036, 2023.
[19] M. Gherlone, P. Cerracchio, M. Mattone, M.D. Sciuva, A. Tessler. "Shape sensing of 3D frame structures using an Inverse Finite Element Method." International Journal of Solids and Structures, vol. 49, pp. 3100-3112, 2012.
[20] M. Gherlone, P. Cerracchio, M. Mattone, M.D. Sciuva, A. Tessler. "An Inverse Finite Element method for beam shape sensing: Theoretical framework and experimental validation." Smart Materials and Structures, vol. 23, pp. 045027, 2014.
[21] R. Roy, M. Gherlone, C. Surace. "Shape Sensing of Beams with Complex Cross-sections Using the Inverse Finite Element Method." In Proceedings of the Twelfth International Workshop on Structural Health Monitoring, 2019.
[22] F. Zhao, L. Xu, H. Bao, J. Du. "Shape sensing of variable cross-section beam using the Inverse Finite Element method and isogeometric analysis." Measurement, vol. 158, pp. 107656, 2020.
[23] R. Roy, M. Gherlone, C. Surace. "A shape sensing methodology for beams with generic cross-sections: Application to airfoil beams." Aerospace Science and Technology, vol. 110, pp. 106484, 2021.
[24] T. Dong, S. Yuan, T. Huang. "Beam Element-Based Inverse Finite Element Method for Shape Reconstruction of a Wing Structure." In Proceedings of the ASME International Mechanical Engineering Congress and Exposition, 2021.
[25] H. Zhu, Z. Du, Y. Tang. "Numerical study on the displacement reconstruction of subsea pipelines using the improved Inverse Finite Element method." Ocean Engineering, vol. 248, pp. 110763, 2022.
[26] R. Roy, M. Esposito, M. Gherlone, C. Surace. "Structural deformation reconstruction using the Hybrid Shell-Beam Inverse Finite Element method: Theory & numerical results." In Proceedings of the Computational Methods in Structural Dynamics and Earthquake Engineering, 2023.
[27] M. Esposito, R. Roy, M. Gherlone, C. Surace. "Structural deformation reconstruction using the Hybrid Shell-Beam Inverse Finite Element method: Experimental application on a Thin-Walled stiffened panel." In Proceedings of the Computational Methods in Structural Dynamics and Earthquake Engineering, 2023.
[28] M. Esposito, R. Roy, C. Surace, M. Gherlone. "Hybrid Shell-Beam Inverse Finite Element Method for the Shape Sensing of Stiffened Thin-Walled Structures: Formulation and Experimental Validation on a Composite Wing-Shaped Panel." Sensors, vol. 23, pp. 5962, 2023.
[29] R.J. "Guyan. Reduction of stiffness and mass matrices." AIAA Journal, vol. 3, pp. 380, 1965.
[30] R.L. Kidder. "Reduction of structural frequency equations." AIAA Journal, vol. 11, pp. 892, 1984.
[31] F. Bourquin. "Component mode synthesis and eigenvalues of second order operators : discretization and algorithm." M2AN, vol. 26, pp. 385-423, 1992.
[32] N. Bouhaddi, R. Fillod. "Substructuring by a two level dynamic condensation method." Computers & Structures, vol. 60, pp. 403-409, 1996.
[33] M. Paz. "Dynamic Condensation." AIAA Journal, vol. 22, pp. 724-727, 1984.
[34] R. Lin, Y. Xia. "A new eigensolution of structures via dynamic condensation." Journal of Sound and Vibration, vol. 266, pp. 93-106, 2003.
[35] D.E. Carlson. "Linear Thermoelasticity, encyclopedia of physics." Springer, Berlin, 1973.
[36] W. Nowacki "Thermoelasticity, 2nd ed." PWN-Polish Scientific Publishers, Oxford, 1986.
[37] R.B. Hetnarski, M.R. Eslami. "Thermal stresses: advanced theory and applications." Springer, New York, 2009.
[38] C.T. Nguyen, S. Oterkus. "Peridynamics for the thermomechanical behavior of shell structures." Engineering Fracture Mechanics, vol. 219, pp. 106623, 2019.
[39] ANSYS. "Mechanical User’s Guide." ANSYS, Inc., 2023.
[40] International Association of Classification Societies(IACS). "Recommendations for the wave statistics intended for design of sea-going ships above 90 meters including the effect of bad weather avoidance." IACS, UK, 2022.