Finite Element Analysis of Elastic Inherent Strain of Saddle Plates with Multiple Heating Lines During Induction Heating

Abstract

This study adopts an elastic inherent-strain finite element method to address the deformation prediction for saddle plates with multiple heating lines during induction heating. First, a thermal–elastic–plastic finite element model is established to simulate the forming process of a saddle plate with multiple heating lines, from which inherent strain values for each heating path are derived. These actual inherent strain values are then applied as loading conditions in an elastic inherent strain finite element analysis to predict the deformation of a large saddle plate during induction heating. Experimental and numerical comparisons confirm that the proposed approach, incorporating inherent strains specific to each heating line, significantly increases the deformation prediction accuracy over conventional methods that use either averaged or single heating line inherent strain values.

Keywords

Saddle plate / Induction heating / Inherent strain / Multiple heating lines / Prediction

References

[1] Ahmad SN, Manurung YHP, Prajadhiana KP, Busari YO, Mat MF, Muhammad N, Leitner M, Saidin S. Numerical modelling and experimental analysis on angular strain induced by bead-on-plate SS316L GMAW using inherent strain and thermomechanical methods. The International Journal of Advanced Manufacturing Technology, 2022, 120(1): 627-644

[2] Anderson RJ. Experiments and simulation of line heating of plates, 1999, Cambridge, Massachusetts Institute of Technology

[3] Cong MZ. Numerical calculation of the deformation of the saddle plate with multiple heating lines by induction heating, 2024, Dalian, Dalian University of Technology121(in Chinese)

[4] Dai JL. Research on deflection prediction for the line heating of high strength steel saddle plates, 2024, Dalian, Dalian Maritime University143(in Chinese)

[5] Deng GY. Research on key technology of control and forming of the line heating robot, 2019, Guangzhou, Guangdong University of Technology150(in Chinese)

[6] Mun H, Jang C. Prediction of welding deformation of hull panel blocks using an advanced inherent strain analysis method considering the heat equivalent layer effect. Metals and Materials International, 2011, 17(6): 993-1000

[7] Vega A, Escobar E, Fong A, Ma N, Murakawa H. Analysis and prediction of parallel effect on inherent deformation during the line heating process. Computer Modeling in Engineering & Sciences, 2013, 90(3): 197-210

[8] Vega A, Rashed S, Murakawa H. Analysis of cross effect on inherent deformation during the line heating process – Part 1 – single crossed heating lines. Marine Structures, 2015, 40(5): 92-103

[9] Vega A, Rashed S, Tango Y, Ishiyama M, Murakawa H. Analysis and prediction of multi-heating lines effect on plate forming by line heating. Computer Modeling in Engineering & Sciences, 2008, 28(1): 1-14

[10] Wang J, Liu YJ, Ji ZS, Deng YP. Prediction of line heating parameters for saddle shape plate. Shipbuilding of China, 2005, 46(4): 52-57(in Chinese)

[11] Wang JC, Yi B, Zhang CH. Experiments of double curvature plate bending with induction heating and processing parameters investigation by computational analysis. Ocean Engineering, 2019, 192: 65-72

[12] Wang JC, Zhang CH, Yi B, Zhou H, Liu JC, Ren Q. FE analysis and process planning of plate forming with induction heating. Ship Engineering, 2020, 42(1): 84-92(in Chinese)

[13] Wang JC, Zhang CH, Yi B, Zhou H, Ren Q, Wu TF. An investigation of the induction heating forming process of hull curved plate. Chinese Journal of Ship Research, 2021, 16(2): 141-150(in Chinese)

[14] Wang S, Jia HH, Fu YX, Wang J, Li R. Numerical calculation of line heating for hull curved plate based on strain direct boundary. Ocean Engineering, 2025, 341: 122816

[15] Wang S, Wang J, Xu Z, Wang JY, Wang J, Li R. Numerical calculation of overlapping line heating for marine titanium alloy curved plate. Ocean Engineering, 2024, 296: 117021

[16] Wang S, Xu ZK, Zhao ZB, Wang J, Li R. Numerical calculation of high frequency induction heating for complex hull plate considering deflection. Thin-Walled Structures, 2025, 212: 113158

[17] Woo D, Kitamura M. Numerical prediction of welding distortion considering gravity force on general ship grillage structure by elastic finite element method using inherent strain. Journal of Marine Science and Engineering, 2020, 8: 454

[18] Yazıcıoğlu A, Yaylacı M, Sekban DM, Kuleyin H, Uzun Yaylacı E, Birinci A, Mahmoud SR. Analysis of the contact problem functionally graded layer placed on a Pasternak foundation. ZAMM-Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik, 2025, 105(8): e70152

[19] Yi B, Niu XY, Yue Q, Zheng JX, Zhou H. Bending forming of marine steel plates with high frequency induction heating. Ship Engineering, 2019, 41(7111-116(in Chinese)

[20] Yi B, Wang JC. Mechanism clarification of mitigating welding induced buckling by transient thermal tensioning based on inherent strain theory. Journal of Manufacturing Processes, 2021, 68: 1280-1294

[21] Yuan MG, Ueda Y. Prediction of residual stresses in welded T-and I-joints using inherent strains. Journal of Engineering Materials and Technology, 1996, 118(2229-234

[22] Zeng P, Gao Y, Lei LP. Welding process simulation under varying temperatures and constraints. Materials Science and Engineering: A, 2009, 499(1): 287-292

[23] Zhang XB, Chen C, Liu YJ. Numerical analysis and experimental research of triangle induction heating of the rolled plate. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2017, 231(5): 844-859

[24] Zhang XB, Cong MZ. Numerical simulation and experimental analysis of induction heating deformation of saddle plate with multiple heating lines. Journal of Wuhan University of Technology, 2023, 45(9): 91-95(in Chinese)

[25] Zhang XB, Jia DD. Elastic finite element analysis of saddle plate formed by induction heating. Ship & Boat, 2023, 34(3): 70-75(in Chinese)

[26] Zhao ZW, Yuan H, Zhao Y, Zeng FL. Processing-scheme design for forming curved ship plate and analysis of calculation cases. Journal of Marine Science and Engineering, 2022, 10(10): 1418

[27] Zhu Y, Li ZL, Li M, Ding AB, Luo Y, Li ZG. An equivalent volumetric heat source model for thermal conduction of plate forming by inducted line heating. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2023, 45(8412-1-412-9

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