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An iterative
Trefftz method for the inverse Cauchy problem in isotropic
thin plate bending
Chong Yan, Xiaohua Zhao and Huiming Hou |
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Vol. 20 (2025), No. 4, 453–470
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DOI: 10.2140/jomms.2025.20.453
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Abstract |
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A novel Trefftz function is employed in this study to address the inverse Cauchy boundary value problem arising in thin plate bending. The Trefftz functions are constructed by applying the method of separation of variables to the governing equilibrium equation of the plate. Due to the ill-conditioned nature of the resulting matrix equations, the Kozlov iterative method is introduced to transform them into two well-posed problems, which are subsequently solved using the collocation approach. The effectiveness of the method is demonstrated through numerical experiments involving both smooth and piecewise smooth domains, with scenarios considering exact as well as noisy boundary data. A comprehensive investigation is conducted into how the algorithm’s performance is influenced by key parameters, including the number of series terms, collocation points, iterations, and noise levels. The results suggest that the proposed numerical scheme attains good accuracy and stable, convergent performance across the tested cases while maintaining practical computational cost, indicating promise for inverse Cauchy problems in isotropic thin plate bending. |
Keywords
Cauchy problem, elasticity, iterative Trefftz method,
inverse problem, thin plate bending
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Milestones
Received: 22 July 2025
Revised: 6 September 2025
Accepted: 18 October 2025
Published: 1 November 2025
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Authors |
| Chong Yan | |
| Department of Civil Engineering and
Smart Cities Shantou University Shantou, 515000 China |
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| Xiaohua Zhao | |
| Department of Civil Engineering and
Smart Cities Shantou University Shantou, 515000 China |
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| Huiming Hou | |
| Department of Civil Engineering and
Smart Cities Shantou University Shantou, 515000 China |
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| © 2025 MSP (Mathematical Sciences Publishers). |
