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Geometrically Nonlinear Deformation Reconstruction Based on iQS4 Elements Using a Linearized Iterative iFEM Algorithm

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Abstract

Structural shape monitoring plays a vital role in the structural health monitoring systems. The inverse finite element method (iFEM) has been demonstrated to be a practical method of deformation reconstruction owing to its unique advantages. Current iFEM formulations have been applied to small deformation of structures based on the small-displacement assumption of linear theory. However, this assumption may be inapplicable to some structures with large displacements in practical applications. Therefore, geometric nonlinearity needs to be considered. In this study, to expand the practical utility of iFEM for large displacement monitoring, we propose a nonlinear iFEM algorithm based on a four-node inverse quadrilateral shell element iQS4. Taking the advantage of an iterative iFEM algorithm, a nonlinear response is linearized to compute the geometrically nonlinear deformation reconstruction, like the basic concept of nonlinear FE analysis. Several examples are solved to verify the proposed approach. It is demonstrated that large displacements can be accurately estimated even if the in-situ sensor data includes different levels of randomly generated noise. It is proven that the nonlinear iFEM algorithm provides a more accurate displacement response as compared to the linear iFEM methodology for structures undergoing large displacement. Hence, the proposed approach can be utilized as a viable tool to effectively characterize geometrically nonlinear deformations of structures in real-time applications.

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All data generated or analyzed during this study are included in this published article.

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Acknowledgements

This research is supported by the National Natural Science Foundation of China (Grant No. 11902253) and the Fundamental Research Funds for the Central Universities of China. The authors are grateful for this support.

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Authors and Affiliations

  1. School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University, Xi’an, 710129, China

    Mengying Li, Dawei Jia, He Huang & Ziyan Wu

  2. Faculty of Engineering and Natural Sciences, Sabanci University, Tuzla, Istanbul, 34956, Turkey

    Adnan Kefal

  3. Integrated Manufacturing Technologies Research and Application Center, Sabanci University, Tuzla, Istanbul, 34956, Turkey

    Adnan Kefal

Authors
  1. Mengying Li
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  2. Dawei Jia
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  3. He Huang
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  4. Ziyan Wu
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  5. Adnan Kefal
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Contributions

ML was involved in data curation, validation and writing—original draft. DJ performed software. HH and ML were involved in formal analysis. HH was involved in funding acquisition. ZW was involved in supervision. ML, ZW, HH and AK were involved in writing—review & editing.

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Correspondence to He Huang.

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The results of this paper presented clearly, honestly, and without fabrication, falsification or inappropriate data manipulation.

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The submitted manuscript was original and was not published elsewhere in any form or languages. The paper was maintaining integrity of the research and its presentation is helped by following the rules of good scientific practice.

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Li, M., Jia, D., Huang, H. et al. Geometrically Nonlinear Deformation Reconstruction Based on iQS4 Elements Using a Linearized Iterative iFEM Algorithm. Acta Mech. Solida Sin. 36, 166–180 (2023). https://doi.org/10.1007/s10338-022-00369-6

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  • DOI: https://doi.org/10.1007/s10338-022-00369-6

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