Elastic compensation for dynamic rigid-plastic solutions of structures

YU Tongxi; HU Qingjie; ZHU Ling

doi:10.11883/bzycj-2023-0414

Volume 44 Issue 1

Jan. 2024

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YU Tongxi, HU Qingjie, ZHU Ling. Elastic compensation for dynamic rigid-plastic solutions of structures[J]. Explosion And Shock Waves, 2024, 44(1): 011001. doi: 10.11883/bzycj-2023-0414

Citation:

YU Tongxi, HU Qingjie, ZHU Ling. Elastic compensation for dynamic rigid-plastic solutions of structures[J]. Explosion And Shock Waves, 2024, 44(1): 011001. doi: 10.11883/bzycj-2023-0414

YU Tongxi, HU Qingjie, ZHU Ling. Elastic compensation for dynamic rigid-plastic solutions of structures[J]. Explosion And Shock Waves, 2024, 44(1): 011001. doi: 10.11883/bzycj-2023-0414

Citation:

YU Tongxi, HU Qingjie, ZHU Ling. Elastic compensation for dynamic rigid-plastic solutions of structures[J]. Explosion And Shock Waves, 2024, 44(1): 011001. doi: 10.11883/bzycj-2023-0414

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Elastic compensation for dynamic rigid-plastic solutions of structures

doi: 10.11883/bzycj-2023-0414

1.
Department of Mechanical and Aerospace Engineering, Hong Kong University of Science and Technology, Kowloon, Hong Kong, China
2.
School of Naval Architecture, Ocean and Energy Power Engineering, Wuhan University of Technology, Wuhan 430063, Hubei, China

Received Date: 2023-11-15
Rev Recd Date: 2023-12-18

Available Online: 2023-12-25

Publish Date: 2024-01-11

Abstract

Abstract

In recent years, by combining membrane factor method (MFM) and saturation analysis (SA) as a powerful theoretical tool, scholars in China have made comprehensive studies on the large dynamic plastic deformation of beams, plates and other structures under pulse loading, leading to the best rigid-plastic predictions for the final deflection of the pulse-loaded structures, which are superior to the previously proposed various approximate rigid-plastic solutions. However, due to the complexity of the dynamic elastic-plastic response of structures used in engineering and the limitations of numerical simulations, it is critical to clarify how large is the error generated from the rigid-plastic solutions in predicting the final deflection of pulse-loaded structures compared to the result that takes the elastic effect of material into consideration. Our preliminary study on this issue, which has been published in leading international journals, reveals the effect of material’s elasticity on the large dynamic plastic deformation of structures under pulse loading, and quantitatively evaluates the discrepancies between the final deflection predicted by the best theoretical rigid-plastic solutions and that extracted from elastic-plastic numerical simulations. On this basis, the present paper proposes a strategy to compensate for elastic effect; that is, (1) adding a compensation term to the final deflection predicted by the existing best rigid-plastic solution; (2) expressing the compensation term as an elemental function of variables separation to respectively represent the effects of the pulse intensity and the structural stiffness; and (3) adopting minimum number of undetermined coefficients (or power) in the fitting function to achieve concise formulae. Meanwhile, the variation ranges of structural stiffness and dimensionless load parameter are investigated with reference to metallic structures used in their main application fields. Finally, by implementing the fitting and compensation for the cases of fully-clamped beams and square plates, simple and engineer-friendly formulae for predicting the final deflection of beams and plates are eventually obtained. With the compensation terms being added, the rigid-plastic-solution-based predictions on the final deflection of beams and plates possess a relative error within the range of 3%, which are appropriate and suitable for applications in the engineering design stage. A table at the end of the paper summarizes the major notations and formulae, as well as the comparison between the results on beams and square plates.

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References(18)

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