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On dynamic response of double-layer rectangular sandwich plates with FML face-sheets and metal foam cores under blast loading

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Abstract

In this paper, the dynamic response of fiber-metal laminate (FML) double-layer sandwich plates under blast loading is studied through theoretical analysis and finite element (FE) calculation. The membrane mode solution is obtained for the dynamic response of the clamped FML double-layer sandwich plate under blast loading, and the so-called ‘bounds’ are obtained through circumscribing and inscribing lines of the exact yield locus. The FE model is established, and the analytical model is proved by the FE method. The influences of geometrical parameters and material properties on the dynamic response of FML double-layer sandwich plates are researched based on the analytical model. Finally, it is found that FML double-layer sandwich plates have better anti-explosion performance with equal mass by comparing with the metal sandwich plates.

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Acknowledgements

The authors are grateful for their financial support through the Fund for the Shandong Key Laboratory of Civil Engineering Disaster Prevention and Mitigation (CDPM2021KF07) and NSFC (12272290 and 11872291), opening project of State Key Laboratory of Structural Analysis for Industrial Equipment, China (GZ22110).

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Authors and Affiliations

  1. Shandong Key Laboratory of Civil Engineering Disaster Prevention and Mitigation, Shandong University of Science and Technology, Qingdao, 266590, China

    Jinlong Du & Jianxun Zhang

  2. State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian, 116024, People’s Republic of China

    Jinlong Du & Jianxun Zhang

  3. State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace Engineering, Xi’an Jiaotong University, Xi’an, 710049, China

    Jinlong Du, Jinwen Bai, Yongzheng Zhang & Jianxun Zhang

  4. China Nuclear Power Engineering Co., LTD., Beijing, 100840, China

    Hao Su

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  1. Jinlong Du
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Appendix A: The inscribing coefficient of inscribing yield criterion

Appendix A: The inscribing coefficient of inscribing yield criterion

The inscribing coefficient of compressed double-layer metal sandwich section is given in Ref. [30], and the inscribing coefficient of compressed sandwich section with FML face-sheets \(\vartheta^{\prime}\) can be expressed as

$$\vartheta^{\prime} = \left\{ {\begin{array}{*{20}l} {\frac{{\sqrt {1 + 4k_{0} } - 1}}{{2k_{0} }},} \hfill & {J_{1} \ge 0} \hfill \\ {\frac{{\sqrt {k_{1}^{2} + 4k_{2} } + k_{1} }}{2},} \hfill & {J_{1} < 0{\text{ and }}J_{2} > 0} \hfill \\ {\frac{{\sqrt {k_{3}^{2} + 4k_{4} } - k_{3} }}{2},} \hfill & { \, J_{2} \le 0} \hfill \\ \end{array} } \right.$$
(A1)

where

$$k_{0} = \frac{{\left[ {2\overline{h} + \frac{1}{{f\overline{\sigma }_{1} + \left( {1 - f} \right)\overline{\sigma }_{2} }}} \right]^{2} }}{A},$$
$$k_{1} = \frac{{4\overline{h}\left( {1 - \frac{1}{{f\overline{\sigma }_{1} + \left( {1 - f} \right)\overline{\sigma }_{2} }} - \varepsilon_{c2} } \right)\left( {1 - \varepsilon_{c2} } \right)\left[ {2\overline{h} + \frac{1}{{f\overline{\sigma }_{1} + \left( {1 - f} \right)\overline{\sigma }_{2} }}} \right] - \frac{3A}{{f\overline{\sigma }_{1} + \left( {1 - f} \right)\overline{\sigma }_{2} }}\left( {1 - \varepsilon_{c2} } \right)}}{{3\left[ {2\overline{h} + \frac{1}{{f\overline{\sigma }_{1} + \left( {1 - f} \right)\overline{\sigma }_{2} }}} \right]^{2} \left( {1 - \varepsilon_{c2} } \right)^{2} }},$$
$$k_{2} = \frac{{9\left[ {C + \frac{{\left( {\frac{2}{3}\overline{h} + 1 - \varepsilon_{c2} } \right)^{2} }}{{f\overline{\sigma }_{1} + \left( {1 - f} \right)\overline{\sigma }_{2} }} + \frac{{\varepsilon_{c2} - \varepsilon_{c1} }}{{2f\overline{\sigma }_{1} + 2\left( {1 - f} \right)\overline{\sigma }_{2} }}} \right]\frac{{1 - \varepsilon_{c2} }}{{f\overline{\sigma }_{1} + \left( {1 - f} \right)\overline{\sigma }_{2} }} - 4\overline{h}^{2} \left[ {1 - \frac{1}{{f\overline{\sigma }_{1} + \left( {1 - f} \right)\overline{\sigma }_{2} }} - \varepsilon_{c2} } \right]^{2} }}{{9\left[ {2\overline{h} + \frac{1}{{f\overline{\sigma }_{1} + \left( {1 - f} \right)\overline{\sigma }_{2} }}} \right]^{2} \left( {1 - \varepsilon_{c2} } \right)^{2} }},$$
$$k_{3} = \frac{{2\left[ {2\overline{h} + \frac{1}{{f\overline{\sigma }_{1} + \left( {1 - f} \right)\overline{\sigma }_{2} }}} \right]\left( {1 - \frac{1}{{f\overline{\sigma }_{1} + \left( {1 - f} \right)\overline{\sigma }_{2} }} - \varepsilon_{c2} } \right) + A}}{{\left[ {2\overline{h} + \frac{1}{{f\overline{\sigma }_{1} + \left( {1 - f} \right)\overline{\sigma }_{2} }}} \right]^{2} }},$$
$$k_{4} = \frac{{2\overline{h} - \frac{1}{{f\overline{\sigma }_{1} + \left( {1 - f} \right)\overline{\sigma }_{2} }} + 2 - 2\varepsilon_{c2} }}{{2\overline{h} + \frac{1}{{f\overline{\sigma }_{1} + \left( {1 - f} \right)\overline{\sigma }_{2} }}}} + \frac{{\frac{4}{3}\overline{h}\left( {\varepsilon_{c2} - \varepsilon_{c1} } \right) + \frac{{\varepsilon_{c2} - \varepsilon_{c1} }}{{2f\overline{\sigma }_{1} + 2\left( {1 - f} \right)\overline{\sigma }_{2} }}}}{{\left[ {2\overline{h} + \frac{1}{{f\overline{\sigma }_{1} + \left( {1 - f} \right)\overline{\sigma }_{2} }}} \right]^{2} }},$$
$$J_{1} = \frac{{3\overline{h}}}{{2\overline{h} + \frac{1}{{f\overline{\sigma }_{1} + \left( {1 - f} \right)\overline{\sigma }_{2} }}}} + \frac{{2\overline{h}^{2} }}{3A} - 1,$$
$$J_{2} = \frac{{3\overline{h} + \frac{3}{{2f\overline{\sigma }_{1} + 2\left( {1 - f} \right)\overline{\sigma }_{2} }}}}{{2\overline{h} + \frac{1}{{f\overline{\sigma }_{1} + \left( {1 - f} \right)\overline{\sigma }_{2} }}}} - \frac{{16\overline{h}^{2} - 6\overline{h}\left( {2 - \varepsilon_{c2} - \varepsilon_{c1} } \right) + \frac{{9\left( {\varepsilon_{c2} - \varepsilon_{c1} } \right)}}{{4f\overline{\sigma }_{1} + 4\left( {1 - f} \right)\overline{\sigma }_{2} }}}}{3A},$$
$$A = 4\overline{h}^{2} + \frac{1}{{f\overline{\sigma }_{1} + \left( {1 - f} \right)\overline{\sigma }_{2} }} + \frac{{8\overline{h}}}{3}\left[ {1 + \frac{1}{{2f\overline{\sigma }_{13} + 2\left( {1 - f} \right)\overline{\sigma }_{2} }}} \right] - \frac{1}{2}\left( {\varepsilon_{c2} + \varepsilon_{c1} } \right) - \frac{{4\overline{h}\left( {\varepsilon_{c2} + \varepsilon_{c1} } \right)}}{3},$$
$$C = \frac{{4\overline{h}}}{3}\left( {\frac{{8\overline{h}}}{3} + 2 - \varepsilon_{c2} - \varepsilon_{c1} } \right).$$

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Du, J., Su, H., Bai, J. et al. On dynamic response of double-layer rectangular sandwich plates with FML face-sheets and metal foam cores under blast loading. J Braz. Soc. Mech. Sci. Eng. 45, 31 (2023). https://doi.org/10.1007/s40430-022-03956-3

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