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Effective Impulse for Fully Clamped Rectangular Plates Under Internal Blast Loading

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Abstract

Under internal blast loading, the response of a beam or plate is highly correlated with the phenomenon of saturated impulse, which governs the deflection of the structure. This paper aims to investigate the phenomenon of saturated impulse for fully clamped rectangular plates subjected to internal blast loading. Based on the rigid, perfectly plastic assumption, the relationship between saturation duration and saturation deflection is derived. Influences of the peak shock wave, the duration of shock wave and the peak quasi-static pressure loading on saturation duration and saturation deflection are discussed. It is found that there is a critical duration for the internal blast impulse to reach saturation, and beyond this duration, the deflection of plate will no longer increase as the loading increases further. The saturation deflection and saturation duration both exhibit regular variation patterns with the changes of the dimensionless peak shock wave, the duration of shock wave and the peak quasi-static pressure loading.

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Abbreviations

E :

Young’s modulus

H :

Thickness of plate

2B :

Side width of plate

2L :

Side length of plate

\(\beta \) :

Aspect ratio

P :

Pressure load

\(P_{R} \) :

Peak load of shock pressure pulse

\(P_{Q} \) :

Peak load of quasi-static pressure pulse

\(P_{y} \) :

Static collapse pressure of plate

\(\tau \) :

Duration of shock pressure pulse

\(T_{0} \) :

Duration of pressure pulse

\(t_{0} \) :

Decaying duration of shock pressure pulse

\(\lambda _{R} \) :

Dimensionless peak load of shock pressure pulse

\(\lambda _{Q} \) :

Dimensionless peak load of quasi-static pressure pulse

W :

Deflection at the plate center

\(\dot{{W}}\) :

Velocity at the plate center

\(\phi \) :

Rotation angles of rigid zone

I :

Impulse

\(\sigma _{y} \) :

Yield stress

\(M_{0} \) :

Fully plastic bending moment per unit length

\(N_{0} \) :

Ultimate stress per unit length

\(\mu \) :

Mass of plate per unit area

w :

Transverse deflection at the hinge

A :

Area of plate under load

r :

Number of plastic hinge lines

\(\dot{\theta } \) :

Relative angular rotation rate across the hinge

\(l_{m} \) :

Length of plastic hinge line

\(\left( \right) ^{sat}\) :

Saturated value

\(\left( \right) _{{max}} \) :

Maximum value

\(\left( \right) _{{f}} \) :

Final value

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Acknowledgements

The authors would like to thank the support from the National Natural Science Foundation of China under Grant No. 11802030.

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Authors and Affiliations

  1. State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing, 100081, China

    Xianben Ren, Xiaoqiang Zhang, Zhixin Huang & Ying Li

  2. Beijing Key Laboratory of Lightweight Multi-functional Composite Materials and Structures, Institute of Advanced Structure Technology, Beijing Institute of Technology, Beijing, 100081, China

    Xianben Ren, Xiaoqiang Zhang, Zhixin Huang & Ying Li

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  1. Xianben Ren
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  2. Xiaoqiang Zhang
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Correspondence to Zhixin Huang or Ying Li.

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Ren, X., Zhang, X., Huang, Z. et al. Effective Impulse for Fully Clamped Rectangular Plates Under Internal Blast Loading. Acta Mech. Solida Sin. 35, 481–494 (2022). https://doi.org/10.1007/s10338-021-00290-4

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