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Applied Mathematics and Mechanics

, Volume 12, Issue 10, pp 935–942 | Cite as

The dynamic plastic behavior of a simply supported circular plate in a damping medium with finite-deflections

  • Zhao Ya-pu
  • Hsueh Dah-wei
Article
  • 20 Downloads

Abstract

A theoretical analysis is presented for the dynamic plastic behavior of a simply supported rigid, perfectly plastic circular plate in damping medium with finite-deflections subjected to a rectangular pressure pulse. Analytical solutions of every moving stage under both medium and high loads are developed.

Key words

simply supported circular plate damping medium dynamic plastic response finite deformation 

Notation

h1

plate thickness

L(t)1

exp[−βt/2](cosω d t + (β/2ω d )sinω d t

m1

mass per unit area of the plate

M01

σ0 h 4/4

Mϕ,M01

radial and circumferential bending moments per unit length

N01

σ0 h

Nr,N01

radial and circumferential membrane forces per unit length

P01

6M 0/R 2

P1

value of the rectangular pressure pulse

r1

radial coordinate of plate

t1

time

u1

displacement in directionr of underformed plate

ω1

transverse deflection Perpendicular to undeformed plate

W(t)1

transverse deflection of the center of the plate

x1

coefficient of damping

z1

a/m

γ1

(4P 0/mh)1/2

λr, λ01

radial and circumferential strains

η1

2(p−p0)/m

kr, kθ

radial and circumferential curvatures

π, π0

radius of hinge circle

σ01

yield stress in simple tension

τ1

duration of pulse

( )1

ϱ( )/ϱt

( )'1

ϱ( )/ϱr

tt:

time, when velocity is finally equal to zero

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References

  1. [1]
    Nurick, G. N. and J. B. Martin, Deformation of thin plates subjected to impulsive loading—a review. Part I: Theoretical considerations,Int. J. Impact Engng.,8, 2 (1989), 159–170.CrossRefGoogle Scholar
  2. [2]
    Hopkins, H. G. and W. Prager, On the dynamics of plastic circular plates,ZAMP,5, 4 (1954), 317–330.MATHMathSciNetCrossRefGoogle Scholar
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    Wang, A. J., The permanent deflection of a plastic plate under blast loading,J. Appl. Mech.,22 (1955), 375–376.MATHGoogle Scholar
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    Yang Gui-tong, Xiong Zhu-hua,Dynamic Plasticity, Qinghua University Press (1984). {cm(in Chinese)}Google Scholar
  5. [5]
    Kumar, A., Dynamic plastic response of circular plates in a damping medium,Int. J. Impact Engng.,6, 4 (1987), 285–290.CrossRefGoogle Scholar
  6. [6]
    Jones, N., Finite deflections of a simply supported rigid-plastic circular plate loaded dynamically. AD656731 (1967).Google Scholar
  7. [7]
    Wang Ren, et al.,Foundation of Plasticity, Science Press (1982). {cm(in Chinese)}Google Scholar
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    Hsueh, D. W.,Theory of Plates & Shells, Beijing Inst. Tech. Press (1988). (in Chinese)Google Scholar
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    Hodge, P. G., Yield conditions for rotationally symmetric shells under axisymmetric loading,J. Appl. Mech., 6 (1960), 323–331.MathSciNetGoogle Scholar

Copyright information

© Shanghai University of Technology (SUT) 1991

Authors and Affiliations

  • Zhao Ya-pu
    • 1
  • Hsueh Dah-wei
    • 1
  1. 1.Peking Institute of TechnologyBeijing

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