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TECHNICAL PAPERS

Dynamic Response of a Clamped Circular Sandwich Plate Subject to Shock Loading

[+] Author and Article Information
X. Qiu, V. S. Deshpande, N. A. Fleck

Engineering Department, Cambridge University, Trumpington Street, Cambridge CB1 1PZ, UK

J. Appl. Mech 71(5), 637-645 (Nov 09, 2004) (9 pages) doi:10.1115/1.1778416 History: Received September 30, 2003; Revised January 20, 2004; Online November 09, 2004
Copyright © 2004 by ASME
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References

Wang,  A. J., and Hopkins,  H. G., 1954, “On the Plastic Deformation of Built-in-Circular Plates Under Impulsive Load,” J. Mech. Phys. Solids, 3, pp. 22–37.
Symmonds, P. S., 1954, “Large Plastic Deformations of Beams Under Blast Type Loading,” Proceedings of the Second US National Congress of Applied Mechanics, pp. 505–515.
Jones,  N., 1971, “A Theoretical Study of the Dynamic Plastic Behavior of Beams and Plates With Finite Deflections,” Int. J. Solids Struct., 7, pp. 1007–1029.
Jones, N., 1989, Structural Impact, Cambridge University Press, Cambridge, UK.
Xue,  Z., and Hutchinson,  J. W., 2003, “A Preliminary Assessment of Sandwich Plates Subject to Blast Loads,” Int. J. Mech. Sci., 45, pp. 687–705.
Fleck,  N. A., and Deshpande,  V. S., 2004, “The Resistance of Clamped Sandwich Beams to Shock Loading,” ASME J. Appl. Mech., 71, 386–401.
Qiu,  X., Deshpande,  V. S., and Fleck,  N. A., 2003, “Finite Element Analysis of the Dynamic Response of Clamped Sandwich Beams Subject to Shock Loading,” Eur. J. Mech. A/Solids, 22, 801–814.
Taylor, G. I., 1963, The Scientific Papers of G I Taylor, Vol III, pages 287–303. Cambridge University Press, Cambridge, UK, pp. 287–303 (The Pressure and Impulse of Submarine Explosion Waves on Plates, 1941).
Cole, R. H., 1948, Underwater Explosions, Princeton University Press, Princeton, NJ.
Jones,  N., and Gomes de Oliveira,  J., 1980, “Dynamic Plastic Response of Circular Plates With Transverse Shear and Rotary Inertia,” ASME J. Appl. Mech., 47, pp. 27–34.
Perrone,  N., and Bhadra,  P., 1984, “Simplified Large Deflection Mode Solutions for Impulsively Loaded, Viscoplastic, Circular Membranes,” ASME J. Appl. Mech., 51, pp. 505–509.
Deshpande,  V. S., and Fleck,  N. A., 2000, “Isotropic Constitutive Models for Metallic Foams,” J. Mech. Phys. Solids, 48(6–7), pp. 1253–1283.
Deshpande,  V. S., Fleck,  N. A., and Ashby,  M. F., 2001, “Effective Properties of the Octet-Truss Lattice Material,” J. Mech. Phys. Solids, 49(8), pp. 1747–1769.

Figures

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Geometry of the clamped sandwich plate
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Sketches of the exact, inscribing and circumscribing yield loci of (a) the sandwich plate and (b) the monolithic plate. Here, Mo and No are the fully plastic bending moments and axial loads, respectively, of the plates.
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Analytical and FE predictions of (a) maximum central deflection and (b) structural response time, of a monolithic plate with aspect ratio R/H=50 as a function of the applied impulse
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Design chart for a clamped sandwich plate with core strength σ̄=0.05 and densification strain εD=0.5 and an assumed face-sheet material ductility εf=0.2. Contours of the maximum normalized central deflection w̄ of the inner face-sheet subject to a normalized impulse Ī=10−3 are included. The symbols denote the sandwich plate geometries selected for the FE calculations.
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Analytical and FE predictions of the maximum central deflection w̄ of the inner face-sheet of sandwich plates with reference material properties subjected to a normalized impulse Ī=10−3. (a) w̄ as a function of h̄ for two values of c̄. (b) w̄ as a function of c̄ for two values of h̄.
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Analytical and FE predictions of the (a) maximum central deflection w̄ of the inner face-sheet and (b) core compression εc as a function of the applied impulse for sandwich plates. c̄=0.03 and h̄=0.1 and the sandwich plate is made from the reference core material, with both ideally plastic and strain hardening face-sheets.
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A comparison between analytical and FE predictions of the structural response time T̄ and core compression time T̄c, as a function of the applied impulse, for sandwich plates with c̄=0.03 and h̄=0.1 made from the reference materials
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A comparison between the analytical and FE predictions of the maximum central deflection w̄ of the inner face-sheet of sandwich plates with c=0.03 and h̄=0:1, subject to a normalized impulse I=10−3 as a function of the normalized core strength σ̄
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(a) FE predictions of the time histories of the normalized plastic dissipation in sandwich plates for three selected core strengths. (b) Ratio ϕ of the plastic dissipation in the core compression stage to the initial kinetic energy of the outer face as a function of the mass ratio m̄ for two selected core strengths. The sandwich plates in both cases have geometry c̄=0.03 and h̄=0.1 and are subjected to an impulse Ī=10−3.
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Analytical and FE predictions of the maximum central deflections w̄ of the inner face-sheet for clamped sandwich plates and beams, as a function of the applied impulse. Both the sandwich plates and beams have a geometry c̄=0.03 and h̄=0.1, and are made from the reference materials.
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Design chart for a clamped sandwich plate made from the reference materials for a fixed maximum central deflection of the inner face w̄=0.1. Contours of the applied impulse Ī and nondimensional mass M̄ are displayed. The underlined values denote the nondimensional impulse values while the arrows trace the path of the optimal designs with increasing M̄.
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A comparison of the maximum shock impulse sustained by monolithic plates and by optimal designs of the sandwich plates subject to the constraints w̄<0:1 and w̄≤0:2 for two relative densities ρ̄ of the core material

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