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TECHNICAL PAPERS

The Resistance of Clamped Sandwich Beams to Shock Loading

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

Engineering Department, Cambridge University, Trumpington Street, Cambridge, CB2 1PZ, UK

J. Appl. Mech 71(3), 386-401 (Jun 22, 2004) (16 pages) doi:10.1115/1.1629109 History: Received May 19, 2002; Revised July 10, 2003; Online June 22, 2004
Copyright © 2003 by ASME
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References

Figures

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Geometry of the sandwich beam
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Sketches of the sandwich core topologies; (a) pyramidal core, (b) diamond-celled core, (c) corrugated core, (d) hexagonal-honeycomb core, and (e) square-honeycomb core
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The ratio of the impulse transmitted to the structure Itrans, and the impulse transmitted to a fixed rigid structure 2poθ, as a function of the fluid-structure interaction parameter ψ
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(a) Sketch of the propagation of a one-dimensional shock in the sandwich core, (b) the nondimensional core compression time T⁁c as a function of the nondimensional impulse I⁁ transmitted to the structure
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Analysis of stage III of the blast response. (a) Velocity profile in phase I, (b) a free-body diagram of the half-beam in phase I, with the deflected shape sketched approximately, (c) velocity profile in phase II, and (d) a free-body diagram of the half-beam in phase II, with the deflected shape sketched approximately. The accelerations of the beam are shown in (d).
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Response of a clamped sandwich beam (c̄=0.1,h̄=0.1) with a pyramidal core (ρ̄=0.1,εY=0.002,εD=0.5) for an assumed ψ=1.78; (a) the normalized response time T̄ and deflection w̄ and (b) core compression εc, and tensile strain in beam εm, as a function of the normalized blast impulse Ī
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Design chart for a monolithic beam of tensile ductility εf=0.2, subjected to a water blast with ψ̄=5×10−3. Contours of the midspan displacement w̄ are given as solid lines and contours of dimensionless mass M̄ are shown as dotted lines.
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Design chart for a sandwich beam, with a pyramidal core (ρ̄=0.1,εY=0.002,εD=0.5), subjected to a water blast. The nondimensional impulse is Ī=10−2, and the fluid-structure interaction parameter is taken as ψ̄=5×10−3. The regime of tensile failure is shown for an assumed tensile ductility of face sheets of εf=0.2. Contours of w̄ and εc are included.
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The effect of ψ̄ upon the magnitude of the tensile failure regime within the design chart, for face sheets of ductility εf=0.2. The sandwich beam has a pyramidal core (ρ̄=0.1,εY=0.002,εD=0.5) and the nondimensional impulse is taken as Ī=10−2.
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Design chart for a sandwich beam, with a pyramidal core (ρ̄=0.1,εY=0.002,εD=0.5), subjected to a water blast. The beam deflection is w̄=0.1 and the fluid-structure interaction parameter is taken as ψ̄=5×10−3. Contours of Ī and M̄ are displayed. The dotted lines trace the paths of selected values of h/L.
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A comparison of the maximum blast impulse sustained by monolithic beams and by optimal designs of sandwich beams, subjected to the constraints w̄≤0.1 and h/L≥10−2. Results are presented for ψ̄=5×10−3 and 0.02. The core relative density is ρ̄=0.1 and densification strain is εD=0.5.
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A comparison of the maximum blast impulse sustained by monolithic beams and by optimal designs of sandwich beams, subjected to the constraint w̄≤0.1 with ψ̄=5×10−3. Results are presented for constraints h/L≥10−2 and 10−3. The core relative density is ρ̄=0.1,εY=0.002 and densification strain is εD=0.5.
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A comparison of the maximum blast impulse sustained by monolithic beams and by optimal designs of sandwich beams, subjected to the constraint h/L≥10−2 with ψ̄=5×10−3. Results are presented for constraints w̄≤0.1 and 0.4. The core relative density is ρ̄=0.1,εY=0.002 and densification strain is εD=0.5.
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Comparison of the maximum blast impulse sustained by optimal (a) diamond-celled and (b) pyramidal core sandwich beams for selected core densities, with ψ̄=5×10−3 and h/L≥10−2,w̄≤0.1. The yield strain of the core parent material is assumed to be εY=0.002 and densification strain of the core is taken as εD=0.5.
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Design chart for a sandwich beam, with a pyramidal core (ρ̄=0.1,εY=0.002,εD=0.5), subjected to an air blast. The nondimensional impulse is Ī=10−3. The regime of tensile failure is shown for an assumed tensile ductility of face sheets of εf=0.2. Contours of w̄ and εc are included.
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Design chart for a sandwich beam, with a pyramidal core (ρ̄=0.1,εY=0.002,εD=0.5), subjected to an air blast. The beam deflection is w̄=0.1. Contours of Ī and M̄ are displayed. The arrows trace the path of designs which maximize the impulsive resistance with increasing mass.
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(a) Comparison of the maximum impulse sustained by monolithic and sandwich beams for an air blast with the constraint w̄≤0.1. The core relative density and densification strain are, ρ̄=0.1 and εD=0.5, respectively, and εY=0.002. (b) The optimal designs of sandwich beams with pyramidal and diamond-celled core.
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The normalized deflection of the bottom face of a diamond-celled core (ρ̄=0.1,εY=0.002) sandwich beam with c̄=h̄=0.2 as a function of the normalized impulse, for two selected values of the core densification strain εD. The response of a monolithic beam of the same mass M̄=0.2 is included.
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Comparison of the analytical predictions and the three-dimensional FE predictions of Xue and Hutchinson 6 for the deflection of sandwich beams with a corrugated core. The beams have a mass M̄=0.04 and are subjected to an impulse Ī=5×10−3. The effect upon w̄ and w̄o of (a) core relative density ρ̄ for c̄=0.1 and (b) c̄ with the core relative density held fixed at ρ̄=0.04. The solid lines give the analytic solutions and the dotted lines (with symbols) give the FE results.
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Comparison of the analytical predictions and the three-dimensional FE predictions of Xue and Hutchinson 6 for the deflection w̄ of monolithic beams and sandwich beams with corrugated, square-honeycomb, and pyramidal cores. The beams have a fixed mass M̄=0.04 and the sandwich beams have a core of relative density ρ̄=0.04 and aspect ratio c̄=0.1. The symbols denote the FE results while the lines are the analytical predictions.

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