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Research Papers

2D Elastodynamic Solution for the Impact Response of Laminated Composites

[+] Author and Article Information
Jiawen Xie

Research Assistant
e-mail: jwxie@umich.edu

Anthony M. Waas

Professor
e-mail: dcw@umich.edu
Department of Aerospace Engineering,
University of Michigan,
Ann Arbor, MI 48109-2140

1Corresponding author.

Manuscript received July 2, 2013; final manuscript received August 20, 2013; accepted manuscript posted August 23, 2013; published online October 16, 2013. Editor: Yonggang Huang.

J. Appl. Mech 81(4), 041015 (Oct 16, 2013) (12 pages) Paper No: JAM-13-1272; doi: 10.1115/1.4025276 History: Received July 02, 2013; Revised August 20, 2013; Accepted August 23, 2013

This paper presents a general, exact, two-dimensional (2D) elastodynamic analysis of the response of laminated composite panels subjected to transverse impact loading under conditions of planar deformation. The natural frequencies and mode shapes of free vibration are first extracted. Inspired by a transformation technique for solving a special class of partial differential equations, the forced vibration problem of an impacted laminated panel is solved using an eigenfunction expansion technique. Several examples are studied by varying the laminate lay-up and length-to-thickness ratio. The distributions of transverse stresses in the through-the-thickness direction are further compared with two one-dimensional theories, classical lamination theory (CLT) and first-order shear deformation theory (FSDT), showing the inadequacy of these theories and the necessity to establish a benchmark solution for 2D elastodynamics. The 2D elastodynamic theory that is formulated is also applicable for studying other multilayered structures subjected to arbitrary loading profiles.

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Figures

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Fig. 1

2D geometry of the laminated composite. The composite is assumed in a state-of-plane strain in the xz plane and simply supported at its left and right ends.

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Fig. 2

Parabolic impact loading

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Fig. 6

The half-time snapshots of impact response of stress σ¯z off the central area

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Fig. 7

The half-time snapshots of impact response of stress τ¯xz at the left end x = 0

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Fig. 8

The half-time snapshots of impact response of stress τ¯xz off the central area

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Fig. 9

The vibrational motion versus time for three-layer laminate (0/90/0)

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Fig. 4

Fourier expansion of impact loading in space for aspect ratios of 6 and 21

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Fig. 5

The half-time snapshots of impact response of stress σ¯z at the central line x = L/2

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Fig. 3

FEM model used for the numerical simulation of the impact event

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