Research Papers

Shear Deformation in Rectangular Auxetic Plates

[+] Author and Article Information
Teik-Cheng Lim

School of Science and Technology,
SIM University,
461 Clementi Road,
S599491, Singapore
e-mail: alan_tc_lim@yahoo.com

Contributed by the Materials Division of ASME for publication in the JOURNAL OF ENGINEERING MATERIALS AND TECHNOLOGY. Manuscript received March 21, 2014; final manuscript received May 7, 2014; published online June 5, 2014. Assoc. Editor: Tetsuya Ohashi.

J. Eng. Mater. Technol 136(3), 031007 (Jun 05, 2014) (6 pages) Paper No: MATS-14-1065; doi: 10.1115/1.4027711 History: Received March 21, 2014; Revised May 07, 2014

Solids that exhibit negative Poisson's ratio are called auxetic materials. This paper examines the extent of transverse shear deformation with reference to bending deformation in simply supported auxetic plates as a ratio of Mindlin-to-Kirchhoff plate deflection for polygonal plates in general, with special emphasis on rectangular plates. Results for square plates show that the Mindlin plate deflection approximates the Kirchhoff plate deflection not only when the plate thickness is negligible, as is obviously known, but also when (a) the Poisson's ratio of the plate is very negative under all load distributions, as well as (b) at the central portion of the plate when the load is uniformly distributed. Hence geometrically thick plates are mechanically equivalent to thin plates if the plate Poisson's ratio is sufficiently negative. The high suppression of shear deformation in favor of bending deformation in auxetic plates suggests its usefulness for bending-based plate sensors that require larger difference in the in-plane strains between the opposing plate surfaces with minimal transverse deflection.

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Fig. 2

Plots of Mindlin-to-Kirchhoff deflection ratio of the center of a simply supported square plate under uniform load, taking into consideration based on (a) κ = 5/6 and (b) κ = 5/(6-v)

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Fig. 3

A graphical comparison on the Mindlin-to-Kirchhoff deflection ratio versus plate Poisson's ratio at the center of a simply supported square plate under sinusoidal and uniform loads at various dimensionless plate thickness

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Fig. 1

A family of Mindlin-to-Kirchhoff deflection ratio curves of a simply supported square plate under sinusoidal load

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Fig. 4

Mindlin-to-Kirchhoff deflection ratio of simply supported square plate under sinusoidal load (with m = n = 1) and under uniform load: (a) comparison from center to middle of plate side parallel to either axes, (b) comparison along plate diagonal from center to corner, and (c) boundary of equal Mindlin-to-Kirchhoff deflection ratio for both types of load distributions




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