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Technical Brief

Bending Stresses in Triangular Auxetic Plates

[+] Author and Article Information
Teik-Cheng Lim

School of Science and Technology,
SIM University,
461 Clementi Road,
Singapore S599491
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 February 6, 2015; final manuscript received September 17, 2015; published online October 8, 2015. Assoc. Editor: Toshio Nakamura.

J. Eng. Mater. Technol 138(1), 014501 (Oct 08, 2015) (3 pages) Paper No: MATS-15-1033; doi: 10.1115/1.4031665 History: Received February 06, 2015; Revised September 17, 2015

This technical brief considers bending stress minimization as a basis for obtaining the optimal Poisson's ratio of simply supported equilateral triangular plates under (a) bending loads at the plate boundary, (b) uniform load throughout the entire plate, and (c) concentrated load at the plate center. Results suggest that the use of auxetic materials is not appropriate for triangular plates under applied bending at the boundary, while mildly auxetic and highly auxetic materials are appropriate for triangular plates under uniform and central point loads, respectively. In addition, obtained results show that the optimal Poisson's ratios for circular and square auxetic plates are not necessarily applicable for triangular plates. The use of auxetic materials offers an additional choice for decreasing bending stresses under specific boundary conditions and loading patterns.

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Figures

Grahic Jump Location
Fig. 1

Geometrical description of a simply supported equilateral triangular plate

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Fig. 2

Dimensionless bending stress distributions of σx* and σy* versus x/l arising from uniformly applied bending moment along the plate edge

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Fig. 3

Dimensionless bending stress distributions of (a) σx** and (b) σy** versus x/l along y=0 arising from uniform load for the entire range of Poisson's ratio, as well as the dimensionless bending stress distribution (c) at the optimal σx** at v=−1/3 with σx** at v=−1/3±2/3 for comparison, and (d) at the optimal σy** at v=−1/15 with σy** at v=−1/15±2/15 for comparison

Grahic Jump Location
Fig. 4

Dimensionless bending stress distributions of σx*** and σy*** versus c/l arising from central point load

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