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Simply-Supported Elliptical Auxetic Plates

Published online by Cambridge University Press:  24 November 2015

T.-C. Lim
T.-C. Lim*
Affiliation:
School of Science and TechnologySIM UniversitySingapore
*
*Corresponding author (alan_tc_lim@yahoo.com)
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Abstract

While the maximum bending moment, and hence maximum bending stress, of a fully clamped elliptical plate under uniform load is independent from the Poisson's ratio of the plate material, the same cannot be said so when the plate is simply supported. This paper develops a simple but sufficiently accurate model for evaluating the bending stresses along the principal axes of a simply supported elliptical under uniform load. Plotted results suggest that bending stresses at plate center along the longer principal axis is minimized by the use of highly auxetic materials if the elliptical plate is almost circular but the use of mildly auxetic material is preferred if the aspect ratio of the elliptical plate is very high. Results also reveal that bending stresses at plate center along the shorter principal axis is minimized when the plate material is highly auxetic. Upon considering the von Mises stress state as the effective stress, it was found that the maximum effective stress is reduced with the use of auxetic and conventional materials for simply supported elliptical plates of low and high aspect ratios, respectively.

Keywords

Auxetic materialsBending stressesElliptical plates
Type
Research Article
Information
Journal of Mechanics , Volume 32 , Issue 4 , August 2016 , pp. 413 - 419
Copyright
Copyright © The Society of Theoretical and Applied Mechanics 2016 

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References

1. Wojciechowski, K. W., “Two-Dimens System with a Negative Poisson Ratio,” Physics Letters A, 137, pp. 60–64 (1989).Google Scholar
2. Lakes, R., “Foam Structures with Negative Poisson's Ratio,” Science, 235, pp. 1038–1040 (1987).Google Scholar
3. Pozniak, A. A. and Wojciechowski, K. W., “Poisson's Ratio of Rectangular Anti-Chiral Structures with Size Dispersion of Circular Nodes,” Physica Status Solidi B, 251, pp. 367–374 (2014).Google Scholar
4. Sanami, M., Ravirala, N., Alderson, K. and Alderson, A., “Auxetic Materials for Sports Applications,” Procedia Engineering, 72, pp. 453–458 (2014).Google Scholar
5. Cauchi, R. and Grima, J. N., “Modelling of the Static and Dynamic Properties of THO-Type Silicates,” TASK Quarterly, 18, pp. 5–65 (2014).Google Scholar
6. Kołat, P., Maruszewski, B. T., Tretiakov, K. V. and Wojciechowski, K. W., “Solitary Waves in Auxetic Rods,” Physica Status Solidi B, 248, pp. 148–157 (2011).Google Scholar
7. Lim, T. C., “Longitudinal Wave Velocity in Auxetic Rods,” ASME Journal of Engineering Materials and Technology, 137, article 024502 (2015).Google Scholar
8. Strek, T., Maruszewski, B., Narojczyk, J. W. and Wojciechowski, K. W., “Finite Element Analysis of Auxetic Plate Deformation,” Journal of Non-Crystalline Solids, 354, pp. 4475–4480 (2008).Google Scholar
9. Pozniak, A. A., et al., “Anomalous Deformation of Constrained Auxetic Square,” Reviews on Advanced Materials Science, 23, pp. 169–174 (2010).Google Scholar
10. Kołat, P., Maruszewski, B. T. and Wojciechowski, K. W., “Solitary Waves in Auxetic Plates,” Journal of Non-Crystalline Solids, 356, pp. 2001–2009 (2010).Google Scholar
11. Ho, D. T., Park, S. D., Kwon, S. Y., Park, K. and Kim, S. Y., “Negative Poisson's Ratio in Metal Nanoplates,” Nature Communication, 5, article 3255 (2014).Google Scholar
12. Lim, T. C., “Buckling and Vibration of Circular Auxetic Plates,” ASME Journal of Engineering Materials and Technology, 136, article 021007 (2014).Google Scholar
13. Lim, T. C., “Shear Deformation in Rectangular Auxetic Plates,” ASME Journal of Engineering Materials and Technology, 136, article 031007 (2014).CrossRefGoogle Scholar
14. Karnessis, N. and Burriesci, G., “Uniaxial and Buckling Mechanical Response of Auxetic Cellular Tubes,” Smart Materials and Structures, 22, article 084008 (2013).CrossRefGoogle Scholar
15. Lim, T. C., “In-Plane Stiffness of Semiauxetic Laminates,” ASCE Journal of Engineering Mechanics, 136, pp. 1176–1180 (2010).Google Scholar
16. Hou, Y., et al., “The Bending and Failure of Sandwich Structures with Auxetic Gradient Cellular Cores,” Composites Part A, 49, pp. 119–131 (2013).Google Scholar
17. Hou, Y., et al., “Graded Conventional-Auxetic Kirigami Sandwich Structures: Flatwise Compression and Edgewise Loading,” Composites Part B, 59, pp. 33–42 (2014).Google Scholar
18. Lim, T. C., Auxetic Materials and Structures, Springer, Singapore (2015).CrossRefGoogle Scholar
19. Sato, K., “Bending of an Elliptical Plate on Elastic Foundation and Under the Combined Action of Lateral Load and In-Plane Force,” III European Conference on Computational Mechanics, p. 49 (2006).Google Scholar
20. Sundaresan, M. K. and Radhakrishnan, G., “Vibration and Stability of Simply Supported Elliptical Plates,” AIAA Journal, 34, pp. 2637–2639 (1996).CrossRefGoogle Scholar
21. Ceribasi, S. and Altay, G., “Free Vibration of Super Elliptical Plates with Constant and Variable Thickness by Ritz Method,” Journal of Sound and Vibration, 319, pp. 668–680 (2009).Google Scholar
22. Georgiev, V.B., Cuenca, J., Gautier, F., Simon, L. and Krylov, V. V., “Damping of Structural Vibrations in Beams and Elliptical Plates Using the Acoustic Black Hole Effect,” Journal of Sound and Vibration, 330, pp. 2497–2508 (2011).Google Scholar
23. Hasheminejad, S. M. and Ghaheri, A., “Exact Solution for Free Vibration Analysis of an Eccentric Elliptical Plate,” Archive of Applied Mechanics, 84, pp. 543–552 (2013).CrossRefGoogle Scholar
24. Ghaheri, A., Keshmiri, A. and Taheri-Behrooz, F., “Buckling and Vibration of Symmetrically Laminated Composite Elliptical Plates on an Elastic Foundation Subjected to Uniform In-Plane Force,” Journal of Engineering Mechanics, ASCE, 140, p. 04014049 (2014).Google Scholar
25. Garcia, J. G., Albus, J. and Reimerdes, H. G., “Static and Stability of Elliptical Cylindrical Shells Under Mechanical and Thermal Loads,” Editor: Burke, W.R., Proceedings of the Spacecraft Structures, Materials and Mechanical Engineering, pp. 295–303 (1996).Google Scholar
26. Boiko, D. V., Zhelevnov, L. P. and Kabanov, V. V., “The Non-Linear Deformation and Stability of Elliptical Cylindrical Shells Under Transverse Bending,” Journal of Applied Mathematics and Mechanics, 67, pp. 819–824 (2003).Google Scholar
27. Silvestre, N., “Buckling Behaviour of Elliptical Cylindrical Shells and Tubes Under Compression,” International Journal of Solids an Structures, 45, pp. 4427–4447 (2008).Google Scholar
28. Lim, T. C., “Circular Auxetic Plates,” Journal of Mechanics, 29, pp. 121–133 (2013).Google Scholar
29. Timoshenko, S. P. and Woinowsky-Krieger, S., Theory of Plates and Shells, 2nd Edition, McGraw-Hill, New York (1959).Google Scholar
30. Ventsel, E. and Krauthammer, T., Thin Plates and Shells, Marcel Dekker, New York (2001).Google Scholar