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A New Higher Order Shear Deformation Model for Static Behavior of Functionally Graded Plates

Published online by Cambridge University Press:  03 June 2015

Tahar Hassaine Daouadji ,
Abdelouahed Tounsi  and
El Abbes Adda Bedia
Tahar Hassaine Daouadji*
Affiliation:
Université Ibn Khaldoun, BP 78 Zaaroura, 14000 Tiaret, Algérie Laboratoire des Matériaux & Hydrologie, Université de Sidi Bel Abbes, Algérie
Abdelouahed Tounsi
Affiliation:
Laboratoire des Matériaux & Hydrologie, Université de Sidi Bel Abbes, Algérie
El Abbes Adda Bedia
Affiliation:
Laboratoire des Matériaux & Hydrologie, Université de Sidi Bel Abbes, Algérie
*
*Corresponding author. Email: [email protected]
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Abstract

In this paper, a new displacement based high-order shear deformation theory is introduced for the static response of functionally graded plate. Unlike any other theory, the number of unknown functions involved is only four, as against five in case of other shear deformation theories. The theory presented is variationally consistent, has strong similarity with classical plate theory in many aspects, does not require shear correction factor, and gives rise to transverse shear stress variation such that the transverse shear stresses vary parabolically across the thickness satisfying shear stress free surface conditions. The mechanical properties of the plate are assumed to vary continuously in the thickness direction by a simple power-law distribution in terms of the volume fractions of the constituents. Numerical illustrations concerned flexural behavior of FG plates with Metal-Ceramic composition. Parametric studies are performed for varying ceramic volume fraction, volume fraction profiles, aspect ratios and length to thickness ratios. The validity of the present theory is investigated by comparing some of the present results with those of the classical, the first-order and the other higher-order theories. It can be concluded that the proposed theory is accurate and simple in solving the static behavior of functionally graded plates.

Keywords

74K20Functionally graded materialpower law indexvolume fractionhigher-order shear deformation theoryNavier solution
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 5 , Issue 3 , June 2013 , pp. 351 - 364
Copyright
Copyright © Global-Science Press 2013

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References

[1]Koizumi, M., The concept of FGM, Ceramic Transactions, Functionally Gradient Materials, 34 (1993), pp. 3–10.Google Scholar
[2]Hirai, T. and Chen, L., Recent and prospective development of functionally graded materials in Japan, Materials Science Forum, (1999), pp. 308–311.Google Scholar
[3]Tanigawa, Y., Some basic thermoelastic problems for nonhomogeneous structural materials, Appl. Math. Mech., 48 (1995), pp. 287–300.Google Scholar
[4]Reddy, J. N., Analysis of functionally graded plates, Int. J. Numer. Meth. Eng., 47 (2000), pp. 663–684.Google Scholar
[5]Cheng, Z. Q. and Batra, R. C., Deflection relationships between the homogeneous Kirchhoff plate theory and different functionally graded plate theories, Arch. Mech., 52 (2000), pp. 143–158.Google Scholar
[6]Timoshenko, S. P. and Woinowsky-Krieger, S., Theory of Plates and Shells, McGraw-Hill, New York, 1959.Google Scholar
[7]Zenkour, A. M., Generalised shear deformation theory for bending analysis of functionally graded plates, Appl. Math. Model., 30 (2006), pp. 67–84.Google Scholar
[8]Şimşek, M., Vibration analysis of a functionally graded beam under a moving mass by using different beam theories, Compos. Struct., 92 (2010), pp. 904–917.CrossRefGoogle Scholar
[9]ŞimŞek, M., Fundamental frequency analysis of functionally graded beams by using different higherorder beam theories, Nuclear Eng. Design, 240 (2010), pp. 697–705.Google Scholar
[10]Benachour, A., Hassaine Daouadji, T., Ait Atmane, H., Tounsi, A. and Meftah, S. A., A four variable refined plate theory for free vibrations of functionally graded plates with arbitrary gradient, Composites part B: Engineering, 42(6) (2011), pp. 1386–1394.CrossRefGoogle Scholar
[11]Abdelaziz, H. H., Ait Atmane, H., Mechab, I., Boumia, L., Tounsi, A. and Bedia, E.A. Adda, Static analysis of functionally graded sandwich plates using an efficient and simple refined theory, Chinese J. Aaeronautics, 24(4) (2011), pp. 434–448.Google Scholar
[12]ŞimŞek, M., Non-linear vibration analysis of a functionally graded Timoshenko beam under action of a moving harmonic load, Compos. Struct., 92 (2010), pp. 2532–2546.Google Scholar
[13]Werner, H., A three-dimensional solution for rectangular plate bending free of transversal normal stresses, Commun. Numer. Methods Eng., 15 (1999), pp. 295–302.Google Scholar
[14]Bouazza, M., Tounsi, A., Adda Bedia, E. A. and Meguenni, M., Stability analysis of functionally graded plates subject to thermal load, Adv. Struct. Materials, 15 (2011), pp. 669– 680.Google Scholar