The Stability of Cylindrical Shells Containing an FGM Layer Subjected to Axial Load on the Pasternak Foundation

Abdullah Heydaroglu Sofiyev, Mehmet Avcar

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DOI: 10.4236/eng.2010.24033                

Abstract

In this study, the stability of cylindrical shells that composed of ceramic, FGM, and metal layers subjected to axial load and resting on Winkler-Pasternak foundations is investigated. Material properties of FGM layer are varied continuously in thickness direction according to a simple power distribution in terms of the ceramic and metal volume fractions. The modified Donnell type stability and compatibility equations on the Pasternak foundation are obtained. Applying Galerkin’s method analytic solutions are obtained for the critical axial load of three-layered cylindrical shells containing an FGM layer with and without elastic foundation. The detailed parametric studies are carried out to study the influences of thickness variations of the FGM layer, radius-to-thickness ratio, material composition and material profile index, Winkler and Pasternak foundations on the critical axial load of three-layered cylindrical shells. Comparing results with those in the literature validates the present analysis.

Keywords

FGM Layer, Stability, Cylindrical Shell, Critical Axial Load, Winkler and Pasternak Foundations

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	M. Koizumi, “The Concept of FGM,” Ceramic Transactions, Functionally Gradient Materials, Vol. 34, 1993, pp. 3-10.
[2]	B. Kieback, A. Neubrand and H. Riedel, “Processing techniques for Functionally Graded Materials,” Materials Science and Engineering A, Structural Materials: Properties, Microstructure and Processing, Vol. 362, No. 1-2, 2003, pp. 81-105.
[3]	V. Birman, “Buckling of Functionally Graded Hybrid Composite Plates,” Proceedings of the 10th Conference on Engineering Mechanics, Boulder, USA, 1995.
[4]	J. N. Reddy and C. D. Chin, “Thermomechanical Analysis of Functionally Graded Cylinders and Plates,” Journal of Thermal Stresses, Vol. 21, 1998, pp. 593-602.
[5]	T. Y. Ng, K. Y. Lam, K. M. Liew and J. N. Reddy, “Dynamic Stability Analysis of Functionally Graded Cylindrical Shells under Periodic Axial Loading,” International Journal of Solids Structures, Vol. 38, No. 8, 2001, pp. 1295-1309.
[6]	A. H. Sofiyev, “Dynamic Buckling of Functionally Graded Cylindrical Shells under Non-periodic Impulsive Loading,” Acta Mechanica, Vol. 165, No. 3-4, 2003, pp. 153-162.
[7]	H. S. Shen and N. Noda, “Post-buckling of FGM Cylindrical Shell under Combined Axial and Radial Mechanical Loads in Thermal Environments,” International Journal of Solids Structures, Vol. 42, No. 16, 2005, pp. 4641- 4662.
[8]	H. S. Shen, “Functionally Graded Materials: Nonlinear Analysis of Plates and Shells,” CRC Press, Boca Raton, 2009.
[9]	S. Pitakthapanaphong and E. P. Busso, “Self-consistent elasto-plastic Stress Solutions for Functionally Graded Material Systems Subjected to Thermal Transients,” Journal of Mechanics and Physics of Solids, Vol. 50, No. 4, 2002, pp. 695-716.
[10]	K. S. Na and J. H. Kim, “Three-dimensional Thermo- mechanical Buckling Analysis for Functionally Graded Composite Plates,” Composite Structures, Vol. 73, No. 4, 2006, pp. 413-422.
[11]	K. M. Liew, J. Yang and Y. F. Wu, “Nonlinear Vibration of a Coating-FGM-substrate Cylindrical Panel Subjected to a Temperature Gradient,” Computer Methods in Applied Mechanics and Engineering, Vol. 195, No. 9-12, 2006, pp. 1007-1026.
[12]	S. R. Lia and R. C. Batra, “Buckling of Axially Compressed Thin Cylindrical Shells with Functionally Graded Middle Layer,” Thin Walled Structures, Vol. 44, No. 10, 2006, pp. 1039-1047.
[13]	A. H. Sofiyev, A. Deniz, I. H. Akcay and E. Yusufoglu, “The Vibration and Stability of a Three-layered Conical Shell Containing a FGM Layer Subjected to Axial Compressive Load,” Acta Mechanica, Vol. 183, No. 3-4, 2006, pp. 129-144.
[14]	A. H. Sofiyev, “Vibration and Stability of Composite Cylindrical Shells Containing a FG Layer Subjected to Various Loads,” Structural Engineering and Mechanics an International Journal, Vol. 27, No. 3, 2007, pp. 365- 391.
[15]	P. L. Pasternak, “On a New Method of Analysis of an Elastic Foundation by Means of Two Foundation Constants,” Gosudarstvennoe Izdatelstvo Literaturi po Stroitelstvu I Arkhitekture, Moscow, 1954.
[16]	V. A. Bajenov, “The Bending of the Cylindrical Shells in an Elastic Medium,” Visha Shkola, Kiev, 1975.
[17]	D. N. Paliwal, R. K. Pandey and T. Nath, “Free Vibration of Circular Cylindrical Shell on Winkler and Pasternak Foundation,” International Journal of Pressure Vessels and Piping, Vol. 69, 1996, pp. 79-89.
[18]	T. Y. Ng and K. Y. Lam, “Free Vibrations Analysis of Rotating Circular Cylindrical Shells on an Elastic Foundation,” Journal of Vibration and Acoustics, Vol. 122, No. 1, 2000, pp. 85-89.
[19]	H. G. Tj, T. Mikami, S. Kanie and M. Sato, “Free Vibration Characteristics of Cylindrical Shells Partially Buried in Elastic Foundations,” Journal of Sound and Vibration, Vol. 290, No. 3, 2006, pp. 785-793.
[20]	A. H. Sofiyev, S. N. Keskin and Al. H. Sofiyev, “Effects of Elastic Foundation on the Vibration of Laminated Non- homogeneous Orthotropic Circular Cylindrical Shells,” Journal of Shock and Vibration, Vol. 11, 2004, pp. 89-101.
[21]	Z. Q. Cheng and S. Kitipornchai, “Membrane Analogy of Buckling and Vibration of Inhomogeneous Plates,” Journal of Engineering Mechanics–ASCE, Vol. 125, No. 11, 1999, pp. 1293-1297.
[22]	Z. Y. Huang, C. F. Lu and W. Q. Chen, “Benchmark Solutions for Functionally Graded Thick Plates Resting on Winkler–Pasternak Elastic Foundations,” Composite Structures, Vol. 85, No. 2, 2008, pp. 95-104.
[23]	P. Malekzadeh, “Three-dimensional Free Vibration Analysis of Thick Functionally Graded Plates on Elastic Foundations,” Composite Structures, Vol. 89, No. 3, 2009, pp. 367-373.
[24]	V. L. Agamirov, “Dynamic problems of nonlinear shells theory”, Nauka, Moscow, 1990.
[25]	R. M. Jones and H. S. Morgan, “Buckling and Vibration of Cross-ply Laminated Circular Cylindrical Shells,” American Institute of Aeronautics and Astronautics Journal, Vol. 13, No. 5, 1975, pp. 664-671.