Technical Papers
May 8, 2013

Buckling Analysis of a Functionally Graded Thin Circular Plate Made of Saturated Porous Materials

Publication: Journal of Engineering Mechanics
Volume 140, Issue 2

Abstract

This study presents the buckling analysis of a radially loaded, solid, circular plate made of porous material. Properties of the plate vary across the thickness. The edge of the plate is either simply supported or clamped and the plate is assumed to be geometrically perfect. The geometrical nonlinearities are considered in the Love-Kirchhoff hypothesis sense. The equilibrium and stability equations, derived through the variational formulation, are used to determine the prebuckling forces and critical buckling loads. The equations are based on the Sanders nonlinear strain-displacement relation. The porous plate is assumed to be of the form where pores are saturated with fluid. The results obtained for porous plates are compared with the homogeneous and porous/nonlinear, symmetric distribution, circular plates.

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References

Abrate, S. (2006). “Free vibration, buckling, and static deflections of functionally graded plates.” Compos. Sci. Technol., 66(14), 2383–2394.
Biot, M. A. (1964). “Theory of buckling of a porous slab and its thermoelastic analogy.” J. Appl. Mech., 31(2), 194–198.
Brush, D. O., and Almorth, B. O. (1975). Buckling of bars, plates and shells, McGraw-Hill, New York.
Chen, C. Sh. (2005). “Nonlinear vibration of a shear deformable functionally graded plate.” Compos. Struct., 68(3), 295–302.
Detournay, E., and Cheng, A. H. D. (1993). “Fundamentals of poroelasticity.” Chapter 5, Comprehensive rock engineering: Principles, practice and projects, Vol. II, Pergamon Press, Oxford. U.K., 113–171.
Jasion, P., Magnucka-Blandzi, E., Szyc, W., and Magnucki, K. (2012). “Global and local buckling of sandwich circular and beam-rectangular plates with metal foam core.” Thin-Walled Struct., 61(December), 154–161.
Javaheri, R., and Eslami, M. R. (2002a). “Buckling of functionally graded plates under in-plane comppressive loading.” Z. Angew. Math. Mech., 82(4), 277–283.
Javaheri, R., and Eslami, M. R. (2002b). “Thermal buckling of functionally graded plates.” AIAA J., 40(1), 162–169.
Javaheri, R., and Eslami, M. R. (2002c). “Thermal buckling of functionally graded plates based on higher order theory.” J. Therm. Stresses, 25(7), 603–625.
Javaheri, R., and Eslami, M. R. (2005). “Buckling of functionally graded plates under in-plane compressive loading based on various theories.” Trans. ISME, 6(1), 76–93.
Khorshidvand, A. R., Jabbari, M., and Eslami, M. R. (2012). “Thermoelastic buckling analysis of functionally graded circular plates integrated with piezoelectric layers.” J. Therm. Stresses, 35(8), 695–717.
Krizhevsky, G., and Stavsky, Y. (1996). “Refined theory for vibrations and buckling of laminated isotropic annular plates.” Int. J. Mech. Sci., 38(5), 539–555.
Lanhe, W. (2004). “Thermal buckling of a simply supported moderately thick rectangular FGM plate.” Compos. Struct., 64(2), 211–218.
Liew, K. M., Yang, J., and Kitipornchai, S. (2003). “Postbuckling of piezoelectric FGM plates subject to thermo-electro-mechanical loadin.” Int. J. Solids Struct., 40(15), 3869–3892.
Ma, L. S., and Wang, T. J. (2003a). “Axisymmetric post-buckling of a functionally graded circular plate subjected to uniformly distributed radial compression.” Mater. Sci. Forum, 423–425, 719–724.
Ma, L. S., and Wang, T. J. (2003b). “Nonlinear bending and post-buckling of a functionally graded circular plate under mechanical and thermal loadings.” Int. J. Solids Struct., 40(13–14), 3311–3330.
Ma, L. S., and Wang, T. J. (2004). “Relationships between axisymmetric bending and buckling solutions of FGM circular plates based on third-order plate theory and classical plate theory.” Int. J. Solids Struct., 41(1), 85–101.
Magnucka-Blandzi, E. (2008). “Axi-symmetrical deflection and buckling of circular porous-cellular plate.” Thin-Walled Struct., 46(3), 333–337.
Magnucka-Blandzi, E. (2009). “Dynamic stability of a metal foam circular plate.” J. Theor. Appl. Mech., 47(2), 421–433.
Magnucka-Blandzi, E. (2011). “Mathematical modelling of a rectangular sandwich plate with metal foam core.” J. Theor. Appl. Mech., 49(2), 439–455.
Magnucki, K., Malinowski, M., and Kasprzak, J. (2006). “Bending and buckling of a rectangular porous plate.” Steel Compos. Struct., 6(4), 319–333.
Magnucki, K., and Stasiewicz, P. (2004). “Elastic buckling of a porous beam.” J. Theor. Appl. Mech., 42(4), 859–868.
Mirzavand, B., and Eslami, M. R. (2007). “Thermal buckling of simply supported piezoelectric FGM cylindrical shells.” J. Therm. Stresses, 30(11), 1117–1135.
Najafizadeh, M. M., and Eslami, M. R. (2002a). “Buckling analysis of circular plates of functionally graded materials under uniform radial compression.” Int. J. Mech. Sci., 44(12), 2479–2493.
Najafizadeh, M. M., and Eslami, M. R. (2002b). “Thermoelaslic stability of orthotropic circular plates.” J. Therm. Stresses, 25(10), 985–1005.
Reddy, J. N. (2004). Mechanics of laminated composite plates and shells: Theory and analysis, CRC Press, New York.
Reddy, J. N., and Khdeir, A. A. (1989). “Buckling and vibration of laminated composite plate using various plate theories.” AIAA J., 27(12), 1808–1817.
Reddy, J. N., Wang, C. M., and Kitipornchai, S. (1999). “Axisymmetric bending of functionally graded circular and annular plates.” Eur. J. Mech.: A/Solids, 18(2), 185–199.
Samsam Shariat, B. A., and Eslami, M. R. (2006). “Thermal buckling of imperfect functionally graded plates.” Int. J. Solids Struct., 43(14–15), 4082–4096.
Samsam Shariat, B. A., Javaheri, R., and Eslami, M. R. (2005). “Buckling of imperfect functionally graded plates under in-plane compressive loading.” Thin-Walled Struct., 43(7), 1020–1036.
Shen, H. S. (2005a). “Postbuckling of FGM plates with piezoelectric actuators under thermo-electro-mechanical loadings.” Int. J. Solids Struct., 42(23), 6101–6121.
Shen, H. S. (2005b). “Postbuckling of axially loaded FGM hybrid cylindrical shells in thermal environments.” Compos. Sci. Technol., 65(11–12), 1675–1690.
Shen, H. S., and Noda, N. (2007). “Postbuckling of pressure-loaded FGM hybrid cylindrical shells in thermal environments.” Comp. Struct., 77(4), 546–560.
Viliani, N. S., Khalili, S. M. R., and Porrostami, H. (2009). “Buckling analysis of FG plate with smart sensor/actuator.” J Solid Mech., 1(3), 201–212.
Wang, Q., Quek, S. T., Sun, C. T., and Liu, X. (2001). “Analysis of piezoelectric coupled circular plate.” Smart Mater. Struct., 10(2), 229–239.
Wen, P. H. (2012). “The analytical solutions of incompressible saturated poroelastic circular Mindlin’s plate.” J. Appl. Mech., 79(5), 051009.
Woo, J., and Meguid S.A. (2001). “Nonlinear analysis of functionally graded plates and shallow shells.” Int. J Solids Struct., 38(42–43), 7409–7421.

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Published In

Go to Journal of Engineering Mechanics
Journal of Engineering Mechanics
Volume 140Issue 2February 2014
Pages: 287 - 295

History

Received: Jul 19, 2012
Accepted: May 6, 2013
Published online: May 8, 2013
Published in print: Feb 1, 2014

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Authors

Affiliations

Ph.D. Candidate, Dept. of Mechanical Engineering, South Tehran Branch, Islamic Azad Univ., Tehran, Iran. E-mail: [email protected]
A. Mojahedin [email protected]
M.Sc. Candidate, Dept. of Mechanical Engineering, South Tehran Branch, Islamic Azad Univ., Tehran, Iran. E-mail: [email protected]
A. R. Khorshidvand [email protected]
Ph.D. Candidate, Dept. of Mechanical Engineering, South Tehran Branch, Islamic Azad Univ., Tehran, Iran (corresponding author). E-mail: [email protected]
M. R. Eslami [email protected]
Professor and Fellow of the Academy of Sciences, Mechanical Engineering Dept., Amirkabir Univ. of Technology, Tehran 15914, Iran. E-mail: [email protected]

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