Contact Us

For Marketing, Sales and Subscriptions Inquiries
Rockefeller Center, 45 Rockefeller Plaza
20th Flr Unit #5, New York, NY 10111
United States

Conference List

Review of Information Engineering and Applications

March 2015, Volume 2, 1, pp 1-14

Postbuckling Analysis of Functionally Graded Beams Using Hyperbolic Shear Deformation Theory

Mokhtar Bouazza


Khaled Amara


Mohamed Zidour


Abedlouahed Tounsi


EL Abbas Adda-Bedia

Mokhtar Bouazza 1

Khaled Amara 2
Mohamed Zidour 3

Abedlouahed Tounsi 4 EL Abbas Adda-Bedia 4 

  1. Department of Civil Engineering, University of Bechar, Bechar, Algeria; Laboratory of Materials and Hydrology (LMH), University of Sidi Bel Abbes, Sidi Bel Abbes, Algeria 1

  2. Laboratory of Materials and Hydrology (LMH), University of Sidi Bel Abbes, Sidi Bel Abbes, Algeria; Department of Civil Engineering, University centre of Ain Temouchent , Ain Temouchent, Algeria 2

  3. Laboratory of Materials and Hydrology (LMH), University of Sidi Bel Abbes, Sidi Bel Abbes, Algeria; Department of Civil Engineering, University of Ibn Khaldoun, Zaaroura, Tiaret, Algeria 3

  4. Laboratory of Materials and Hydrology (LMH), University of Sidi Bel Abbes, Sidi Bel Abbes, Algeria 4

Pages: 1-14

DOI: 10.18488/journal.79/2015.2.1/

Share :


In the present study, post-buckling of a thick FGM rectangular beam is carried out using the hyperbolic shear deformation theory (HYSDT). The theory accounts for parabolic distribution of transverse shear stresses across the thickness satisfying the stress free boundary conditions at top and bottom surfaces of the beam. It is assumed that elasticity modulus is changing in the thickness direction and all other material properties are taken to be constant. Variation of elasticity modulus in the thickness direction, are described by a simple power law distribution in terms of the volume fractions of constituents. Governing equations of FGM beam for post-buckling problem were found by applying Hamilton principle and Navier type solution method was used to solve post-buckling problem. The results obtained for post-buckling analysis of functionally graded beams are compared with those obtained by other theories, to validate the accuracy of the presented theory.
Contribution/ Originality
This study originates new formula to investigate the postbuckling behaviors of simply supported FGM beams subjected to mechanical loads.




  1. V. Birman and L. W. Byrd, "Modeling and analysis of functionally graded materials and structures," Appl. Mech. Rev., vol. 60, pp. 195–216, 2007.
  2. Y. Miyamoto, W. Kaysser, B. Rabin, A. Kawasaki, and R. Ford, Functionally graded materials: Design, processing and application. Boston-Dordrecht-London: Kluwer Academic Publishers, 1999.
  3. A. Chakraborty, S. Gopalakrishnan, and J. Reddy, "A new beam finite element for the analysis of functionally graded materials," Int J Mech Sci., vol. 45, pp. 519–39, 2003.
  4. F. Q. Zhao, A. M. Wang, and H. Z. Liu, "Thermal post-buckling analyses of functionally graded material rod," Appl. Math. Mech., vol. 28, pp. 59–67, 2007.
  5. S. R. Li, J. H. Zhang, and Y. G. Zhao, "Thermal post-buckling of functionally graded material Timoshenko beams," Appl. Math. Mech., vol. 27, pp. 803–810, 2006.
  6. A. Rastgo, H. Shafie, and A. Allahverdizadeh, "Instability of curved beams made of functionally graded material under thermal loading," Int. J. Mech. Mater. Des., vol. 2, pp. 117–128, 2005.
  7. L. L. Ke, J. Yang, and S. Kitipornchai, "Postbuckling analysis of edge cracked functionally graded timoshenko beams under end-shortening," Compos. Struct., vol. 90, pp. 152–160, 2009a.
  8. L. L. Ke, J. Yang, S. Kitipornchai, and Y. Xiang, "Flexural vibration and elastic buckling of a cracked timoshenko beam made of functionally graded materials," Mech. Adv. Mater. Struct. , vol. 16, pp. 488–502, 2009b.
  9. J. Reddy, "Analysis of functionally graded plates," International Journal for Numerical Methods in Engineering, vol. 47, pp. 663–84, 2000.
  10. S. Vel and R. Batra, "Exact solution for thermoelastic deformations of functionally graded thick rectangular plates," AIAA Journal, vol. 40, pp. 1021–33, 2002.
  11. S. Vel and R. Batra, "Three-dimensional exact solution for the vibration of functionally graded rectangular plates," Journal of Sound and Vibration, vol. 272, pp. 703–30, 2004.
  12. M. Bouazza and E. A. Adda-Bedia, "Elastic stability of functionally graded rectangular plates under mechanical and thermal loadings," Academic Journals, Scientific Research and Essays, vol. 8, pp. 1933-1943, 2013.
  13. M. Bouazza, K. Amara, M. Zidour, A. Tounsi, and E. A. Adda-Bedia, "Post-buckling of simply supported FGM beams using non-linear model," Journal of Materials Science and Technology, vol. 22, pp. 133–150, 2014.
  14. G. Praveen and J. Reddy, "Nonlinear transient thermoelastic analysis of func- tionally graded ceramic-metal plates," International Journal of Solids and Structures, vol. 34, pp. 4457–76, 1998.
  15. K. P. Soldatos, "On certain refined theories for plate bending," ASME Journal of Applied Mechanics, vol. 55, pp. 994–995, 1988.
  16. K. P. Soldatos, "A transverse shear deformation theory for homogeneous monoclinic plates," Acta Mechanica, vol. 94, pp. 195–200, 1992.
  17. A. Nayfeh and D. Mook, Nonlinear oscillations. New York: Wiley, 1979.
  18. A. Nayfeh and S. Emam, "Exact solution and stability of postbuckling configurations of beams," Nonlin Dyn, vol. 54, pp. 395–408, 2008.


Google Scholor ideas Microsoft Academic Search bing Google Scholor


Competing Interests:


Related Article

( 1 ) Postbuckling Analysis of Functionally Graded Beams Using Hyperbolic Shear Deformation Theory
( 2 ) Web Pages Categorization Based on Classification & Outlier Analysis through FSVM
( 4 ) Classification and Identification of Risk Management Techniques for Mitigating Risks with Factor Analysis Technique in Software Risk Management
( 5 ) A Detailed Analysis of Software Cost Estimation Using Cosmic-FFP
( 6 ) Performance Analysis of Routing Protocols for CBR Traffic in Mobile Ad-Hoc Networks
( 7 ) Analysis of Suitable Security Protocols for Apply a Model of Identity in the Civil Registry of Ecuador
( 8 ) Comprehensive Analysis & Performance Comparison of Clustering Algorithms for Big Data
( 9 ) Development and Performance Analysis of Bisection Method-Based Optimal Path Length Algorithm for Terrestrial Microwave Link
( 10 ) Network Traffic Analysis Using Queuing Model and Regression Technique
( 11 ) Stability Analysis of Type-2 Fuzzy Process Control Using LMI
( 12 ) A Survey on Sentiment Analysis Algorithms and Datasets
( 13 ) Analysis of Cyber Attacks on Load Frequency Control in Smart Grid
( 14 ) Design and Analysis of Compact Microstrip Circular Resonator with Slotted in Ground Plane as a Grain Moisture Sensor
( 15 ) Study and Comparative Analysis of Programming Languages Used for Big Data
( 19 ) Investigate of Mechanical Fuse in Cardan Shaft Using FEM
( 20 ) Vlsi Architecture of Mimo Detector Using Fixed Complexity Sphere Decoding
( 21 ) Predict Survival of Patients with Lung Cancer Using an Ensemble Feature Selection Algorithm and Classification Methods in Data Mining
( 24 ) Received Signal Strength in a Macrocell in Lagos Environs Using Finite Element Method
( 25 ) RLS Fixed-Lag Smoother Using Covariance Information Based on Innovation Approach in Linear Continuous Stochastic Systems
( 26 ) Lossless Image Compression and Decompression to Improve the PSNR and MSE Values Using Architecture
( 27 ) PAPR Reduction Using Eight Factors Rotating Phase Shift Technique Based on Local Search Algorithm in OFDM
( 28 ) Using ICT Policy Framework as a Panacea for Economic Recession and Instability in Nigeria
( 29 ) Detection and Prevention of Phishing Attack Using Linkguard Algorithm