Cover
Vol. 21 No. 3 (2021)

Published: October 31, 2021

Pages: 10-24

Original Article

Buckling Simulation of Simply Support FG Beam Based on Different beam Theories

Raghad Azeez Neamah 1 Ameen Ahmad Nassar 2 Luay S. Alansari 1
1 Department of Mechanical Engineering, College of Engineering, University of Kufa, Najaf, Iraq
2 Department of Mechanical Engineering, College of Engineering, University of Basrah, Basrah, Iraq
History
  • Received: July 24, 2021
  • Revised: August 2, 2021
  • Accepted: August 12, 2021
  • Available Online: October 5, 2021
DOI

https://doi.org/10.33971/bjes.21.3.2

Abstract

In this paper, a new model of beam was built to study and simulate the buckling behavior of function graded beam. All equations of motion are derived using the principal of the minimum total potential energy and based on Euler-Bernoulli, first and high order shear deformation Timoshenko beam theory. The Navier solution is used for simply supported beam, and exact formulas found for buckling load. The properties of material of FG beam are assumed to change in thickness direction by using the power law formula. The dimensionless critical buckling load is calculated analytically by the FORTRAN program and numerically by ANSYS software. In the beginning, the analytical and numerical results are validated with results available in previous works and it is also has very good agreement in comparison with and some researchers. In the present study, the lower layer of the graded beam is made up of aluminum metal. As for the properties of the rest of the layers, they are calculated based on the modulus ratios studied. The effect of length to thickness ratio, modulus ratio, and power law index on the dimensionless critical buckling load of function graded beam calculating by FORTRAN and ANSYS programs are discussed. The numerical analysis of function graded beam offers accurate results and very close to the analytical solution using Timoshenko Beam theory.

Keywords

References

  1. B. A. Samsam Shariat, and M. R. Eslami, “Buckling of thick functionally graded plates under mechanical and thermal loads”, Composite Structures, Vol. 78, pp. 433439, 2007.
  2. M. Aydogdu, “A general nonlocal beam theory: Its application to nanobeam bending, buckling and vibration”, Physica E: Low-dimensional Systems and Nanostructures, Vol. 41, Issue 9, pp. 1651-1655, 2009.
  3. F. Farhatnia, M. A. Bagheri, and A. Ghobadi, “Buckling Analysis of FGM Thick Beam under Different Boundary Conditions using GDQM”, Advanced Materials Research, Vol. 433-440, pp. 4920-4924, 2012.
  4. S. R. Li and R. C. Batra, “Relations between buckling loads of functionally graded Timoshenko and homogeneous Euler-Bernoulli beams”, Composite Structures, Vol. 95, pp. 5-9, 2013.
  5. T. K. Nguyen, T. P. Vo, and H. T. Thai, “Static and free vibration of axially loaded functionally graded beams based on the first-order shear deformation theory”, Composites Part B: Engineering, Vol. 55, pp. 147-157, 2013. https://doi.org/10.1016/j.compositesb.2013.06.011
  6. Z. X. Lei, K. M. Liew, J. L. Yu, “Buckling analysis of functionally graded carbon nanotube-reinforced composite plates using the element-free kp-Ritz method”, Composite Structures, Vol. 98, pp. 160-168, 2013.
  7. J. Rychlewska, “Buckling analysis of axially functionally Graded beams”, Journal of Applied Mathematics and Computational Mechanics, Vol. 13, Issue 4, pp. 103-108, 2014. https://doi.org/10.17512/JAMCM.2014.4.13
  8. R. Saljooghi, M. T. Ahmadian, and G. H. Farrahi, “Vibration and buckling analysis of functionally graded beams using reproducing kernel particle method”, Scientia Iranica B, Vol. 21, Issue 6, pp. 1896-1906, 2014.
  9. T. Nguyen, T. T. Nguyen, T. P. Vo, and H. Thai, “Vibration and buckling analysis of functionally graded sandwich beams by a new higher-order shear deformation theory”, Composites Part B: Engineering, Vol. 76, pp. 273-285, 2015. https://doi.org/10.1016/j.compositesb.2015.02.032
  10. M. U. Uysal, and M. Kremzer, “Buckling Behaviour of Short Cylindrical Functionally Gradient Polymeric Materials”, Acta Physica Polonica A, Vol. 127, pp. 13551357, 2015.
  11. T. P. Vo, H. T. Thai, T. K. Nguyen, F. Inam, and J. Lee, “A quasi-3D theory for vibration and buckling of functionally graded sandwich beams”, Composite Structures, Vol. 119, pp. 1-12, 2015.
  12. J. Yang, H. Wu, and S. Kitipornchai, “Buckling and postbuckling of functionally graded multilayer graphene platelet-reinforced composite beams”, Composite Structures, Vol. 161, pp. 111-118, 2017. http://dx.doi.org/10.1016/j.compstruct.2016.11.048
  13. M. Z. Nejad, A. Hadi, and A. Rastgoo, “Buckling analysis of arbitrary two-directional functionally graded EulerBernoulli nano-beams based on nonlocal elasticity theory”, International Journal of Engineering Science, Vol. 103, pp. 1-10, 2016. https://doi.org/10.1016/j.ijengsci.2016.03.001
  14. K. Khorshidi, and A. Fallah, “Buckling analysis of functionally graded rectangular nano-plate based on nonlocal exponential shear deformation theory”, International Journal of Mechanical Sciences, Vol. 113, pp. 94-104, 2016. http://dx.doi.org/10.1016/j.ijmecsci.2016.04.014
  15. N. Fouda, T. El-midany, and A. M. Sadoun, “Bending, Buckling and Vibration of a Functionally Graded Porous Beam Using Finite Elements”, Journal of Applied and Computational Mechanics, Vol. 3, Issue 4, pp. 274-282, 2017. http://dx.doi.org/10.22055/JACM.2017.21924.1121
  16. M. Song, J. Yang, and S. Kitipornchai, “Bending and buckling analyses of functionally graded polymer composite plates reinforced with graphene nanoplatelets”, Composites Part B: Engineering, Vol. 134, pp. 106-113, 2018. https://doi.org/10.1016/j.compositesb.2017.09.043
  17. V. Kahya, and M. Turan, “Finite element model for vibration and buckling of functionally graded beams based on the first order shear deformation theory”, Composites Part B: Engineering, Vol. 109, pp. 108-115, 2017.
  18. A. S. Sayyad, and Y. M. Ghugal, “Analytical solutions for bending, buckling, and vibration analyses of exponential functionally graded higher order beams”, Asian Journal of Civil Engineering, Vol. 19, pp. 607-623, 2018.
  19. A. Zenkour, F. Ebrahimi, M. R. Barati, “Buckling analysis of a size-dependent functionally graded nanobeam resting on Pasternak's foundations”, International Journal of Nano Dimension, Vol. 10, Issue 2, pp. 141-153, 2019. http://www.ijnd.ir/article_662465.html
  20. V. H. Nam, P. V. Vinh, N. V. Chinh, D. V. Thom and T. T. Hong, “A New Beam Model for Simulation of the Mechanical Behaviour of Variable Thickness Functionally Graded Material Beams Based on Modified First Order Shear Deformation Theory”, Materials, Vol. 12, Issue 3, pp. 1-23, 2019. https://doi.org/10.3390/ma12030404
  21. F. Rahmani, R. Kamgar, and R. Rahgozar, “Finite Element Analysis of Functionally Graded Beams using Different Beam Theories”, Civil Engineering Journal, Vol. 6, No. 11, pp. 2086-2102, 2020.
  22. Z. Yang, A. Liu, J. Yang, J. Fu, and B. Yang, “Dynamic buckling of functionally graded grapheme nanoplatelets reinforced composite shallow arches under a step central point load”, Journal of Sound and Vibration, Vol. 465, 2020. https://doi.org/10.1016/j.jsv.2019.115019
  23. S. M. Aldousari, “Bending analysis of different material distributions of functionally graded beam”, Applied Physics A, Vol. 123, No. 296, pp. 1-9, 2017.
  24. A. Nateghi, M. Salamat-talab, J. Rezapour, and B. Daneshian, “Size dependent buckling analysis of functionally graded micro beams based on modified couple stress theory”, Applied Mathematical Modelling, Vol. 36, Issue 10, pp. 4971-4987, 2012.
  25. M. Şimşek, “Buckling of Timoshenko Beams Composed of Two-Dimensional Functionally Graded Material (2DFGM) Having Different Boundary Conditions”, Composite Structures, Vol. 149, pp. 304-314, 2016. http://dx.doi.org/10.1016/j.compstruct.2016.04.034
  26. K. Amara, M. Bouazza, and B. Fouad, “Postbuckling Analysis of Functionally Graded Beams Using Nonlinear Model”, Periodica Polytechnica Mechanical Engineering, Vol. 60, No. 2, pp. 121-128, 2016.
  27. M. Simsek and H. H. Yurtcu, “Analytical solutions for bending and buckling of functionally graded nanobeams based on the nonlocal Timoshenko beam theory”, Composite Structures, Vol. 97, pp. 378-386, 2013.
  28. ANSYS Mechanical APDL Element Reference, ANSYS, Inc., 2016.
  29. F. Farhatnia1 and M. Sarami, “Finite Element Approach of Bending and Buckling Analysis of FG Beams Based on Refined Zigzag Theory”, Universal Journal of Mechanical Engineering, Vol. 7, No. 4, pp. 147-158, 2019.