Buckling of porous FGM beams considering the thickness stretching effect

##plugins.themes.academic_pro.article.sidebar##

Published Feb 24, 2025
Date
Received: 2024-10-05
Accepted: 2025-01-19
Published: 2025-02-24
Download
PDF
Statistic
View: 45
PDF downloads: 0

Downloads

Download data is not yet available.
15(1)2025 (IN PRESS)

##plugins.themes.academic_pro.article.main##

Ahmed Amine DAIKH
University Center of Naama, Naama, Algeria
https://orcid.org/0000-0002-4666-2750
Belarbi Mohamed Ouejdi
Université de Biskra, Biskra, Algeria
Hourai Mohamed Sid Ahmed
Université Mustapha Stambouli, Mascara, Algerie
Eltaher Mohamed A.
King Abdulaziz University, Jeddah, Saudi Arabia

Abstract

This study explores the incorporation of porosity in functionally graded structures. Researchers typically integrate the porosity function into the rule of mixtures without accounting for specific fabrication processes, which relate to the volume fraction of material constituents. This paper presents an analytical investigation of buckling behavior in functionally graded beams, introducing a novel perspective on porosity that directly connects it to the volume fraction. Two porosity schemes are examined: volume fraction-dependent porosity (VFD) and rule of mixtures-dependent porosity (RMD). Four types of porosity are defined: Even, Uneven, Linear (1), and Linear (2). A higher-order shear deformation theory is proposed, based on a generalized displacement field. The equilibrium equations are derived using the principle of virtual work and solved with the Galerkin method to accommodate various boundary conditions. This work thoroughly investigates how structural geometry, material combination parameters, porosity types, and boundary conditions impact the critical buckling loads of the functionally graded beam.

##plugins.themes.academic_pro.article.details##

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

How to Cite
DAIKH, A. A., Mohamed Ouejdi, B., Mohamed Sid Ahmed, H., & Mohamed A., E. (2025). Buckling of porous FGM beams considering the thickness stretching effect. HCMCOU Journal of Science – Advances in Computational Structures, 15(1). Retrieved from http://journalofscience.acs.ou.edu.vn/index.php/acs/article/view/69

References

  1. Adhikari, B., Dash, P., & Singh, B. (2020). Buckling analysis of porous FGM sandwich plates under various types of non-uniform edge compression based on higher order shear deformation theory. Composite Structures, 251(issue) , 112597.
  2. Akbaş, S. D. (2017). Nonlinear static analysis of functionally graded porous beams under thermal effect. Coupled Systems Mechanics, 6(4) , 399–415.
  3. Anirudh, B., Ganapathi, M., Anant, C., & Polit, O. (2019). A comprehensive analysis of porous graphene-reinforced curved beams by finite element approach using higher-order structural theory: bending, vibration and buckling. Composite Structures, 222(issue) , Article ID 110899.
  4. Atmane, H. A., Tounsi, A., & Bernard, F. (2017). Effect of thickness stretching and porosity on mechanical response of a functionally graded beams resting on elastic foundations. International Journal of Mechanical Materials Design, 13(issue) , 71-84.
  5. Bagheri, Z., Fiouz, A., & Seraji, M. (2024). Effect of porosity on free vibration and buckling of functionally graded porous beams with non-uniform cross-section. Journal of Central South University, 31(3), 841–857.
  6. Beitollahi, A., Bazargan-Lari, Y., & Janghorban, M. (2024). On the variable length scale parameter in functionally graded non-porous and porous microplate/nanoplate. Mechanics of Advanced Materials and Structures, volume30), 12481-12503.
  7. Burlayenko, V. N., & Kouhia, R. (2024). Analysis of natural frequencies in non-uniform cross-section functionally graded porous beams. Journal of Vibration Engineering and Technologies, 12(issue) , 6527–6547.
  8. Chen, D., Kitipornchai, S., & Yang, J. (2016). Nonlinear free vibration of shear deformable sandwich beams with a functionally graded porous core. Thin-Walled Structures, 107(issue) , 39–48.
  9. Chen, D., Yang, J., & Kitipornchai, S. (2015). Elastic buckling and static bending of shear deformable functionally graded porous beams. Composite Structures, 133(issue) , 54–61.
  10. Chinh, T. H., Tu, T. M., Duc, D. M., Hung, T. Q. , (2021). Static flexural analysis of sandwich beam with functionally graded face sheets and porous core via point interpolation meshfree method based on polynomial basic function. Archives of Applied Mechanics, 91(3), 933–947.
  11. Eltaher, M. A., Fouda, N., El-Midany, T., & Sadoun, A. M. (2018). Modified porosity model in analysis of functionally graded porous nanobeams. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 40(3), page-page .
  12. Fahsi, B., Bouiadjra, R. B., Mahmoudi, A., Benyoucef, S., & Tounsi, A. (2019). Assessing the effects of porosity on the bending, buckling, and vibrations of functionally graded beams resting on an elastic foundation by using a new refined quasi-3D theory. Mechanics of Composite Materials, 55(2), 219–230.
  13. Fallah, A., & Aghdam, M. M. (2024). Physics-informed neural network for bending and free vibration analysis of three-dimensional functionally graded porous beams resting on elastic foundation. Engineering Computations, 40(1), 437–454.
  14. Gao, Y., & Xiao, W. (2019). Nonlinear bending of functionally graded porous nanobeam subjected to multiple physical loads based on nonlocal strain gradient theory. Steel and Composite Structures, 31(5), 469–488.
  15. Hamed, M., Abo-Bakr, R., Mohamed, S., & Eltaher, M. (2020). Influence of axial load function and optimization on static stability of sandwich functionally graded beams with porous core. Engineering Computations, 36(4), 1929–1946.
  16. Hamed, M., Sadoun, A., & Eltaher, M. A. (2019). Effects of porosity models on static behavior of size dependent functionally graded beams. Structural Engineering and Mechanics, 71(1) , 89–98.
  17. Li, S.-R., & Batra, R. C. (2013). Relations between buckling loads of functionally graded Timoshenko and homogeneous Euler–Bernoulli beams. Composite Structures, 95(issue) , 5–9.
  18. Liu, Y., Su, S., Huang, H., & Liang, Y. (2019). Thermal-mechanical coupling buckling analysis of porous functionally graded sandwich beams based on physical neutral plane. Composites Part B: Engineering, 168(issue) , 236–242.
  19. Masjedi, P. K., Maheri, A., & Weaver, P. M. (2019). Large deflection of functionally graded porous beams based on a geometrically exact theory with a fully intrinsic formulation. Applied Mathematical Modelling, 76(issue) , 938–957.
  20. Mellal, F., Bennai, R., Nebab, M., Atmane, H. A., Bourada, F., Hussain, M., & Tounsi, A. (2021). Investigation on the effect of porosity on wave propagation in FGM plates resting on elastic foundations via a quasi-3D HSDT. Waves in Random and Complex Media, 30(13), 2765–2779.
  21. Mojahedin, A., Jabbari, M., & Rabczuk, T. (2018). Thermoelastic analysis of functionally graded porous beams. Journal of Thermal Stresses, 41(8), 937–950.
  22. Nebab, M., Dahmane, M., Belqassim, A., Atmane, H. A., Bernard, F., Benadouda, M., Bennai, R., & Hadji, L. (2023). Fundamental frequencies of cracked FGM beams with influence of porosity and Winkler/Pasternak/Kerr foundation support using a new quasi-3D HSDT. Mechanics of Advanced Materials and Structures, 31 (28), 10639-10651.
  23. Polit, O., Anant, C., Anirudh, B., & Ganapathi, M. (2019). Functionally graded graphene reinforced porous nanocomposite curved beams: bending and elastic stability using a higher-order model with thickness stretch effect. Composites Part B: Engineering, 166(issue) , 310–327.
  24. Sah, S. K., & Ghosh, A. (2022). Influence of porosity distribution on free vibration and buckling analysis of multi-directional functionally graded sandwich plates. Composite Structures, 279(issue) , 114795.
  25. Srikarun, B., Songsuwan, W., & Wattanasakulpong, N. (2021). Linear and nonlinear static bending of sandwich beams with functionally graded porous core under different distributed loads. Composite Structures, 276(issue) , 114538.
  26. Su, J., Xiang, Y., Ke, L.-L., & Wang, Y.-S. (2019). Surface effect on static bending of functionally graded porous nanobeams based on Reddy’s beam theory. International Journal of Structural Stability and Dynamics, 19(06), 1950062.
  27. Vo, T. P., Thai, H.-T., Nguyen, T.-K., Inam, F., & Lee, J. (2015). A quasi-3D theory for vibration and buckling of functionally graded sandwich beams. Composite Structures, 119(issue) , 1–12.
  28. Vo, T. P., Thai, H.-T., Nguyen, T.-K., Maheri, A., & Lee, J. (2014). Finite element model for vibration and buckling of functionally graded sandwich beams based on a refined shear deformation theory. Engineering Structures, 64(issue) , 12–22.
  29. Wang, Y., Zhou, A., Fu, T., & Zhang, W. (2020). Transient response of a sandwich beam with functionally graded porous core traversed by a non-uniformly distributed moving mass. International Journal of Mechanical Materials Design, 16(3), 519–540.
  30. Wattanasakulpong, N., & Ungbhakorn, V. (2014). A study on functionally graded materials. Aerospace Science and Technology, 32(issue) , 111.
  31. Zghal, S., & Dammak, F. (2021). Buckling responses of porous structural components with gradient power-based and sigmoid material variations under different types of compression loads. Composite Structures, 273(issue) , 114313.
  32. Zghal, S., Ataoui, D., & Dammak, F. (2020). Static bending analysis of beams made of functionally graded porous materials. Mechanics Based Design of Structures and Machines, 50(3) , 1–18.
  33. Zhang, X., Wang, H., Zheng, S., & Chen, D. (2024). Size-dependent nonlinear free vibration of multilayer functionally graded graphene platelet-reinforced composite tapered microbeams. Journal of Vibration Engineering and Technologies, 12(issue), 7653-7670.
  34. Zhang, Y., Jin, G., Chen, M., Ye, T., Yang, C., & Yin, Y. (2020). Free vibration and damping analysis of porous functionally graded sandwich plates with a viscoelastic core. Composite Structures, 244(issue) , 112298.
  35. Zouatnia, N., Hadji, L., Atmane, H. A., Nebab, M., Madan, R., Bennai, R., & Dahmane, M. (2024). Analysis of free vibration in bi-directional power law-based FG beams employing RSD theory. Coupled Systems Mechanics, 13(4), 359.