Buckling of porous FGM beams considering the thickness stretching effect

issue 15(1)2025
Published Feb 24, 2025
https://doi.org/10.46223/HCMCOUJS.acs.en.15.1.69.2025
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Received: 2024-10-05
Accepted: 2025-01-19
Published: 2025-02-24
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15(1)2025

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Ahmed Amine Daikh - daikhresearch@gmail.com
University Center of Naama, Naama, Algeria; Université Mustapha Stambouli, Mascara, Algerie
https://orcid.org/0000-0002-4666-2750
Mohamed Ouedjdi Belarbi
Université de Biskra, Biskra, Algeria
Mohamed Sid Ahmed Houari
Université Mustapha Stambouli, Mascara, Algerie
Mohamed A. Eltaher
King Abdulaziz University, Jeddah, Saudi Arabia; Zagazig University, Zagazig, Egypt

Abstract

This study presents a novel analytical investigation into the buckling behavior of porous Functionally Graded (FG) beams, incorporating the effects of thickness stretching and porosity variations. Unlike conventional approaches that assume the rule of mixtures purely governs porosity, this work introduces a novel perspective by directly relating porosity to the material volume fraction. Two distinct porosity schemes are analyzed: Volume Fraction-Dependent porosity (VFD) and Rule of Mixtures-Dependent porosity (RMD), with four porosity distribution types - Even, Uneven, Linear (1), and Linear (2). A higher-order shear deformation theory is developed to account for the thickness stretching effect, enabling precise modeling of transverse shear stresses without correcting factors. The equilibrium equations are derived using the principle of virtual work and solved via the Galerkin method for a range of boundary conditions. Comprehensive parametric studies reveal the influence of structural geometry, material grading, and porosity types on critical buckling loads. The findings demonstrate the robustness of the proposed framework and offer new insights for designing lightweight and efficient FG structures.

Keywords

buckling behavior, functionally graded beam, galerkin method, higher-order shear deformation plate theory, Rule of Mixture porosity Dependent (RMD), Volume Fraction porosity-Dependent (VFD)

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

How to Cite
Daikh, A. A., Belarbi, M. O., Hourai, M. S. A., & Eltaher, M. A. (2025). Buckling of porous FGM beams considering the thickness stretching effect. HCMCOU Journal of Science – Advances in Computational Structures, 15(1), 41–58. https://doi.org/10.46223/HCMCOUJS.acs.en.15.1.69.2025
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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, Article 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, Article 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, 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, (30), 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, 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, 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, 54-61.
  10. 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).
  11. 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.
  12. 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.
  13. 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.
  14. 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
  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. Li, S. R., & Batra, R. C. (2013). Relations between buckling loads of functionally graded Timoshenko and homogeneous Euler-Bernoulli beams. Composite Structures, 95, 5-9.
  17. 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, 236-242.
  18. 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, 938-957.
  19. 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.
  20. Mojahedin, A., Jabbari, M., & Rabczuk, T. (2018). Thermoelastic analysis of functionally graded porous beams. Journal of Thermal Stresses, 41(8), 937-950.
  21. 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.
  22. 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, 310-327.
  23. 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, Article 114795.
  24. 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, Article 114538.
  25. 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(6), Article 1950062.
  26. Truong, C. H., Tran, T. M., Do, D. M., & Tran, H. 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.
  27. Vo, T. P., Thai, T. H., Nguyen, K. T., Inam, F., & Lee, J. (2015). A quasi-3D theory for vibration and buckling of functionally graded sandwich beams. Composite Structures, 119, 1-12.
  28. Vo, T. P., Thai, T. H., Nguyen, K. T., 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, 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, Article 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, Article 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, 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, Article 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), Article 359.

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