Research Article

Buckling of Porous FGM Sandwich Beams: A Spectral Analysis

Volume: 18 Number: 2 October 13, 2026

Buckling of Porous FGM Sandwich Beams: A Spectral Analysis

Abstract

This research studies the mathematical modelling and buckling behaviour of sandwich beam structures featuring a homogeneous metallic core and porous, functionally graded material (FGM) face sheets. A power-law distribution is used to model the continuous variation in material properties across the thickness of the FGM layers. To evaluate the impact of manufacturing-induced micro-voids, two specific porosity topographies—uniform (even) and cosine-based (uneven) distributions—are embedded into the constitutive relations. The governing equations of equilibrium are established using Timoshenko beam theory, ensuring that transverse shear deformation is rigorously accounted for. The resulting differential equations are solved using the Chebyshev Pseudospectral Method, which converts the formulation into a robust eigenvalue problem. The CPM achieves spectral convergence, with the relative error dropping below 10⁻⁹ using as few as N = 12 collocation points. The critical buckling loads agree with exact analytical benchmarks to four decimal places (e.g., β = 9.8709 vs the exact value 9.8696 for a homogeneous simply-supported beam, a relative error of 0.013%). For the baseline FGM sandwich configuration (L/h = 10, p = 1.0, α = 0.1, λ = 0.4, P-P boundary conditions), the dimensionless buckling load is β = 25.99 under the uniform porosity model (Model I) and β = 27.45 under the cosine porosity model (Model II). A comprehensive parametric study explores the synergistic influence of the power-law exponent, porosity volume fraction, thickness-to-length ratios, and diverse boundary conditions on the critical buckling thresholds. The results indicate that, while porosity generally reduces structural stiffness, the uneven distribution model leads to a greater reduction in stability than its uniform counterpart. Additionally, a comparison with Euler-Bernoulli theory underscores the need to employ shear-deformable models for deep beams. The developed semi-analytical framework serves as a computationally efficient tool for the structural optimization of porous FGM-based sandwich systems in high-performance engineering fields.

Keywords

Supporting Institution

This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.

Project Number

None

Ethical Statement

The authors declare that this study does not involve any human participants or animals. The research is based on theoretical and numerical modeling, and no ethical approval was required for the presented work.

Thanks

The authors would like to thank the reviewers for their constructive comments and suggestions that helped improve the quality of this manuscript.

References

  1. Adıyaman, G. and Turan, M., Bending and Buckling Analysis of Porous 2D Functionally Graded Beams with Exponential Material Property Variation. Iranian Journal of Science and Technology, Transactions of Civil Engineering, 49, 1359-1386, 2024.
  2. Atmane, H., Tounsi, A. and Bernard, F., Effect of thickness stretching and porosity on mechanical response of a functionally graded beams resting on elastic foundations. International Journal of Mechanics and Materials in Design, 13, 71-84, 2017.
  3. Chen, D., Yang, J. and Kitipornchai, S., Elastic buckling and static bending of shear deformable functionally graded porous beam. Composite Structures, 133, 54-61, 2015.
  4. Chen, D., Rezaei, S., Rosendahl, P. L., Xu, B. X., and Schneider, J. Multiscale modelling of functionally graded porous beams: Buckling and vibration analyses. Engineering Structures, 266, 114568, 2022.
  5. Chen, D., Yang, J. and Kitipornchai, S., Buckling and bending analyses of a novel functionally graded porous plate using Chebyshev-Ritz method. Archives of Civil and Mechanical Engineering, 19, 157-170, 2018.
  6. Chen, D., Kitipornchai, S. and Yang, J., Nonlinear free vibration of shear deformable sandwich beam with a functionally graded porous core. Thin-walled Structures, 107, 39-48, 2016.
  7. Derikvand, M., Farhatnia, F. and Hodges, D., Functionally graded thick sandwich beams with porous core: Buckling analysis via differential transform method. Mechanics Based Design of Structures and Machines, 51, 3650-3677, 2021.
  8. Hamed, M., Abo-Bakr, R., Mohamed, S. and Eltaher, M., Influence of axial load function and optimization on static stability of sandwich functionally graded beams with porous core. Engineering with Computers, 36, 1929-1946, 2020.

Details

Primary Language

English

Subjects

Numerical Methods in Mechanical Engineering

Journal Section

Research Article

Publication Date

October 13, 2026

Submission Date

April 25, 2026

Acceptance Date

August 2, 2026

Published in Issue

Year 2026 Volume: 18 Number: 2

APA
Keles, İ. (2026). Buckling of Porous FGM Sandwich Beams: A Spectral Analysis. International Journal of Engineering and Applied Sciences, 18(2). https://doi.org/10.24107/ijeas.1937798
AMA
1.Keles İ. Buckling of Porous FGM Sandwich Beams: A Spectral Analysis. IJEAS. 2026;18(2). doi:10.24107/ijeas.1937798
Chicago
Keles, İbrahim. 2026. “Buckling of Porous FGM Sandwich Beams: A Spectral Analysis”. International Journal of Engineering and Applied Sciences 18 (2). https://doi.org/10.24107/ijeas.1937798.
EndNote
Keles İ (October 1, 2026) Buckling of Porous FGM Sandwich Beams: A Spectral Analysis. International Journal of Engineering and Applied Sciences 18 2
IEEE
[1]İ. Keles, “Buckling of Porous FGM Sandwich Beams: A Spectral Analysis”, IJEAS, vol. 18, no. 2, Oct. 2026, doi: 10.24107/ijeas.1937798.
ISNAD
Keles, İbrahim. “Buckling of Porous FGM Sandwich Beams: A Spectral Analysis”. International Journal of Engineering and Applied Sciences 18/2 (October 1, 2026). https://doi.org/10.24107/ijeas.1937798.
JAMA
1.Keles İ. Buckling of Porous FGM Sandwich Beams: A Spectral Analysis. IJEAS. 2026;18. doi:10.24107/ijeas.1937798.
MLA
Keles, İbrahim. “Buckling of Porous FGM Sandwich Beams: A Spectral Analysis”. International Journal of Engineering and Applied Sciences, vol. 18, no. 2, Oct. 2026, doi:10.24107/ijeas.1937798.
Vancouver
1.İbrahim Keles. Buckling of Porous FGM Sandwich Beams: A Spectral Analysis. IJEAS. 2026 Oct. 1;18(2). doi:10.24107/ijeas.1937798

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