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New Enriched Beam Element for Static Bending Analysis of Functionally Graded Porous Beams Resting on Elastic Foundations

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Abstract

This paper presents a novel approach for analyzing functionally graded beams with porosity on elastic foundations. A new first-order shear mixed beam element is proposed, incorporating enriched transverse shear stiffness and parabolic stress distributions. The element avoids shear locking and demonstrates high convergence and accuracy. Compared to existing models, the proposed beam element convergence with only one to two elements, so it provides a reliable numerical tool for analyzing both homogeneous and functionally graded beams. The study investigates the influence of elastic foundations and porosity, offering benchmark solutions for future research. The proposed element finds applications in civil, mechanical, and aerospace engineering, enabling efficient analysis and optimization of structural systems under complex loading. It also holds potential for vibration and buckling analysis, enhancing structural design and stability.

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REFERENCES

  1. H. A. Atmane, E. A. A. Bedia, M. Bouazza, et al., “On the thermal buckling of simply supported rectangular plates made of a sigmoid functionally graded Al/Al2O3 based material,” Mech. Solids 51, 177–187 (2016). https://doi.org/10.3103/S0025654416020059

    Article  ADS  Google Scholar 

  2. V. Katiyar, A. Gupta, and A. Tounsi, “Microstructural/geometric imperfection sensitivity on the vibration response of geometrically discontinuous bi-directional functionally graded plates (2D-FGPs) with partial supports by using FEM,” Steel Compos. Struct. 35, 621–640 (2022). https://doi.org/10.12989/scs.2022.45.5.621

    Article  Google Scholar 

  3. E. Sobhani and M. Avcar, “Natural frequency analysis of imperfect GNPRN conical shell, cylindrical shell, and annular plate structures resting on Winkler-Pasternak Foundations under arbitrary boundary conditions,” Eng. Anal. Bound. Elem. 144, 145–164 (2022). https://doi.org/10.1016/j.enganabound.2022.08.018

    Article  MathSciNet  Google Scholar 

  4. P. Van Vinh, M. O. Belarbi, M. Avcar, and Ö. Civalek, “An improved first-order mixed plate element for static bending and free vibration analysis of functionally graded sandwich plates,” Arch. Appl. Mech. (2023). https://doi.org/10.1007/s00419-022-02359-z

  5. A. O. Vatulyan and V. O. Yurov, “On the determination of the mechanical characteristics of rod elements made of functionally graded materials,” Mech. Solids 55, 907–917 (2020). https://doi.org/10.3103/S0025654420660036

    Article  ADS  Google Scholar 

  6. A. O. Vatulyan and S.A. Nesterov, “On determination of the thermomechanical characteristics of a functionally graded finite cylinder,” Mech. Solids 56, 1429–1438 (2021). https://doi.org/10.3103/S0025654421070256

    Article  ADS  MATH  Google Scholar 

  7. P. Van Vinh, N. Van Chinh, and A. Tounsi, “Static bending and buckling analysis of bi-directional functionally graded porous plates using an improved first-order shear deformation theory and FEM,” Eur. J. Mech. A/Solids 96, 104743 (2022). https://doi.org/10.1016/j.euromechsol.2022.104743

  8. M. Avcar and W. K. M. Mohammed, “Free vibration of functionally graded beams resting on Winkler-Pasternak foundation,” Arab. J. Geosci. 11, 232 (2018). https://doi.org/10.1007/s12517-018-3579-2

    Article  Google Scholar 

  9. N. Wattanasakulpong and A. Chaikittiratana, “Flexural vibration of imperfect functionally graded beams based on Timoshenko beam theory: Chebyshev collocation method,” Meccanica 50, 1331–1342 (2015). https://doi.org/10.1007/s11012-014-0094-8

    Article  MathSciNet  MATH  Google Scholar 

  10. F. Ebrahimi and M. Zia, “Large amplitude nonlinear vibration analysis of functionally graded Timoshenko beams with porosities,” Acta Astronaut. 116, 117–125 (2015). https://doi.org/10.1016/j.actaastro.2015.06.014

    Article  Google Scholar 

  11. Ş. D. Akbaş, “Forced vibration responses of axially functionally graded beams by using Ritz method,” J. Appl. Comput. Mech. 7, 109–115 (2021). https://doi.org/10.22055/jacm.2020.34865.2491

    Article  Google Scholar 

  12. H. N. Nguyen, T. T. Hong, P. Van Vinh, et al., “A refined simple first-order shear deformation theory for static bending and free vibration analysis of advanced composite plates,” Mater. 12, (2019). https://doi.org/10.3390/ma12152385

  13. T. Vo, T. Thai, T. Nguyen, and F. Inam, “Static and vibration analysis of functionally graded beams using refined shear deformation theory,” Meccanica 49, 155–168 (2014). https://doi.org/10.1007/s11012-013-9780-1

    Article  MathSciNet  MATH  Google Scholar 

  14. F. Mellal, R. Bennai, M. Avcar, et al., “On the vibration and buckling behaviors of porous FG beams resting on variable elastic foundation utilizing higher-order shear deformation theory,” Acta Mech. (2023). https://doi.org/10.1007/s00707-023-03603-5

  15. Hassen Ait Atmane, Abdelouahed Tounsi, Fabrice Bernard, and S. R. Mahmoud, “A computational shear displacement model for vibrational analysis of functionally graded beams with porosities,” Steel Compos. Struct. 19, 369–384 (2015). https://doi.org/10.12989/SCS.2015.19.2.369

    Article  Google Scholar 

  16. B. Fouad, B. A. Anis, B. Mohamed, et al., “Dynamic investigation of porous functionally graded beam using a sinusoidal shear deformation theory,” Wind Struct. 28, 19–30 (2019). https://doi.org/10.12989/WAS.2019.28.1.019

    Article  Google Scholar 

  17. M. A. Hamed, R. M. Abo-bakr, S. A. Mohamed, and M. A. Eltaher, “Influence of axial load function and optimization on static stability of sandwich functionally graded beams with porous core,” Eng. Comput. 36, 1929–1946 (2020). https://doi.org/10.1007/s00366-020-01023-w

    Article  Google Scholar 

  18. T. P. Vo, H.-T. Thai, T.-K. Nguyen, et al., “Static behaviour of functionally graded sandwich beams using a quasi-3D theory,” Compos. Part B Eng. 68, 59–74 (2015). https://doi.org/10.1016/j.compositesb.2014.08.030

    Article  Google Scholar 

  19. B. Fahsi, R.B. Bouiadjra, A. Mahmoudi, et al., “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,” Mech. Compos. Mater. 55, 219–230 (2019). https://doi.org/10.1007/s11029-019-09805-0

    Article  ADS  Google Scholar 

  20. A. Frikha, A. Hajlaoui, M. Wali, and F. Dammak, “A new higher order C0 mixed beam element for FGM beams analysis,” Compos. Part B Eng. 106, 181–189 (2016). https://doi.org/10.1016/j.compositesb.2016.09.024

    Article  Google Scholar 

  21. V. H. Nam, P. Van Vinh, N. Van Chinh, et al., “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,” Mater. 12, (2019). https://doi.org/10.3390/ma12030404

  22. H. N. Nguyen, T. T. Hong, P. Van Vinh, and D. Van Thom, “An efficient beam element based on Quasi-3D theory for static bending analysis of functionally graded beams,” Mater. 12, (2019). https://doi.org/10.3390/ma12132198

  23. P. Van Vinh, “Static bending analysis of functionally graded sandwich beams using a novel mixed beam element based on first-order shear deformation theory,” Forces Mech. 4, 100039 (2021). https://doi.org/10.1016/j.finmec.2021.100039

  24. A. Mesbah, Z. Belabed, K. Amara, et al., “Formulation and evaluation a finite element model for free vibration and buckling behaviours of functionally graded porous (FGP) beams,” Struct. Eng. Mech. 86, 291–309 (2023). https://doi.org/10.12989/sem.2023.86.3.291

    Article  Google Scholar 

  25. J. N. Reddy, “Analysis of functionally graded plates,” Int. J. Numer. Methods Eng. 47, 663–684 (2000). https://doi.org/10.1002/(SICI)1097-0207(20000110/30)47:1/3<663::AID-NME787>3.0.CO;2-8

  26. H.-T. Thai and T.P. Vo, “Bending and free vibration of functionally graded beams using various higher-order shear deformation beam theories,” Int. J. Mech. Sci. 62, 57–66 (2012). https://doi.org/10.1016/j.ijmecsci.2012.05.014

    Article  Google Scholar 

  27. A. R. Noori, T. A. Aslan, and B. Temel, “Dynamic analysis of functionally graded porous beams using complementary functions method in the Laplace domain,” Compos. Struct. 256, 113094 (2021). https://doi.org/10.1016/j.compstruct.2020.113094

  28. P. Van Vinh and L. T. Son, “A new first-order mixed beam element for static bending analysis of functionally graded graphene oxide powder-reinforced composite beams,” Struct. 36, 463–472 (2022). https://doi.org/10.1016/j.istruc.2021.12.032

    Article  Google Scholar 

  29. J. Ying, C. F. Lu, and W. Q. Chen, “Two-dimensional elasticity solutions for functionally graded beams resting on elastic foundations,” Compos. Struct. 84, 209–219 (2008). https://doi.org/10.1016/j.compstruct.2007.07.004

    Article  Google Scholar 

  30. P. Van Vinh, N. Q. Duoc, and N. D. Phuong, “A new enhanced first-order beam element based on neutral surface position for bending analysis of functionally graded porous beams,” Iran. J. Sci. Technol. Trans. Mech. Eng. 46, 1141–1156 (2022). https://doi.org/10.1007/s40997-022-00485-1

    Article  Google Scholar 

  31. Y. M. Ghugal, M. State, and R. Sharma, “A refined shear deformation theory for flexure of thick beams,” Lat. Am. J. Solids Struct. 8, 183–195 (2011). https://doi.org/10.1590/S1679-78252011000200005

    Article  Google Scholar 

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ACKNOWLEDGMENTS

The authors extend their appreciation to the Deputyship for Research & Innovation, Ministry of Education in Saudi Arabia for funding this research work through the project number ISP23-69.

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  1. Department of Mechanical Engineering, Jazan University, P. O. Box 114, 45142, Jazan, Saudi Arabia

    M. H. Ghazwani

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  1. M. H. Ghazwani
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Correspondence to M. H. Ghazwani.

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Ghazwani, M.H. New Enriched Beam Element for Static Bending Analysis of Functionally Graded Porous Beams Resting on Elastic Foundations. Mech. Solids 58, 1878–1893 (2023). https://doi.org/10.3103/S0025654423600885

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