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Buckling Analysis of Functionally Graded Beams Using the Finite Element Method

Year 2022, Volume: 15 Issue: Special Issue I - 4th International Conference on Advanced Engineering Technologies, 98 - 109, 23.12.2022

Muhittin Turan Mahmut İlter Hacıoğlu

https://doi.org/10.18185/erzifbed.1199454

Abstract

This study developed a finite element model according to higher-order shear deformation beam theory (HSDT) for the buckling analysis of functionally graded (FG) beams. Equilibrium equations of the FG beam are obtained from Lagrange’s equations. The beam element to be discussed within the scope of the study has 5 nodes and 16 degrees of freedom (DOF). As a result of the buckling analysis, the critical buckling load of the beam was obtained for various boundary conditions, power-law index (p), and slenderness (L/h). When the critical buckling loads obtained as a result of the analysis were compared with the literature, it was seen that they were quite compatible.

Keywords

Finite element model FG beam Buckling analysis Higher-order shear deformation beam theory

References

  • [1] Turan, M., (2018). Tabakalı kirişlerin statik, serbest titreşim ve burkulma analizleri için bir sonlu eleman modeli, PhD Thesis, Karadeniz Technical University Institute of Science and Technology.
  • [2] Nguyen, T. K., Truong-Phong Nguyen, T., Vo, T. P., Thai, H. T., (2015). Vibration and buckling analysis of functionally graded sandwich beams by a new higher-order shear deformation theory. Composites Part B: Engineering, 76, 273–285.
  • [3] Nguyen, T. K., Nguyen, B. D., (2015). A new higher-order shear deformation theory for static, buckling and free vibration analysis of functionally graded sandwich beams. Journal of Sandwich Structures and Materials, 17(6), 613–631.
  • [4] Nguyen, T. K., Vo, T. P., Nguyen, B. D., Lee, J., (2016). An analytical solution for buckling and vibration analysis of functionally graded sandwich beams using a quasi-3D shear deformation theory. Composite Structures, 156, 238–252.
  • [5] Turan, M., (2022). Bending analysis of two-directional functionally graded beams using trigonometric series functions. Archive of Applied Mechanics, 92(6), 1841–1858.
  • [6] Turan, M., Kahya, V., (2021). Free vibration and buckling analysis of functionally graded sandwich beams by Navier’s method. Journal of the Faculty of Engineering and Architecture of Gazi University, 36(2), 743–757.
  • [7] Liu, J., He, B., Ye, W., Yang, F., (2021). High performance model for buckling of functionally graded sandwich beams using a new semi-analytical method. Composite Structures, 262(January), 113614.
  • [8] Avcar, M., Hadji, L., Civalek, Ö., (2021). Natural frequency analysis of sigmoid functionally graded sandwich beams in the framework of high order shear deformation theory. Composite Structures, 276(June).
  • [9] Keleshteri, M. M., Jelovica, J., (2022). Beam theory reformulation to implement various boundary conditions for generalized differential quadrature method. Engineering Structures, 252, 113666.
  • [10] Oyekoya, O. O., Mba, D. U., El-Zafrany, A. M., (2009). Buckling and vibration analysis of functionally graded composite structures using the finite element method. Composite Structures, 89(1), 134–142.
  • [11] Alshorbagy, A. E., Eltaher, M. A., Mahmoud, F. F., (2011). Free vibration characteristics of a functionally graded beam by finite element method. Applied Mathematical Modelling, 35(1), 412–425.
  • [12] 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, 12–22.
  • [13] 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, 1–12.
  • [14] Liu, B., Ferreira, A. J. M., Xing, Y. F., Neves, A. M. A., (2016). Analysis of functionally graded sandwich and laminated shells using a layerwise theory and a differential quadrature finite element method. Composite Structures, 136, 546–553.
  • [15] Yarasca, J., Mantari, J. L., Arciniega, R. A., (2016). Hermite-Lagrangian finite element formulation to study functionally graded sandwich beams. Composite Structures, 140, 567–581.
  • [16] Kahya, V., Turan, M., (2017). Finite element model for vibration and buckling of functionally graded beams based on the first-order shear deformation theory. Composites Part B: Engineering, 109, 108–115.
  • [17] Kahya, V., Turan, M., (2018). Vibration and buckling of laminated beams by a multi-layer finite element model. Steel and Composite Structures, 28(4), 415–426.
  • [18] Reddy, J. N., Nampally, P., Srinivasa, A. R., (2020). Nonlinear analysis of functionally graded beams using the dual mesh finite domain method and the finite element method. International Journal of Non-Linear Mechanics, 127(August), 103575.
  • [19] Yaghoobi, M., Sedaghatjo, M., Alizadeh, R., Karkon, M., (2021). An efficient simple element for free vibration and buckling analysis of FG beam. Journal of Engineering Research, 1–25.
  • [20] Koutoati, K., Mohri, F., Daya, E. M., (2021). Finite element approach of axial bending coupling on static and vibration behaviors of functionally graded material sandwich beams. Mechanics of Advanced Materials and Structures, 28(15), 1537–1553.
  • [21] Belarbi, M. O., Houari, M. S. A., Hirane, H., Daikh, A. A., Bordas, S. P. A., (2022). On the finite element analysis of functionally graded sandwich curved beams via a new refined higher order shear deformation theory. Composite Structures, 279(July 2021).

Year 2022, Volume: 15 Issue: Special Issue I - 4th International Conference on Advanced Engineering Technologies, 98 - 109, 23.12.2022

Muhittin Turan Mahmut İlter Hacıoğlu

https://doi.org/10.18185/erzifbed.1199454

Abstract

References

  • [1] Turan, M., (2018). Tabakalı kirişlerin statik, serbest titreşim ve burkulma analizleri için bir sonlu eleman modeli, PhD Thesis, Karadeniz Technical University Institute of Science and Technology.
  • [2] Nguyen, T. K., Truong-Phong Nguyen, T., Vo, T. P., Thai, H. T., (2015). Vibration and buckling analysis of functionally graded sandwich beams by a new higher-order shear deformation theory. Composites Part B: Engineering, 76, 273–285.
  • [3] Nguyen, T. K., Nguyen, B. D., (2015). A new higher-order shear deformation theory for static, buckling and free vibration analysis of functionally graded sandwich beams. Journal of Sandwich Structures and Materials, 17(6), 613–631.
  • [4] Nguyen, T. K., Vo, T. P., Nguyen, B. D., Lee, J., (2016). An analytical solution for buckling and vibration analysis of functionally graded sandwich beams using a quasi-3D shear deformation theory. Composite Structures, 156, 238–252.
  • [5] Turan, M., (2022). Bending analysis of two-directional functionally graded beams using trigonometric series functions. Archive of Applied Mechanics, 92(6), 1841–1858.
  • [6] Turan, M., Kahya, V., (2021). Free vibration and buckling analysis of functionally graded sandwich beams by Navier’s method. Journal of the Faculty of Engineering and Architecture of Gazi University, 36(2), 743–757.
  • [7] Liu, J., He, B., Ye, W., Yang, F., (2021). High performance model for buckling of functionally graded sandwich beams using a new semi-analytical method. Composite Structures, 262(January), 113614.
  • [8] Avcar, M., Hadji, L., Civalek, Ö., (2021). Natural frequency analysis of sigmoid functionally graded sandwich beams in the framework of high order shear deformation theory. Composite Structures, 276(June).
  • [9] Keleshteri, M. M., Jelovica, J., (2022). Beam theory reformulation to implement various boundary conditions for generalized differential quadrature method. Engineering Structures, 252, 113666.
  • [10] Oyekoya, O. O., Mba, D. U., El-Zafrany, A. M., (2009). Buckling and vibration analysis of functionally graded composite structures using the finite element method. Composite Structures, 89(1), 134–142.
  • [11] Alshorbagy, A. E., Eltaher, M. A., Mahmoud, F. F., (2011). Free vibration characteristics of a functionally graded beam by finite element method. Applied Mathematical Modelling, 35(1), 412–425.
  • [12] 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, 12–22.
  • [13] 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, 1–12.
  • [14] Liu, B., Ferreira, A. J. M., Xing, Y. F., Neves, A. M. A., (2016). Analysis of functionally graded sandwich and laminated shells using a layerwise theory and a differential quadrature finite element method. Composite Structures, 136, 546–553.
  • [15] Yarasca, J., Mantari, J. L., Arciniega, R. A., (2016). Hermite-Lagrangian finite element formulation to study functionally graded sandwich beams. Composite Structures, 140, 567–581.
  • [16] Kahya, V., Turan, M., (2017). Finite element model for vibration and buckling of functionally graded beams based on the first-order shear deformation theory. Composites Part B: Engineering, 109, 108–115.
  • [17] Kahya, V., Turan, M., (2018). Vibration and buckling of laminated beams by a multi-layer finite element model. Steel and Composite Structures, 28(4), 415–426.
  • [18] Reddy, J. N., Nampally, P., Srinivasa, A. R., (2020). Nonlinear analysis of functionally graded beams using the dual mesh finite domain method and the finite element method. International Journal of Non-Linear Mechanics, 127(August), 103575.
  • [19] Yaghoobi, M., Sedaghatjo, M., Alizadeh, R., Karkon, M., (2021). An efficient simple element for free vibration and buckling analysis of FG beam. Journal of Engineering Research, 1–25.
  • [20] Koutoati, K., Mohri, F., Daya, E. M., (2021). Finite element approach of axial bending coupling on static and vibration behaviors of functionally graded material sandwich beams. Mechanics of Advanced Materials and Structures, 28(15), 1537–1553.
  • [21] Belarbi, M. O., Houari, M. S. A., Hirane, H., Daikh, A. A., Bordas, S. P. A., (2022). On the finite element analysis of functionally graded sandwich curved beams via a new refined higher order shear deformation theory. Composite Structures, 279(July 2021).
There are 21 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Makaleler
Authors

Muhittin Turan 0000-0002-5703-0580

Mahmut İlter Hacıoğlu 0000-0002-6666-7380

Early Pub Date December 21, 2022
Publication Date December 23, 2022
Published in Issue Year 2022 Volume: 15 Issue: Special Issue I - 4th International Conference on Advanced Engineering Technologies

Cite

APA Turan, M., & Hacıoğlu, M. İ. (2022). Buckling Analysis of Functionally Graded Beams Using the Finite Element Method. Erzincan University Journal of Science and Technology, 15(Special Issue I), 98-109. https://doi.org/10.18185/erzifbed.1199454