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Yüksek mertebe sonlu eleman modeliyle fonksiyonel derecelendirilmiş kirişlerin serbest titreşim ve statik analizi

Year 2023, Volume: 13 Issue: 2, 414 - 431, 15.04.2023

Muhittin Turan Mahmut İlter Hacıoğlu

https://doi.org/10.17714/gumusfenbil.1185301

Abstract

Bu çalışmada, fonksiyonel derecelendirilmiş (FD) kirişlerin yüksek mertebeden kayma deformasyonlu kiriş teorisine dayalı sonlu eleman yöntemiyle serbest titreşim ve statik analizleri incelenmiştir. Sonlu elemanlar yöntemi için 5 düğümlü ve 16 serbestlikli bir sonlu eleman önerilmiştir. FD kirişin malzeme özelliği kiriş kalınlığı boyunca belli bir kuvvet kuralı fonksiyona bağlı olarak değişmektedir. Lagrange eşitliği ile denge denklemleri türetilmiştir. Farklı kuvvet fonksiyonu üst indisine (p), farklı sınır şartlarına ve farklı narinliklere (L/h) göre FD kirişin boyutsuz doğal frekansları, boyutsuz yer değiştirmeleri, boyutsuz normal ve kayma gerilmeleri elde edilmiştir. Çalışmadan elde edilen sonuçlar literatür ile karşılaştırılmış ve önerilen sonlu elemanın FD kirişler için oldukça uyumlu sonuçlar verdiği görülmüştür.

Keywords

Fonksiyonel derecelendirilmiş kiriş Serbest titreşim analizi Statik analiz Sonlu eleman yöntemi Yüksek mertebeden kayma deformasyonlu kiriş teorisi

References

  • Aboudi, J., Pindera, M. J., & Arnold, S. M. (1999). Higher-order theory for functionally graded materials. Composites Part B: Engineering, 30(8), 777–832. https://doi.org/10.1016/S1359-8368(99)00053-0
  • Akbaş, Ş. D. (2017). Fonksiyonel derecelendirilmiş ortotropik bir kirişin statik ve titreşim davranışlarının incelenmesi. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 20(1), 1–14. https://doi.org/10.25092/baunfbed.343227
  • Akbaş, Ş. D. (2021). Forced vibration responses of axially functionally graded beams by using Ritz method. Journal of Applied and Computational Mechanics, 7(1), 109–115. https://doi.org/10.22055/jacm.2020.34865.2491
  • 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. https://doi.org/10.1016/j.apm.2010.07.006
  • 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). https://doi.org/10.1016/j.compstruct.2021.114564
  • Aydogdu, M., & Taskin, V. (2007). Free vibration analysis of functionally graded beams with simply supported edges. Materials and Design, 28(5), 1651–1656. https://doi.org/10.1016/j.matdes.2006.02.007
  • 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(September 2021). https://doi.org/10.1016/j.compstruct.2021.114715
  • Chakraborty, A., Gopalakrishnan, S., & Reddy, J. N. (2003). A new beam finite element for the analysis of functionally graded materials. International Journal of Mechanical Sciences, 45(3), 519–539. https://doi.org/10.1016/S0020-7403(03)00058-4
  • Filippi, M., Carrera, E., & Zenkour, A. M. (2015). Static analyses of FGM beams by various theories and finite elements. Composites Part B: Engineering, 72, 1–9. https://doi.org/10.1016/j.compositesb.2014.12.004
  • Jin, C., & Wang, X. (2015). Accurate free vibration analysis of Euler functionally graded beams by the weak form quadrature element method. Composite Structures, 125, 41–50. https://doi.org/10.1016/j.compstruct.2015.01.039
  • 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. https://doi.org/10.1016/j.compositesb.2016.10.039
  • 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. https://doi.org/10.12989/scs.2018.28.4.415
  • Koutoati, K., Mohri, F., Daya, E. M., & Carrera, E. (2021). A finite element approach for the static and vibration analyses of functionally graded material viscoelastic sandwich beams with nonlinear material behavior. Composite Structures, 274(February), 114315. https://doi.org/10.1016/j.compstruct.2021.114315
  • Li, W., Ma, H., & Gao, W. (2019). A higher-order shear deformable mixed beam element model for accurate analysis of functionally graded sandwich beams. Composite Structures, 221(March), 110830. https://doi.org/10.1016/j.compstruct.2019.04.002
  • Nguyen, T. K., Vo, T. P., & Thai, H. T. (2013). Static and free vibration of axially loaded functionally graded beams based on the first-order shear deformation theory. Composites Part B: Engineering, 55, 147–157. https://doi.org/10.1016/j.compositesb.2013.06.011
  • 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. https://doi.org/10.1016/j.compstruct.2008.07.022
  • 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. https://doi.org/10.1016/j.ijnonlinmec.2020.103575
  • Şimşek, M. (2010). Fundamental frequency analysis of functionally graded beams by using different higher-order beam theories. Nuclear Engineering and Design, 240(4), 697–705. https://doi.org/10.1016/j.nucengdes.2009.12.013
  • Thai, H. T., & Vo, T. P. (2012). Bending and free vibration of functionally graded beams using various higher-order shear deformation beam theories. International Journal of Mechanical Sciences, 62(1), 57–66. https://doi.org/10.1016/j.ijmecsci.2012.05.014
  • Turan, M. (2018). Tabakalı kirişlerin statik, serbest titreşim ve burkulma analizleri için bir sonlu eleman modeli.[Doktora Tezi, Karadeniz Teknik Üniversitesi Fen Bilimleri Enstitüsü].
  • Turan, M., & Kahya, V. (2018). Fonksiyonel derecelendirilmiş kirişlerin Navier methodu ile serbest titreşim analizi. Karadeniz Fen Bilimleri Dergisi, 8(2), 119–130. https://doi.org/10.31466/kfbd.453833
  • 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. https://doi.org/10.17341/gazimmfd.599928
  • Turan, M. (2022). Bending analysis of two-directional functionally graded beams using trigonometric series functions. Archive of Applied Mechanics, 92(6), 1841–1858. https://doi.org/10.1007/s00419-022-02152-y
  • 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. https://doi.org/10.1016/j.engstruct.2014.01.029
  • Vo, T. P., Thai, H. T., Nguyen, T. K., Inam, F., & Lee, J. (2015a). A quasi-3D theory for vibration and buckling of functionally graded sandwich beams. Composite Structures, 119, 1–12. https://doi.org/10.1016/j.compstruct.2014.08.006
  • Vo, T. P., Thai, H. T., Nguyen, T. K., Inam, F., & Lee, J. (2015b). Static behaviour of functionally graded sandwich beams using a quasi-3D theory. Composites Part B: Engineering, 68, 59–74. https://doi.org/10.1016/j.compositesb.2014.08.030
  • 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. https://doi.org/10.1016/j.compstruct.2016.01.015
  • Yildirim, S. (2022). Free vibration of axially or transversely graded beams using finite-element and artificial intelligence. Alexandria Engineering Journal, 61(3), 2220–2229. https://doi.org/10.1016/j.aej.2021.07.004

Free vibration and static analysis of functionally graded beams with the higher-order finite element model

Year 2023, Volume: 13 Issue: 2, 414 - 431, 15.04.2023

Muhittin Turan Mahmut İlter Hacıoğlu

https://doi.org/10.17714/gumusfenbil.1185301

Abstract

In this study, free vibration and static analysis of functionally graded (FG) beams with the finite element method based on high-order shear deformation beam theory are investigated. A finite element with 5 nodes and 16 degrees of freedom is proposed for the finite element method. The material property of the FG beam changes depending on a specific power-law function along the beam thickness. Equilibrium equations are derived from the Lagrange's equation. Dimensionless natural frequencies, dimensionless displacements, and dimensionless normal and shear stresses of FG beam were obtained according to different power-law indexes (p), various boundary conditions, and various slenderness (L/h). The results obtained from the study were compared with the literature and it was seen that the proposed finite element gave very good results for FG beams. It is concluded that the proposed high-order shear deformation beam element can be used to solve such problems. With the power-law index value increase, the dimensionless natural frequencies decrease while the dimensionless maximum displacements increase.

Keywords

Functionally graded beam Free vibration analysis Static analysis Finite element method Higher-order shear deformation beam theory

References

  • Aboudi, J., Pindera, M. J., & Arnold, S. M. (1999). Higher-order theory for functionally graded materials. Composites Part B: Engineering, 30(8), 777–832. https://doi.org/10.1016/S1359-8368(99)00053-0
  • Akbaş, Ş. D. (2017). Fonksiyonel derecelendirilmiş ortotropik bir kirişin statik ve titreşim davranışlarının incelenmesi. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 20(1), 1–14. https://doi.org/10.25092/baunfbed.343227
  • Akbaş, Ş. D. (2021). Forced vibration responses of axially functionally graded beams by using Ritz method. Journal of Applied and Computational Mechanics, 7(1), 109–115. https://doi.org/10.22055/jacm.2020.34865.2491
  • 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. https://doi.org/10.1016/j.apm.2010.07.006
  • 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). https://doi.org/10.1016/j.compstruct.2021.114564
  • Aydogdu, M., & Taskin, V. (2007). Free vibration analysis of functionally graded beams with simply supported edges. Materials and Design, 28(5), 1651–1656. https://doi.org/10.1016/j.matdes.2006.02.007
  • 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(September 2021). https://doi.org/10.1016/j.compstruct.2021.114715
  • Chakraborty, A., Gopalakrishnan, S., & Reddy, J. N. (2003). A new beam finite element for the analysis of functionally graded materials. International Journal of Mechanical Sciences, 45(3), 519–539. https://doi.org/10.1016/S0020-7403(03)00058-4
  • Filippi, M., Carrera, E., & Zenkour, A. M. (2015). Static analyses of FGM beams by various theories and finite elements. Composites Part B: Engineering, 72, 1–9. https://doi.org/10.1016/j.compositesb.2014.12.004
  • Jin, C., & Wang, X. (2015). Accurate free vibration analysis of Euler functionally graded beams by the weak form quadrature element method. Composite Structures, 125, 41–50. https://doi.org/10.1016/j.compstruct.2015.01.039
  • 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. https://doi.org/10.1016/j.compositesb.2016.10.039
  • 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. https://doi.org/10.12989/scs.2018.28.4.415
  • Koutoati, K., Mohri, F., Daya, E. M., & Carrera, E. (2021). A finite element approach for the static and vibration analyses of functionally graded material viscoelastic sandwich beams with nonlinear material behavior. Composite Structures, 274(February), 114315. https://doi.org/10.1016/j.compstruct.2021.114315
  • Li, W., Ma, H., & Gao, W. (2019). A higher-order shear deformable mixed beam element model for accurate analysis of functionally graded sandwich beams. Composite Structures, 221(March), 110830. https://doi.org/10.1016/j.compstruct.2019.04.002
  • Nguyen, T. K., Vo, T. P., & Thai, H. T. (2013). Static and free vibration of axially loaded functionally graded beams based on the first-order shear deformation theory. Composites Part B: Engineering, 55, 147–157. https://doi.org/10.1016/j.compositesb.2013.06.011
  • 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. https://doi.org/10.1016/j.compstruct.2008.07.022
  • 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. https://doi.org/10.1016/j.ijnonlinmec.2020.103575
  • Şimşek, M. (2010). Fundamental frequency analysis of functionally graded beams by using different higher-order beam theories. Nuclear Engineering and Design, 240(4), 697–705. https://doi.org/10.1016/j.nucengdes.2009.12.013
  • Thai, H. T., & Vo, T. P. (2012). Bending and free vibration of functionally graded beams using various higher-order shear deformation beam theories. International Journal of Mechanical Sciences, 62(1), 57–66. https://doi.org/10.1016/j.ijmecsci.2012.05.014
  • Turan, M. (2018). Tabakalı kirişlerin statik, serbest titreşim ve burkulma analizleri için bir sonlu eleman modeli.[Doktora Tezi, Karadeniz Teknik Üniversitesi Fen Bilimleri Enstitüsü].
  • Turan, M., & Kahya, V. (2018). Fonksiyonel derecelendirilmiş kirişlerin Navier methodu ile serbest titreşim analizi. Karadeniz Fen Bilimleri Dergisi, 8(2), 119–130. https://doi.org/10.31466/kfbd.453833
  • 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. https://doi.org/10.17341/gazimmfd.599928
  • Turan, M. (2022). Bending analysis of two-directional functionally graded beams using trigonometric series functions. Archive of Applied Mechanics, 92(6), 1841–1858. https://doi.org/10.1007/s00419-022-02152-y
  • 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. https://doi.org/10.1016/j.engstruct.2014.01.029
  • Vo, T. P., Thai, H. T., Nguyen, T. K., Inam, F., & Lee, J. (2015a). A quasi-3D theory for vibration and buckling of functionally graded sandwich beams. Composite Structures, 119, 1–12. https://doi.org/10.1016/j.compstruct.2014.08.006
  • Vo, T. P., Thai, H. T., Nguyen, T. K., Inam, F., & Lee, J. (2015b). Static behaviour of functionally graded sandwich beams using a quasi-3D theory. Composites Part B: Engineering, 68, 59–74. https://doi.org/10.1016/j.compositesb.2014.08.030
  • 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. https://doi.org/10.1016/j.compstruct.2016.01.015
  • Yildirim, S. (2022). Free vibration of axially or transversely graded beams using finite-element and artificial intelligence. Alexandria Engineering Journal, 61(3), 2220–2229. https://doi.org/10.1016/j.aej.2021.07.004
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Details

Primary Language Turkish
Subjects Engineering
Journal Section Articles
Authors

Muhittin Turan 0000-0002-5703-0580

Mahmut İlter Hacıoğlu 0000-0002-6666-7380

Publication Date April 15, 2023
Submission Date October 6, 2022
Acceptance Date March 17, 2023
Published in Issue Year 2023 Volume: 13 Issue: 2

Cite

APA Turan, M., & Hacıoğlu, M. İ. (2023). Yüksek mertebe sonlu eleman modeliyle fonksiyonel derecelendirilmiş kirişlerin serbest titreşim ve statik analizi. Gümüşhane Üniversitesi Fen Bilimleri Dergisi, 13(2), 414-431. https://doi.org/10.17714/gumusfenbil.1185301
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