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FONKSİYONEL DERECELENDİRİLMİŞ GÖZENEKLİ KİRİŞLERİN SONLU ELEMANLAR YÖNTEMİYLE STATİK ANALİZİ

Year 2022, , 1362 - 1374, 30.12.2022
https://doi.org/10.21923/jesd.1134356

Abstract

Bu çalışmada, trigonometrik kayma deformasyonlu kiriş teorisine göre fonksiyonel derecelendirilmiş gözenekli kirişlerin (FDGB) sonlu elemanlar yöntemiyle statik analizi incelenmiştir. Sonlu eleman yöntemi için üç düğüm noktalı 12 serbestlik dereceli yüksek mertebe sonlu kiriş elemanı önerilmiştir. Denge denklemleri Lagrange prensibi kullanılarak elde edilmiştir. Kiriş bileşenlerinin hacim içerisindeki değişimleri, bir kuvvet fonksiyonu ile tanımlanmıştır. Kirişin çeşitli mesnet şartlarına, hacimsel değişim üsteline (k), gözeneklilik katsayısına (e) ve narinlik oranlarına (L/h) göre boyutsuz yer değiştirme değerleri, boyutsuz normal ve kayma gerilme değerleri elde edilmiştir. Önerilen yüksek mertebe sonlu kiriş elemanının doğruluğu araştırılmıştır. Sayısal sonuçlar literatürdeki mevcut çalışmaların sonuçları ile karşılaştırılmış ve son derece uyumlu oldukları görülmüştür.

References

  • Vo, T. P., Thai, H. T., Nguyen, T. K., Inam, F., Lee, J., 2015. Static behaviour of functionally graded sandwich beams using a quasi-3D theory. Composites Part B: Engineering, 68, 59–74.
  • Turan, M., 2018. Tabakalı kirişlerin statik, serbest titreşim ve burkulma analizleri için bir sonlu eleman modeli. Doktora Tezi, Karadeniz Teknik Üniversitesi Fen Bilimleri Enstitüsü, Türkiye.
  • 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.
  • Kahya, V., Turan, M., 2018. Vibration and stability analysis of functionally graded sandwich beams by a multi-layer finite element. Composites Part B: Engineering, 146, 198–212.
  • Chen, D., Yang, J., Kitipornchai, S., 2015. Elastic buckling and static bending of shear deformable functionally graded porous beam. Composite Structures, 133, 54–61.
  • Wattanasakulpong, N., Chaikittiratana, A., 2015. Flexural vibration of imperfect functionally graded beams based on Timoshenko beam theory: Chebyshev collocation method. Meccanica, 50(5), 1331–1342.
  • Kitipornchai, S., Chen, D., Yang, J., 2017. Free vibration and elastic buckling of functionally graded porous beams reinforced by graphene platelets. Materials and Design, 116, 656–665.
  • Gao, K., Li, R., Yang, J., 2019. Dynamic characteristics of functionally graded porous beams with interval material properties. Engineering Structures, 197(July), 109441.
  • Ebrahimi, F., Ghasemi, F., Salari, E., 2016. Investigating thermal effects on vibration behavior of temperature-dependent compositionally graded Euler beams with porosities. Meccanica, 51(1), 223–249.
  • Zouatnia, N., Hadji, L., Kassoul, A., 2017. An analytical solution for bending and vibration responses of functionally graded beams with porosities. Wind and Structures, 25(4), 329-342.
  • Hadji, L., Zouatnia, N., Bernard, F., 2019. An analytical solution for bending and free vibration responses of functionally graded beams with porosities: Effect of the micromechanical models. Structural Engineering and Mechanics, 69(2), 231–241.
  • Taşkin, V., Demirhan, P. A., 2020. Fonksiyonel derecelendirilmiş gözenekli kirişlerin serbest titreşim analizi̇. Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi B - Teorik Bilimler, 8(1), 49–60.
  • Derikvand, M., Farhatnia, F., Hodges, D. H., 2021. Functionally graded thick sandwich beams with porous core: Buckling analysis via differential transform method. Mechanics Based Design of Structures and Machines, 0(0), 1–28.
  • Nguyen, N. D., Nguyen, T. N., Nguyen, T. K., Vo, T. P., 2022. A new two-variable shear deformation theory for bending, free vibration and buckling analysis of functionally graded porous beams. Composite Structures, 282, 115095.
  • Sayyad, A. S., Avhad, P. V., Hadji, L., 2022. On the static deformation and frequency analysis of functionally graded porous circular beams. Forces in Mechanics, 7, 100093.
  • Chami, G. M. B., Kahil, A., Hadji, L., 2022. Influence of porosity on the fundamental natural frequencies of FG sandwich beams. Materials Today: Proceedings, 53, 107–112.
  • Fouda, N., El-midany, T., Sadoun, A. M., 2017. Bending, buckling and vibration of a functionally graded porous beam using finite elements. Journal of Applied and Computational Mechanics, 3(4), 274–282.
  • Akbaş, Ş. D., 2018. Forced vibration analysis of functionally graded porous deep beams. Composite Structures, 186(December 2017), 293–302.
  • Hamed, M. A., Sadoun, A. M., Eltaher, M. A., 2019. Effects of porosity models on static behavior of size dependent functionally graded beam. Structural Engineering and Mechanics, 71(1), 89–98.
  • 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), 1012–1029.
  • Alnujaie, A., Akbas, S. D., Eltaher, M. A., Assie, A. E., 2021. Damped forced vibration analysis of layered functionally graded thick beams with porosity. Smart Structures and Systems, 27(4), 679–689.

STATIC ANALYSIS OF FUNCTIONALLY GRADED POROUS BEAMS WITH FINITE ELEMENT METHOD

Year 2022, , 1362 - 1374, 30.12.2022
https://doi.org/10.21923/jesd.1134356

Abstract

In this study, the static analysis of functionally graded porous beams (FDGB) using the finite element method according to the trigonometric shear deformation beam theory was investigated. A high-order finite beam element with three nodes and 12 degrees of freedom is proposed for the finite element method. The governing equations are obtained using Lagrange's principle. The variation of the beam components in the volume is defined by a power-law rule. Dimensionless deflection values and dimensionless normal and shear stress values were obtained according to various boundary conditions, power-law exponent (k), porosity coefficient (e), and slenderness ratio (L/h) of the beam. The accuracy of the proposed higher-order beam element has been investigated. Numerical results are compared with the available literature, and a good agreement has been shown between the results.

References

  • Vo, T. P., Thai, H. T., Nguyen, T. K., Inam, F., Lee, J., 2015. Static behaviour of functionally graded sandwich beams using a quasi-3D theory. Composites Part B: Engineering, 68, 59–74.
  • Turan, M., 2018. Tabakalı kirişlerin statik, serbest titreşim ve burkulma analizleri için bir sonlu eleman modeli. Doktora Tezi, Karadeniz Teknik Üniversitesi Fen Bilimleri Enstitüsü, Türkiye.
  • 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.
  • Kahya, V., Turan, M., 2018. Vibration and stability analysis of functionally graded sandwich beams by a multi-layer finite element. Composites Part B: Engineering, 146, 198–212.
  • Chen, D., Yang, J., Kitipornchai, S., 2015. Elastic buckling and static bending of shear deformable functionally graded porous beam. Composite Structures, 133, 54–61.
  • Wattanasakulpong, N., Chaikittiratana, A., 2015. Flexural vibration of imperfect functionally graded beams based on Timoshenko beam theory: Chebyshev collocation method. Meccanica, 50(5), 1331–1342.
  • Kitipornchai, S., Chen, D., Yang, J., 2017. Free vibration and elastic buckling of functionally graded porous beams reinforced by graphene platelets. Materials and Design, 116, 656–665.
  • Gao, K., Li, R., Yang, J., 2019. Dynamic characteristics of functionally graded porous beams with interval material properties. Engineering Structures, 197(July), 109441.
  • Ebrahimi, F., Ghasemi, F., Salari, E., 2016. Investigating thermal effects on vibration behavior of temperature-dependent compositionally graded Euler beams with porosities. Meccanica, 51(1), 223–249.
  • Zouatnia, N., Hadji, L., Kassoul, A., 2017. An analytical solution for bending and vibration responses of functionally graded beams with porosities. Wind and Structures, 25(4), 329-342.
  • Hadji, L., Zouatnia, N., Bernard, F., 2019. An analytical solution for bending and free vibration responses of functionally graded beams with porosities: Effect of the micromechanical models. Structural Engineering and Mechanics, 69(2), 231–241.
  • Taşkin, V., Demirhan, P. A., 2020. Fonksiyonel derecelendirilmiş gözenekli kirişlerin serbest titreşim analizi̇. Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi B - Teorik Bilimler, 8(1), 49–60.
  • Derikvand, M., Farhatnia, F., Hodges, D. H., 2021. Functionally graded thick sandwich beams with porous core: Buckling analysis via differential transform method. Mechanics Based Design of Structures and Machines, 0(0), 1–28.
  • Nguyen, N. D., Nguyen, T. N., Nguyen, T. K., Vo, T. P., 2022. A new two-variable shear deformation theory for bending, free vibration and buckling analysis of functionally graded porous beams. Composite Structures, 282, 115095.
  • Sayyad, A. S., Avhad, P. V., Hadji, L., 2022. On the static deformation and frequency analysis of functionally graded porous circular beams. Forces in Mechanics, 7, 100093.
  • Chami, G. M. B., Kahil, A., Hadji, L., 2022. Influence of porosity on the fundamental natural frequencies of FG sandwich beams. Materials Today: Proceedings, 53, 107–112.
  • Fouda, N., El-midany, T., Sadoun, A. M., 2017. Bending, buckling and vibration of a functionally graded porous beam using finite elements. Journal of Applied and Computational Mechanics, 3(4), 274–282.
  • Akbaş, Ş. D., 2018. Forced vibration analysis of functionally graded porous deep beams. Composite Structures, 186(December 2017), 293–302.
  • Hamed, M. A., Sadoun, A. M., Eltaher, M. A., 2019. Effects of porosity models on static behavior of size dependent functionally graded beam. Structural Engineering and Mechanics, 71(1), 89–98.
  • 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), 1012–1029.
  • Alnujaie, A., Akbas, S. D., Eltaher, M. A., Assie, A. E., 2021. Damped forced vibration analysis of layered functionally graded thick beams with porosity. Smart Structures and Systems, 27(4), 679–689.
There are 21 citations in total.

Details

Primary Language Turkish
Subjects Civil Engineering
Journal Section Research Articles
Authors

Muhittin Turan 0000-0002-5703-0580

Publication Date December 30, 2022
Submission Date June 22, 2022
Acceptance Date August 19, 2022
Published in Issue Year 2022

Cite

APA Turan, M. (2022). FONKSİYONEL DERECELENDİRİLMİŞ GÖZENEKLİ KİRİŞLERİN SONLU ELEMANLAR YÖNTEMİYLE STATİK ANALİZİ. Mühendislik Bilimleri Ve Tasarım Dergisi, 10(4), 1362-1374. https://doi.org/10.21923/jesd.1134356