TY  - JOUR
T1  - Yüksek mertebe sonlu eleman modeliyle fonksiyonel derecelendirilmiş kirişlerin serbest titreşim ve statik analizi
TT  - Free vibration and static analysis of functionally graded beams with the higher-order finite element model
AU  - Turan, Muhittin
AU  - Hacıoğlu, Mahmut İlter
PY  - 2023
DA  - April
Y2  - 2023
DO  - 10.17714/gumusfenbil.1185301
JF  - Gümüşhane Üniversitesi Fen Bilimleri Dergisi
PB  - Gümüşhane Üniversitesi
WT  - DergiPark
SN  - 2146-538X
SP  - 414
EP  - 431
VL  - 13
IS  - 2
LA  - tr
AB  - 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.
KW  - Fonksiyonel derecelendirilmiş kiriş
KW  - Serbest titreşim analizi
KW  - Statik analiz
KW  - Sonlu eleman yöntemi
KW  - Yüksek mertebeden kayma deformasyonlu kiriş teorisi
N2  - 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.
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CR  - 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
CR  - 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
CR  - 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
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CR  - Turan, M. (2018). Tabakalı kirişlerin statik, serbest titreşim ve burkulma analizleri için bir sonlu eleman modeli.[Doktora Tezi, Karadeniz Teknik Üniversitesi Fen Bilimleri Enstitüsü].
CR  - 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
CR  - 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
CR  - 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
CR  - 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
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CR  - 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
UR  - https://doi.org/10.17714/gumusfenbil.1185301
L1  - https://dergipark.org.tr/tr/download/article-file/2692911
ER  -