Fonksiyonel derecelendirilmiş ortotropik bir kirişin statik ve titreşim davranışlarının incelenmesi

Yıl 2018, Cilt: 20 Sayı: 1, 69 - 82, 17.07.2018

Şeref Doğuşcan Akbaş

https://doi.org/10.25092/baunfbed.343227

Cited By: 3

Öz

Bu çalışmada, fonksiyonel
derecelendirilmiş konsol bir kirişin statik ve serbest titreşim davranışları
ortotropik malzeme modeli kullanılarak incelenmiştir. Fonksiyonel
derecelendirilmiş kirişin incelenmesinde düzlem parçalı sürekli ortam modeli
kullanılmış olup, sonlu elemanlar yöntemi uygulanmıştır. Probleme ait yönetici
denklemleri, virtüel yer değiştirmeler prensibi ile elde edilmiştir. Kirişin
malzeme özellikleri, kiriş yüksekliği boyunca belli bir fonksiyona bağlı olarak
belirlenmiştir. Ele alınan kirişin boyutları, levha modeli olacak biçimde
seçilerek düzlem gerilme problemi uygulanmıştır. Söz konusu problemin, sonlu
elemanlar formülasyonları elde edilip, sonlu eleman çözümü için MATLAB
programında algoritma ve program yazılarak sonuçlar elde edilmiştir. Ele alınan
çalışmada, farklı malzeme dağılımlarının, kirişin statik ve titreşim
davranışına olan etkileri incelenmiştir. Değişik malzeme dağılımlarına göre, en
büyük yer değiştirmeler ve doğal frekanslar elde edilip, yorumlanmıştır.

Anahtar Kelimeler

Fonksiyonel derecelendirilmiş malzeme, düzlem gerilme problemi, sonlu elemanlar yöntemi, statik analiz, titreşim analizi

Investigation of static and vibration behaviors of a functionally graded orthotropic beam

Öz

In this paper, static and vibration behaviors
of a functionally graded orthotropic beam are investigated. In the solution of
the functionally graded beam, plane piecewise solid continua model and finite
element method is used. The governing equations of the problems are obtained by
using the virtual displacement principle. Material properties of functionally graded beam vary across the
height direction. With the dimensions
of the functionally graded beam are assumed as
plane model and the plane stress problem is implemented. In the solution of the finite
element equations, MATLAB program is used. In the study, the effects of the different material distributions on
the static and vibration behaviors of the beam are investigated. The maximum
static deflections and natural frequencies are obtained and discussed for
different material parameters.

Anahtar Kelimeler

Functionally graded materials, plane stress problem, finite element method, static analysis, vibration analysis

Kaynakça

• Huang, G.-Y., Wang, Y.-S. and Yu, S.-Y, A new model for fracture analysis of functionally graded coatings under plane deformation, Mechanics of materials, 37, 507-516, (2005).
• Ding, H.J., Huang, D.J. and Chen, W.Q., Elasticity solutions for plane anisotropic functionally graded beams, International Journal of Solids and Structures, 44, 176-196, (2007).
• Huang, D.J., Ding, H.J. and Chen, W.Q, Analytical solution for functionally graded magneto-electro-elastic plane beams, International Journal of Engineering Science, 45, 467-485, (2007).
• Ke, L.L., Yang, J., Kitipornchai, S. and Wang, Y.S., Frictionless contact analysis of a functionally graded piezoelectric layered half-plane, Smart Materials and Structures, 17, 025003, (2008).
• Zhang, P.W., Zhou, Z.G. and Wu., L.Z., Behaviour of three parallel non-symmetric mode III cracks in a functionally graded material plane, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 222, 2311-2330, (2008).
• Lim, C.W., Qian Y. and Lü., C.F. Two-dimensional elasticity solutions for temperature-dependent in-plane vibration of FGM circular arches, Composite Structures, 90, 323-329, (2009).
• Yang, Y.-H., Wu, L.-Z. and Fang., X.-Q, Non-destructive detection of a circular cavity in a finite functionally graded material layer using anti-plane shear waves, Journal of Nondestructive Evaluation, 29, 233-240, (2010).
• Zhang, H.Z., Zhao, X. H., Zhang, J.Z. and Zhou, Z.G., Random dynamic response of crack in functionally graded materials layer for plane problem, Transactions of Nonferrous Metals Society of China, 22, 198-206, (2012).
• Kocatürk, T. and Akbaş, Ş.D., Post-buckling analysis of Timoshenko beams made of functionally graded material under thermal loading, Structural Engineering and Mechanics, 41, 775-789, (2012).
• Kocatürk, T. and Akbaş Ş.D., Thermal post-buckling analysis of functionally graded beams with temperature-dependent physical properties, Steel and Composite Structures, 15, 481-505, (2013).
• Akbaş, Ş.D. and Kocatürk, T., Post-buckling analysis of functionally graded three-dimensional beams under the influence of temperature, Journal of Thermal Stresses, 36, 1233-1254, (2013).
• Pan, S.-D, Zhou, Z.-G. and Wu, L.-Z, Basic solutions of multiple parallel symmetric mode-III cracks in functionally graded piezoelectric/piezomagnetic material plane, Applied Mathematics and Mechanics, 34,1201-1224, (2013).
• Kubair, D.V., Stress concentration factors and stress-gradients due to circular holes in radially functionally graded panels subjected to anti-plane shear loading, Acta Mechanica, 224, 2845-2862, (2013).
• Akbaş, Ş.D., Free vibration characteristics of edge cracked functionally graded beams by using finite element method, International Journal of Engineering Trends and Technology, 4, 4590-4597, (2013).
• Akbaş, Ş.D., Geometrically nonlinear static analysis of edge cracked Timoshenko beams composed of functionally graded material, Mathematical Problems in Engineering, 2013, (2013).
• Akbaş, Ş.D., On Post-Buckling Behavior of Edge Cracked Functionally Graded Beams Under Axial Loads, International Journal of Structural Stability and Dynamics, 15, 1450065, (2015).
• Akbaş, Ş.D. Wave propagation in edge cracked functionally graded beams under impact force, Journal of Vibration and Control, 22, 2443-2457, (2016).
• Li, S. and Hu, Y., Geometrically Nonlinear Analysis of Simple Plane Frames of Functionally Graded Materials, Sixth International Conference on Nonlinear Mechanics (ICNM-6). DEStech Publications, Inc, (2013).
• Daouadji, T.H., Henni, A.H., Tounsi, A. and El Abbes, A.B., Elasticity solution of a cantilever functionally graded beam, Applied Composite Materials, 20, 1-15, (2013).
• Alibeigloo, A. and Liew, K.M., Free vibration analysis of sandwich cylindrical panel with functionally graded core using three-dimensional theory of elasticity, Composite Structures, 113, 23-30, (2014).
• Çömez, I., Elasticity solution for a functionally graded two-layer beam with simple supported edges, Turkish Journal of Engineering and Environmental Sciences, 38, 373-381, (2016).
• Liu, J., Wang, Y.S., Ke, L.L., Yang, J. and Alam, F., Dynamic instability of an elastic solid sliding against a functionally graded material coated half-plane, International Journal of Mechanical Sciences, 89, 323-331, (2014).
• Akbaş, Ş.D., Post-buckling analysis of axially functionally graded three-dimensional beams, International Journal of Applied Mechanics, 7, 1550047, (2015).
• Yue, Y., Xiaofen Y. and Kaiyu X., Analytical solutions for plane problem of functionally graded magnetoelectric cantilever beam, Applied Mathematics and Mechanics, 36, 955-970, (2015).
• Yuan, F.G. and Hsieh, C.C., Three-dimensional wave propagation in composite cylindrical shells, Composite Structures, 42, 153-167, (1998).
• Akgöz, B. and Civalek, O., Bending analysis of FG microbeams resting on Winklerelastic foundation via strain gradient elasticity, Composite Structures, 134, 294–301, (2015).
• Akbaş, Ş.D.. Static analysis of a functionally graded beam with edge cracks on elastic foundation. In: Proceedings of the 9 th International Fracture Conference, Istanbul, Turkey, pp. 70-80, (2011).
• Akbaş, Ş.D., Free vibration of edge cracked functionally graded microscale beams based on the modified couple stress theory, International Journal of Structural Stability and Dynamics, 17, 1750033, (2017).
• Akbaş, Ş.D., Free vibration and bending of functionally graded beams resting on elastic foundation, Research on Engineering Structures and Materials, 1, (2015).
• Akgoz, B. and Civalek, O., Bending analysis of embedded carbon nanotubes resting on an elastic foundation using strain gradient theory, Acta Astronautica, 119, 1–12, (2016).
• Akbaş, Ş.D., Free vibration of axially functionally graded beams in thermal environment, International Journal of Engineering and Applied Sciences, 6, 37-51, (2014).
• Akbaş, Ş.D., Vibration and Static Analysis of Functionally Graded Porous Plates, Journal of Applied and Computational Mechanics, 3, 199-207, (2017).
• Akbaş, Ş.D., Kirişlerin Geometrik Doğrusal Olmayan Davranışlarının 3 Boyutlu Sürekli Ortam Modeli ile İncelenmesi, Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 17, 28-37, (2016).
• Akbaş, Ş.D., Stability of A Non-Homogenous Porous Plate by Using Generalized Differantial Quadrature Method, International Journal of Engineering and Applied Sciences, 9, 147-155, (2017).
• Akbaş, Ş.D., Post-buckling analysis of edge cracked columns under axial compression loads, International Journal of Applied Mechanics, 8, 1650086, (2016).
• Civalek, O. and Demir C.A., simple mathematical model of microtubules surroundedby an elastic matrix by nonlocal finite element method, Applied Mathematicsand Computation, 289, 335–352, (2016).
• Akbaş, Ş.D., Thermal Effects on the Vibration of Functionally Graded Deep Beams with Porosity, International Journal of Applied Mechanics, 9, 1750076, (2017).
• Akbaş, Ş.D., Post-buckling responses of functionally graded beams with porosities, Steel and Composıte Structures, 24, 481-579-589, (2017).
• Ansari, R., Gholami, R. and Sahmani, S., Size-dependent vibration of functionallygraded curved microbeams based on the modified strain gradient elasticity theory. Archive of Applied Mechanics, 83, 1439–1449, (2013).
• Kocatürk, T. and Akbas, Ş.D., Geometrically non-linear static analysis of a simply supported beam made of hyperelastic material, Structural Engineering and Mechanics, 35, 677-697, (2010).
• Eltaher, M.A., Khater, M.E. and Emam, S.A., A review on nonlocal elastic models for bending, buckling, vibrations, and wave propagation of nanoscale beams, Applied Mathematical Modelling, 40, 4109-4128, (2016).