Emrah MADENCİ

39442

Fonksiyonel Derecelendirilmiş Malzeme Plakların Statik Analizinde Mikro-Mekanik Modellerin Katkısı

Yeni nesil mühendislik malzemelerinden biri olarak bilinen fonksiyonel derecelendirilmiş malzemeler (FDM), tabakalı yapılarda ortaya çıkan arayüz problemlerini kaldırarak modern mühendislik uygulamalarında yüksek mukavemet ve ısıl direnç sağlar. Tipik FDM'nin karakteristik özellikleri, yüksek eğilme-gerilme bağlantısı ve bileşen malzemelerin hacim oranının kademeli olarak değişmesi gibi mekanik özelliklerinden dolayı termal dirençtir. Bu çalışmada; FDM plakların malzeme özelliklerini belirlemek için kullanılan "Voigt, Reuss, Tamura, yerel temsili hacim elemanı (LRVE) ve Mori-Tanaka" gibi çeşitli mikro-mekanik modellerin kalınlık koordinatı boyunca malzeme özelliği değişen FDM plakların eğilme davranışına tepkisi üzerindeki etkisi analitik çözüm ile araştırılmıştır. FDM plak elemanının kinematik bağıntıları için birinci dereceden kayma deformasyonu plak teorisi kullanılmış ve virtüel yer değiştirme ilkesinin yardımıyla alan denklemleri elde edilmiştir. Basit mesnetli FDM plakların analitik çözümü için Navier yöntemi kullanıldı. Her bir mikro-mekanik modelden elde edilen sonuçlar literatürde bulunan referans çözümler ile karşılaştırıldı ve uyum içinde oldukları görüldü. Elde edilen sonuçlara göre hacim oranı indeksinin yer değiştirme konusunda modeller arasında farklılık ortaya koyduğu görülmüştür.
Anahtar Kelimeler:

FGM Plak, Mikro-mekanik model, Birinci mertebe kayma deformasyon teorisi, Eğilme.

Contribution of Micro-Mechanical Models to Static Analysis of Functionally Graded Material Plates

The Functionally graded materials (FGM) which are known one of the next generation of engineering materials, renovate interface problems due to graded structures and provide high strength and thermal resistance in modern engineering applications. The characteristic properties of typical FGM are high bending-stretching coupling and thermal resistance due to their mechanical properties such as the volume fraction of constituent materials changes gradually. In this study; the effect of various micro-mechanical models such as "Voigt, Reuss, Tamura, LRVE and Mori-Tanaka" on the response of FGM plates to the bending behavior of FGM plates, which are used to determine the material properties of FGM plates with varying properties throughout the thickness, have been analyzed by analytical solution. First order shear deformation plate theory was used for the kinematic relations of the FGM plate element and the governing equations were obtained with the help of the virtual displacement principle. Navier method was used for the analytical solution of the simple-supported FGM plate. The results obtained from each micromechanical model were compared with the reference solutions found in the literature and it was found that they were in good agreement. According to the results, it was seen that the volume fraction index revealed a difference between models on displacement.
Keywords:

FGM plates, Micro mechanical models, First order shear deformation theory, Flexure,

PDF

___

  • E. Madenci, A refined functional and mixed formulation to static analyses of fgm beams, Structural Engineering and Mechanics, An Int’l Journal. 69 (2019) 427-437.
  • S. Kumar, Development of Functionally Graded Materials by Ultrasonic Consolidation, CIRP Journal of Manufacturing Science and Technology. 3 (2010) 85-87. doi:https://doi.org/10.1016/j.cirpj.2010.07.006.
  • L. Hadji, M. Meziane, Z. Abdelhak, T.H. Daouadji, E.A. Bedia, Static and dynamic behavior of FGM plate using a new first shear deformation plate theory, Structural engineering and mechanics: An international journal. 57 (2016) 127-140.
  • A.A. Bousahla, S. Benyoucef, A. Tounsi, S.R. Mahmoud, On thermal stability of plates with functionally graded coefficient of thermal expansion, Structural Engineering and Mechanics, An Int’l Journal. 60 (2016) 313-335.
  • L. Gemi, M. Kara, A. Avci, Low velocity impact response of prestressed functionally graded hybrid pipes, Composites Part B: Engineering. 106 (2016) 154-163.
  • M. Rabhi, K.H. Benrahou, A. Kaci, M.S.A. Houari, F. Bourada, A.A. Bousahla, A. Tounsi, E.A.A. Bedia, S.R. Mahmoud, A. Tounsi, A new innovative 3-unknowns HSDT for buckling and free vibration of exponentially graded sandwich plates resting on elastic foundations under various boundary conditions, Geomechanics and Engineering. 22 (2020) 119.
  • M. Guellil, H. Saidi, F. Bourada, A.A. Bousahla, A. Tounsi, M.M. Al-Zahrani, M. Hussain, S.R. Mahmoud, Influences of porosity distributions and boundary conditions on mechanical bending response of functionally graded plates resting on Pasternak foundation, Steel and Composite Structures. 38 (2021) 1.
  • T. Cuong-Le, K.D. Nguyen, N. Nguyen-Trong, S. Khatir, H. Nguyen-Xuan, M. Abdel-Wahab, A three-dimensional solution for free vibration and buckling of annular plate, conical, cylinder and cylindrical shell of FG porous-cellular materials using IGA, Composite Structures. 259 (2021) 113216. doi:https://doi.org/10.1016/j.compstruct.2020.113216.
  • H. Berghouti, E.A. Adda Bedia, A. Benkhedda, A. Tounsi, Vibration analysis of nonlocal porous nanobeams made of functionally graded material, Advances in nano research. 7 (2019) 351-364.
  • M. Uyaner, A. Yar, Nano Elyaf Takviyeli Nanokompozit Üretimi ve Karakterizasyonu, Necmettin Erbakan Üniversitesi Fen ve Mühendislik Bilimleri Dergisi. 1 (t.y.) 10-19.
  • F. Salah, Investigation of thermal buckling properties of ceramic-metal FGM sandwich plates using 2D integral plate model, Steel and Composite Structures, An International Journal. 33 (2019) 805-822.
  • T.H. Daouadji, R. Benferhat, Bending analysis of an imperfect FGM plates under hygro-thermo-mechanical loading with analytical validation, Advances in materials Research. 5 (2016) 035.
  • R. Benferhat, T.H. Daouadji, B. Adim, A novel higher order shear deformation theory based on the neutral surface concept of FGM plate under transverse load, Advances in Materials Research. 5 (2016) 107.
  • R.A. Atmane, N. Mahmoudi, R. Bennai, Investigation on the dynamic response of porous FGM beams resting on variable foundation using a new higher order shear deformation theory, Steel and Composite Structures, An International Journal. 39 (2021) 95-107.
  • A. Chikh, A. Bakora, H. Heireche, M.S.A. Houari, A. Tounsi, E.A. Bedia, Thermo-mechanical postbuckling of symmetric S-FGM plates resting on Pasternak elastic foundations using hyperbolic shear deformation theory, Structural engineering and mechanics: An international journal. 57 (2016) 617-639.
  • A. Attia, A.A. Bousahla, A. Tounsi, S.R. Mahmoud, A.S. Alwabli, A refined four variable plate theory for thermoelastic analysis of FGM plates resting on variable elastic foundations, Structural engineering and mechanics: An international journal. 65 (2018) 453-464.
  • M. Yousfi, H.A. Atmane, M. Meradjah, A. Tounsi, R. Bennai, Free vibration of FGM plates with porosity by a shear deformation theory with four variables, Structural Engineering and Mechanics, An Int’l Journal. 66 (2018) 353-368.
  • M. Aydogdu, Conditions for functionally graded plates to remain flat under in-plane loads by classical plate theory, Composite Structures. 82 (2008) 155-157. doi:https://doi.org/10.1016/j.compstruct.2006.10.004.
  • J. Yang, H.-S. Shen, Dynamic response of initially stressed functionally graded rectangular thin plates, Composite Structures. 54 (2001) 497-508. doi:https://doi.org/10.1016/S0263-8223(01)00122-2.
  • M. Memar Ardestani, B. Soltani, Sh. Shams, Analysis of functionally graded stiffened plates based on FSDT utilizing reproducing kernel particle method, Composite Structures. 112 (2014) 231-240. doi:https://doi.org/10.1016/j.compstruct.2014.01.032.
  • C.-S. Chen, Nonlinear vibration of a shear deformable functionally graded plate, Composite Structures. 68 (2005) 295-302. doi:https://doi.org/10.1016/j.compstruct.2004.03.022.
  • A.M. Zenkour, Generalized shear deformation theory for bending analysis of functionally graded plates, Applied Mathematical Modelling. 30 (2006) 67-84. doi:https://doi.org/10.1016/j.apm.2005.03.009.
  • H.-T. Thai, S.-E. Kim, A simple higher-order shear deformation theory for bending and free vibration analysis of functionally graded plates, Composite Structures. 96 (2013) 165-173. doi:https://doi.org/10.1016/j.compstruct.2012.08.025.
  • L. Dozio, Exact free vibration analysis of Lévy FGM plates with higher-order shear and normal deformation theories, Composite Structures. 111 (2014) 415-425. doi:https://doi.org/10.1016/j.compstruct.2014.01.014.
  • M. Abualnour, M.S.A. Houari, A. Tounsi, E.A.A. Bedia, S.R. Mahmoud, A novel quasi-3D trigonometric plate theory for free vibration analysis of advanced composite plates, Composite Structures. 184 (2018) 688-697. doi:https://doi.org/10.1016/j.compstruct.2017.10.047.
  • C.-L. Thanh, L. V Tran, T.Q. Bui, H.X. Nguyen, M. Abdel-Wahab, Isogeometric analysis for size-dependent nonlinear thermal stability of porous FG microplates, Composite Structures. 221 (2019) 110838. doi:https://doi.org/10.1016/j.compstruct.2019.04.010.
  • K. Xu, Y. Yuan, M. Li, Buckling behavior of functionally graded porous plates integrated with laminated composite faces sheets, Steel and Composite Structures, An International Journal. 32 (2019) 633-642.
  • A. Tounsi, M.S.A. Houari, A. Bessaim, A new 3-unknowns non-polynomial plate theory for buckling and vibration of functionally graded sandwich plate, Structural Engineering and Mechanics, An Int’l Journal. 60 (2016) 547-565.
  • J.N. Reddy, Analysis of functionally graded plates, International Journal for Numerical Methods in Engineering. 47 (2000) 663-684. doi:https://doi.org/10.1002/(SICI)1097-0207(20000110/30)47:1/3<663::AID-NME787>3.0.CO;2-8.
  • X. Zhao, Y.Y. Lee, K.M. Liew, Mechanical and thermal buckling analysis of functionally graded plates, Composite Structures. 90 (2009) 161-171. doi:https://doi.org/10.1016/j.compstruct.2009.03.005.
  • E. Madenci, Ş. Gülcü, Optimization of flexure stiffness of FGM beams via artificial neural networks by mixed FEM, Structural Engineering and Mechanics, An Int’l Journal. 75 (2020) 633-642.
  • H. Bellifa, K.H. Benrahou, L. Hadji, M.S.A. Houari, A. Tounsi, Bending and free vibration analysis of functionally graded plates using a simple shear deformation theory and the concept the neutral surface position, Journal of the Brazilian Society of Mechanical Sciences and Engineering. 38 (2016) 265-275. doi:10.1007/s40430-015-0354-0.
  • C.M. Wang, J.N. Reddy, K.H. Lee, Shear deformable beams and plates: Relationships with classical solutions, Elsevier, 2000.
  • E. Madenci, A. Özütok, Variational approximate for high order bending analysis of laminated composite plates, Structural Engineering and Mechanics, An Int’l Journal. 73 (2020) 97-108.
  • R. Kumar, A. Lal, B.N. Singh, J. Singh, New transverse shear deformation theory for bending analysis of FGM plate under patch load, Composite Structures. 208 (2019) 91-100. doi:https://doi.org/10.1016/j.compstruct.2018.10.014.
  • A.M. Zenkour, D.S. Mashat, Thermal buckling analysis of ceramic-metal functionally graded plates, Natural Science. 2 (2010) 968.
  • L. Hadji, F. Bernard, A. Safa, A. Tounsi, Bending and free vibration analysis for FGM plates containing various distribution shape of porosity, Advances in Materials Research-An International Journal. 10 (2021) 115-135.
  • H.H. Abdelaziz, M.A.A. Meziane, A.A. Bousahla, A. Tounsi, S.R. Mahmoud, A.S. Alwabli, An efficient hyperbolic shear deformation theory for bending, buckling and free vibration of FGM sandwich plates with various boundary conditions, Steel and Composite Structures, an International Journal. 25 (2017) 693-704.
  • F. Benlahcen, K. Belakhdar, M. Sellami, A. Tounsi, Thermal buckling resistance of simply supported FGM plates with parabolic-concave thickness variation, Steel and Composite Structures. 29 (2018) 591-602.
  • A. Bouamoud, Thermomechanical bending investigation of FGM sandwich plates using four shear deformation plate theory, Steel and Composite Structures, An International Journal. 32 (2019) 611-632.
  • H.-S. Shen, Z.-X. Wang, Assessment of Voigt and Mori–Tanaka models for vibration analysis of functionally graded plates, Composite Structures. 94 (2012) 2197-2208. doi:https://doi.org/10.1016/j.compstruct.2012.02.018.
  • N. Sundararajan, T. Prakash, M. Ganapathi, Nonlinear free flexural vibrations of functionally graded rectangular and skew plates under thermal environments, Finite Elements in Analysis and Design. 42 (2005) 152-168. doi:https://doi.org/10.1016/j.finel.2005.06.001.
  • C.S. Huang, O.G. McGee, M.J. Chang, Vibrations of cracked rectangular FGM thick plates, Composite Structures. 93 (2011) 1747-1764. doi:https://doi.org/10.1016/j.compstruct.2011.01.005.
  • M.M. Gasik, Micromechanical modelling of functionally graded materials, Computational Materials Science. 13 (1998) 42-55. doi:https://doi.org/10.1016/S0927-0256(98)00044-5.
  • H.M. Yin, L.Z. Sun, G.H. Paulino, Micromechanics-based elastic model for functionally graded materials with particle interactions, Acta Materialia. 52 (2004) 3535-3543. doi:https://doi.org/10.1016/j.actamat.2004.04.007.
  • M.-J. Pindera, J. Aboudi, S.M. Arnold, Analysis of spallation mechanism in thermal barrier coatings with graded bond coats using the higher-order theory for FGMs, Engineering Fracture Mechanics. 69 (2002) 1587-1606. doi:https://doi.org/10.1016/S0013-7944(02)00048-6.
  • M. Ostoja-Starzewski, I. Jasiuk, W. Wang, K. Alzebdeh, Composites with functionally graded interphases: Mesocontinuum concept and effective transverse conductivity, Acta Materialia. 44 (1996) 2057-2066. doi:https://doi.org/10.1016/1359-6454(95)00269-3.
  • H.-S. Shen, Functionally graded materials: nonlinear analysis of plates and shells, CRC press, 2016.
  • A.H. Akbarzadeh, A. Abedini, Z.T. Chen, Effect of micromechanical models on structural responses of functionally graded plates, Composite Structures. 119 (2015) 598-609. doi:https://doi.org/10.1016/j.compstruct.2014.09.031.
  • L.L. Mishnaevsky Jr, Computational mesomechanics of composites: numerical analysis of the effect of microstructures of composites of strength and damage resistance, John Wiley & Sons, 2007.
  • R.W. Zimmerman, Behavior of the Poisson Ratio of a Two-Phase Composite Material in the High-Concentration Limit, Applied Mechanics Reviews. 47 (1994) S38-S44. doi:10.1115/1.3122819.
  • R.B. Bouiadjra, A. Mahmoudi, S. Benyoucef, A. Tounsi, F. Bernard, Analytical investigation of bending response of FGM plate using a new quasi 3D shear deformation theory: Effect of the micromechanical models, Structural Engineering and Mechanics, An Int’l Journal. 66 (2018) 317-328.
  • A.M. Zenkour, A simple four-unknown refined theory for bending analysis of functionally graded plates, Applied Mathematical Modelling. 37 (2013) 9041-9051. doi:https://doi.org/10.1016/j.apm.2013.04.022.
Necmettin Erbakan Üniversitesi Fen ve Mühendislik Bilimleri Dergisi-Cover
  • Yayın Aralığı: Yılda 2 Sayı
  • Başlangıç: 2019
  • Yayıncı: Necmettin Erbakan Üniversitesi
Arşiv
Sayıdaki Diğer Makaleler

Endodontik NiTi Eğelerden Elde Edilen TiO2' nin Boya Duyarlı Güneş Pillerinde Kullanımının Araştırılması

Muhammed İhsan ÖZGÜN, Ahmet Burçin BATIBAY, Bayram ÜNAL, Yasin Ramazan EKER, Arslan TERLEMEZ

GPS, GLONASS, Galileo ve BeiDou GNSS Sistemlerinin 1. ve 2. Temel Frekanslarının Doluluk Analizi

Sermet ÖĞÜTCÜ, Behlül Numan ÖZDEMİR, Salih ALÇAY, İlkay BUĞDAYCI

Cebirsel Bir Grafın Harary İndeksi

Nihat AKGÜNEŞ, Busra AYDIN

Fonksiyonel Derecelendirilmiş Malzeme Plakların Statik Analizinde Mikro-Mekanik Modellerin Katkısı

Emrah MADENCİ