Buckling of carbon nanotube patterned polymer cylindrical shells under the axial load
Year 2022,
Volume: 11 Issue: 4, 1172 - 1178, 14.10.2022
Mahmure Avey
,
Fethi Kadıoğlu
,
Semra Ahmetolan
Abstract
In this article, the buckling of carbon nanotube (CNT) patterned cylindrical shells subjected to axial compressive load is presented within the framework of shear deformation theory (SDT). The material properties of nanocomposites change as a linear function depending on the thickness coordinate. The basic equations of cylindrical shells with CNT pattern are derived based on Donnell type shell theory and the critical axial load expression is obtained within the framework of SDT by applying Galerkin method. The effects of transverse shear deformations on the critical axial load of functionally graded CNT patterned cylindrical shells are investigated by changing CNT patterns, volume fraction ratio and shell parameters.
References
- W. Khan, R. Sharma and P. Saini, Carbon nanotube-based polymer composites: Synthesis, properties and applications. In Carbon Nanotubes Current Progress of their Polymer Composites; Intech Open: London, UK, 2016.
- S. Iijima, Helical microtubules of graphitic carbon. Nature, 354, 56–58, 1991. https://doi.org/ 10.1038/354056a0
- E.T. Thostenson, Z. Ren and T.W. Chou, Advances in the science and technology of carbon nanotubes and their composites: a review. Composites Science and Technology, 61, 1899-1912, 2001. https://doi.org/ 10.1016/S0266-3538(01)00094-X
- A.M.K. Eswai and M.M. Farag, Carbon nanotube reinforced composites: potential and current challenges. Materials & Design, 28, 2394-2401, 2007. https://doi.org/10.1016/S0266-3538(01) 000 94-X
- P.M. Ajayan, L.S. Schadler, C. Giannaris and A. Rubio, Single-walled nanotube-polymer composites: strength and weaknesses. Advanced Materials, 12(10), 750–753, 2000. https://doi.org/10.1002/(SICI)1521-4 095(200005)12:10<750::AID-ADMA750>3.0.CO;2-6
- Y.J. Liu and X.L. Chen, Evaluation of effective material properties of carbon nanotube-based composites using a nanoscale representative volume element. Mechanics of Materials, 35, 69-81, 2003. https://doi.org/10.1016/S0167-6636 (02) 00200-4
- Y. Han and J. Elliott, Molecular dynamics simulations of the elastic properties of polymer/carbon nanotube composites. Computational Materials Science, 39, 315-323,2007.https://doi.org/10.1016/j.commatsci. 2006.06.011
- H. S. Shen, Postbuckling of nanotube-reinforced composite cylindrical shells in thermal environments, Part I: Axially-loaded shells. Composite Structures, 93, 2096–2108, 2011. https://doi.org/10.1016/ j.compstruct.2011.02.011
- Z.X. Lei, K.M. Liew and J.L. Yu, Buckling analysis of functionally graded carbon nanotube-reinforced composite plates using the element-free kp-Ritz method. Composite Structures, 98, 160-168, 2013. https://doi.org/10.1016/j.compstruct.2012.11.006
- S. Chakraborty, T. Dey and R. Kumar, Stability and vibration analysis of CNT-Reinforced functionally graded laminated composite cylindrical shell panels using semi-analytical approach. Composites Part B-Engineering, 168(209), 1-14, 2019. https://doi.org/ 10.1016/j. compositesb.2018.12.051
- V.H. Nam, N.T. Phuong and V.M. Duc, Nonlinear buckling of orthogonal carbon nanotube-reinforced composite cylindrical shells under axial compression surrounded by elastic foundation in thermal environment. International Journal of Computational Materials Science and Engineering, 8(4), Article Number: 1950016, 2019. https://doi: 10.1142/ S204768411950016
- P.T. Hieu and H.V. Tung, Buckling of shear deformable FG-CNTRC cylindrical shells and toroidal shell segments under mechanical loads in thermal environments. Zamm-Zeitschrift fur Angewandte Mathematik und Mechanik, 100 (11), Article Number: 201900243, 2020. https://doi:10.1002 /zamm.201900243
- J.N. Reddy, Mechanics of Laminated Composite Plates and Shells. Theory and Analysis, Boca Raton, CRC Press, 2004.
- E. Viola, F. Tornabene and N Fantuzzi, General higher-order shear deformation theories for the free vibration analysis of completely doubly-curved laminated shells and panels. Composite Structures, 95, 639-666, 2013. https://doi:10.1016/j. compstruct.2012. 08.005
- Avey M., Fantuzi N., Sofiyev AH. Mathematical modeling and analytical solution of thermoelastic stability problem of functionally graded nanocomposite cylinders within different theories. Mathematics, 10, 1081, 2022. https://doi.org/10.3390/ math10071081
- A.S. Volmir, Stability of Elastic Systems. Moscow, Nauka. English Translation: Foreign Tech. Division, Air Force Systems Command. Wright-Patterson Air Force Base, Ohio, AD 628508, 1967.
Karbon nanotüp örüntülü polymer silindirik kabukların eksenel yük etkisi altında burkulması
Year 2022,
Volume: 11 Issue: 4, 1172 - 1178, 14.10.2022
Mahmure Avey
,
Fethi Kadıoğlu
,
Semra Ahmetolan
Abstract
Bu makalede, eksenel basınç yüküne maruz kalan karbon nanotüp (KNT) örüntülü silindirik kabukların burkulması, kayma deformasyon teorisi (KDT) çerçevesinde sunulmaktadır. Nanokompozitlerin malzeme özellikleri kalınlık koordinatına bağlı olarak lineer fonksiyon şeklinde değişmektedir. KNT örüntülü silindirik kabukların temel denklemleri Donnell tipi kabuk teorisi baz alınarak türetilmekte ve Galerkin yöntemi uygulanarak kritik eksenel yük ifadesi KDT çerçevesinde elde edilmektedir. Enine kayma deformasyonlarının fonksiyonel olarak derecelendirilmiş (FD) KNT örüntülü silindirik kabukların kritik eksenel yük değerlerine etkileri, KNT örüntüleri, hacim kesir oranı ve kabuk parametreleri değiştirilerek araştırılmaktadır.
Supporting Institution
Deatekleyen Kueum Yoktur
References
- W. Khan, R. Sharma and P. Saini, Carbon nanotube-based polymer composites: Synthesis, properties and applications. In Carbon Nanotubes Current Progress of their Polymer Composites; Intech Open: London, UK, 2016.
- S. Iijima, Helical microtubules of graphitic carbon. Nature, 354, 56–58, 1991. https://doi.org/ 10.1038/354056a0
- E.T. Thostenson, Z. Ren and T.W. Chou, Advances in the science and technology of carbon nanotubes and their composites: a review. Composites Science and Technology, 61, 1899-1912, 2001. https://doi.org/ 10.1016/S0266-3538(01)00094-X
- A.M.K. Eswai and M.M. Farag, Carbon nanotube reinforced composites: potential and current challenges. Materials & Design, 28, 2394-2401, 2007. https://doi.org/10.1016/S0266-3538(01) 000 94-X
- P.M. Ajayan, L.S. Schadler, C. Giannaris and A. Rubio, Single-walled nanotube-polymer composites: strength and weaknesses. Advanced Materials, 12(10), 750–753, 2000. https://doi.org/10.1002/(SICI)1521-4 095(200005)12:10<750::AID-ADMA750>3.0.CO;2-6
- Y.J. Liu and X.L. Chen, Evaluation of effective material properties of carbon nanotube-based composites using a nanoscale representative volume element. Mechanics of Materials, 35, 69-81, 2003. https://doi.org/10.1016/S0167-6636 (02) 00200-4
- Y. Han and J. Elliott, Molecular dynamics simulations of the elastic properties of polymer/carbon nanotube composites. Computational Materials Science, 39, 315-323,2007.https://doi.org/10.1016/j.commatsci. 2006.06.011
- H. S. Shen, Postbuckling of nanotube-reinforced composite cylindrical shells in thermal environments, Part I: Axially-loaded shells. Composite Structures, 93, 2096–2108, 2011. https://doi.org/10.1016/ j.compstruct.2011.02.011
- Z.X. Lei, K.M. Liew and J.L. Yu, Buckling analysis of functionally graded carbon nanotube-reinforced composite plates using the element-free kp-Ritz method. Composite Structures, 98, 160-168, 2013. https://doi.org/10.1016/j.compstruct.2012.11.006
- S. Chakraborty, T. Dey and R. Kumar, Stability and vibration analysis of CNT-Reinforced functionally graded laminated composite cylindrical shell panels using semi-analytical approach. Composites Part B-Engineering, 168(209), 1-14, 2019. https://doi.org/ 10.1016/j. compositesb.2018.12.051
- V.H. Nam, N.T. Phuong and V.M. Duc, Nonlinear buckling of orthogonal carbon nanotube-reinforced composite cylindrical shells under axial compression surrounded by elastic foundation in thermal environment. International Journal of Computational Materials Science and Engineering, 8(4), Article Number: 1950016, 2019. https://doi: 10.1142/ S204768411950016
- P.T. Hieu and H.V. Tung, Buckling of shear deformable FG-CNTRC cylindrical shells and toroidal shell segments under mechanical loads in thermal environments. Zamm-Zeitschrift fur Angewandte Mathematik und Mechanik, 100 (11), Article Number: 201900243, 2020. https://doi:10.1002 /zamm.201900243
- J.N. Reddy, Mechanics of Laminated Composite Plates and Shells. Theory and Analysis, Boca Raton, CRC Press, 2004.
- E. Viola, F. Tornabene and N Fantuzzi, General higher-order shear deformation theories for the free vibration analysis of completely doubly-curved laminated shells and panels. Composite Structures, 95, 639-666, 2013. https://doi:10.1016/j. compstruct.2012. 08.005
- Avey M., Fantuzi N., Sofiyev AH. Mathematical modeling and analytical solution of thermoelastic stability problem of functionally graded nanocomposite cylinders within different theories. Mathematics, 10, 1081, 2022. https://doi.org/10.3390/ math10071081
- A.S. Volmir, Stability of Elastic Systems. Moscow, Nauka. English Translation: Foreign Tech. Division, Air Force Systems Command. Wright-Patterson Air Force Base, Ohio, AD 628508, 1967.