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Original Articles

A new finite strip formulation based on Carrera unified formulation for the free vibration analysis of composite laminates

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Pages 4726-4737 | Received 16 Apr 2021, Accepted 26 May 2021, Published online: 08 Jun 2021

References

  • E. Carrera, M. Cinefra, M. Petrolo, and E. Zappino, Finite Element Analysis of Structures through Unified Formulation, John Wiley & Sons Ltd, Chichester, UK, 2014.
  • E. Carrera, A class of two dimensional theories for multilayered plates analysis, Atti Accad. Sci. Torino. Mem. Sci. Fis., vol. 19, pp. 49–87, 1995.
  • E. Carrera, Theories and finite elements for multilayered, anisotropic, composite plates and shells, Arco., vol. 9, no. 2, pp. 87–140, 2002. DOI: 10.1007/BF02736649.
  • E. Carrera, Theories and finite elements for multilayered plates and shells: A unified compact formulation with numerical assessment and benchmarking, Arco., vol. 10, no. 3, pp. 215–296, 2003. DOI: 10.1007/BF02736224.
  • E. Carrera, S. Brischetto, and A. Robaldo, Variable kinematic model for the analysis of functionally graded material plates, AIAA J., vol. 46, no. 1, pp. 194–203, 2008. DOI: 10.2514/1.32490.
  • E. Carrera, and G. Giunta, Refined beam theories based on a unified formulation, Int. J. Appl. Mech., vol. 02, no. 01, pp. 117–143, 2010. DOI: 10.1142/S1758825110000500.
  • G. Giunta, S. Belouettar, and E. Carrera, Analysis of FGM beams by means of classical and advanced theories, Mech. Adv. Mater. Struct., vol. 17, no. 8, pp. 622–635, 2010. DOI: 10.1080/15376494.2010.518930.
  • P. Nali, E. Carrera, and S. Lecca, Assessments of refined theories for buckling analysis of laminated plates, Compos. Struct., vol. 93, no. 2, pp. 456–464, 2011. DOI: 10.1016/j.compstruct.2010.08.035.
  • S. Natarajan, A. Ferreira, S.P.A. Bordas, E. Carrera, and M. Cinefra, Analysis of composite plates by a unified formulation-cell based smoothed finite element method and field consistent elements, Compos. Struct., vol. 105, pp. 75–81, 2013. DOI: 10.1016/j.compstruct.2013.04.040.
  • I. Ramos, J. Mantari, and A. Zenkour, Laminated composite plates subject to thermal load using trigonometrical theory based on Carrera unified formulation, Compos. Struct., vol. 143, pp. 324–335, 2016. DOI: 10.1016/j.compstruct.2016.02.020.
  • M.L. Ribeiro, G.F. Ferreira, R. de Medeiros, A.J. Ferreira, and V. Tita, Experimental and numerical dynamic analysis of laminate plates via Carrera unified formulation, Compos. Struct., vol. 202, pp. 1176–1185, 2018. DOI: 10.1016/j.compstruct.2018.05.085.
  • J. Mantari, I. Ramos, E. Carrera, and M. Petrolo, Static analysis of functionally graded plates using new non-polynomial displacement fields via Carrera unified formulation, Compos. Part B Eng., vol. 89, pp. 127–142, 2016. DOI: 10.1016/j.compositesb.2015.11.025.
  • B. Daraei, S. Shojaee, and S. Hamzehei-Javaran, Analysis of stationary and axially moving beams considering functionally graded material using micropolar theory and Carrera unified formulation, Compos. Struct., pp. 114054, 2021. DOI: 10.1016/j.compstruct.2021.114054.
  • A. Catapano, G. Giunta, S. Belouettar, and E. Carrera, Static analysis of laminated beams via a unified formulation, Compos. Struct., vol. 94, no. 1, pp. 75–83, 2011. DOI: 10.1016/j.compstruct.2011.07.015.
  • A. Pagani, E. Carrera, M. Boscolo, and J.R. Banerjee, Refined dynamic stiffness elements applied to free vibration analysis of generally laminated composite beams with arbitrary boundary conditions, Compos. Struct., vol. 110, pp. 305–316, 2014. DOI: 10.1016/j.compstruct.2013.12.010.
  • E. Carrera, A. Pagani, and J.R. Banerjee, Linearized buckling analysis of isotropic and composite beam-columns by Carrera unified formulation and dynamic stiffness method, Mech. Adv. Mater. Struct., vol. 23, no. 9, pp. 1092–1103, 2016. DOI: 10.1080/15376494.2015.1121524.
  • E. Carrera, M. Filippi, P.K.R. Mahato, and A. Pagani, Advanced models for free vibration analysis of laminated beams with compact and thin-walled open/closed sections, J. Compos. Mater., vol. 49, no. 17, pp. 2085–2101, 2015. DOI: 10.1177/0021998314541570.
  • E. Carrera, M. Filippi, P.K.R. Mahato, and A. Pagani, Accurate static response of single- and multi-cell laminated box beams, Compos. Struct., vol. 136, pp. 372–383, 2016. DOI: 10.1016/j.compstruct.2015.10.020.
  • E. Carrera, M. Filippi, P.K. Mahato, and A. Pagani, Free-vibration tailoring of single- and multi-bay laminated box structures by refined beam theories, Thin-Walled Struct., vol. 109, pp. 40–49, 2016. DOI: 10.1016/j.tws.2016.09.014.
  • B. Daraei, S. Shojaee, and S. Hamzehei-Javaran, Free vibration analysis of composite laminated beams with curvilinear fibers via refined theories, Mech. Adv. Mater. Struct., 2020. DOI: 10.1080/15376494.2020.1797959.
  • B. Daraei, S. Shojaee, and S. Hamzehei-Javaran, Free vibration analysis of axially moving laminated beams with axial tension based on 1D refined theories using Carrera unified formulation, Steel Compos. Struct., vol. 37, no. 1, pp. 37–49, 2020. DOI: 10.12989/scs.2020.37.1.037.
  • G. Giunta, N. Metla, Y. Koutsawa, and S. Belouettar, Free vibration and stability analysis of three-dimensional sandwich beams via hierarchical models, Compos. Part B Eng., vol. 47, pp. 326–338, 2013. DOI: 10.1016/j.compositesb.2012.11.017.
  • Y. Hui, G. Giunta, S. Belouettar, Q. Huang, H. Hu, and E. Carrera, A free vibration analysis of three-dimensional sandwich beams using hierarchical one-dimensional finite elements, Compos. Part B Eng., vol. 110, pp. 7–19, 2017. DOI: 10.1016/j.compositesb.2016.10.065.
  • E. Carrera, and E. Zappino, Carrera unified formulation for free-vibration analysis of aircraft structures, Aiaa J., vol. 54, no. 1, pp. 280–292, 2016. DOI: 10.2514/1.J054265.
  • E. Carrera, M. Filippi, and E. Zappino, Free vibration analysis of rotating composite blades via Carrera unified formulation, Compos. Struct., vol. 106, pp. 317–325, 2013. DOI: 10.1016/j.compstruct.2013.05.055.
  • A.J.M. Ferreira, E. Carrera, M. Cinefra, and C.M.C. Roque, Radial basis functions collocation for the bending and free vibration analysis of laminated plates using the Reissner-Mixed Variational Theorem, Eur. J. Mech. A Solid., vol. 39, pp. 104–112, 2013. DOI: 10.1016/j.euromechsol.2012.10.012.
  • A. Pagani, E. Carrera, and A. J. M. Ferreira, Higher-order theories and radial basis functions applied to free vibration analysis of thin-walled beams, Mech. Adv. Mater. Struct., vol. 23, no. 9, pp. 1080–1091, 2016. DOI: 10.1080/15376494.2015.1121555.
  • Y. Yan, E. Carrera, A. Pagani, I. Kaleel, and A.G. Miguel, Isogeometric analysis of 3D straight beam-type structures by Carrera unified formulation, Appl. Math. Model., vol. 79, pp. 768–792, 2020. DOI: 10.1016/j.apm.2019.11.003.
  • A. Alesadi, M. Galehdari, and S. Shojaee, Free vibration and buckling analysis of cross-ply laminated composite plates using Carrera’s unified formulation based on Isogeometric approach, Comput. Struct., vol. 183, pp. 38–47, 2017. DOI: 10.1016/j.compstruc.2017.01.013.
  • A. Alesadi, M. Galehdari, and S. Shojaee, Free vibration and buckling analysis of composite laminated plates using layerwise models based on isogeometric approach and Carrera unified formulation, Mech. Adv. Mater. Struct., vol. 25, no. 12, pp. 1018–1032, 2018. DOI: 10.1080/15376494.2017.1342883.
  • A. Alesadi, S. Ghazanfari, and S. Shojaee, B-spline finite element approach for the analysis of thin-walled beam structures based on 1D refined theories using Carrera unified formulation, Thin-Walled Struct., vol. 130, pp. 313–320, 2018. DOI: 10.1016/j.tws.2018.05.016.
  • S. Ghazanfari, S. Hamzehei-Javaran, A. Alesadi, and S. Shojaee, Free vibration analysis of cross-ply laminated beam structures using refined beam theories and B-spline basis functions, Mech. Adv. Mater. Struct., vol. 28, no. 5, pp. 467–475, 2019. DOI: 10.1080/15376494.2019.1574939.
  • A. Alesadi, S. Shojaee, and S. Hamzehei-Javaran, Spherical Hankel-based free vibration analysis of cross-ply laminated plates using refined finite element theories, Iran. J. Sci. Technol. Trans. Civ. Eng., vol. 44, no. 1, pp. 127–137, 2020. DOI: 10.1007/s40996-019-00242-6.
  • Y.K. Cheung, Finite Strip Method in Structural Analysis, Pergamon Press, Oxford, UK, 1976.
  • Y.K. Cheung, and L.G. Tham, Finite Strip Method, CRC Press, Boca Raton, FL, 1998.
  • M.A. Bradford, and M. Azhari, Buckling of plates with different end conditions using the finite strip method, Comput. Struct., vol. 56, no. 1, pp. 75–83, 1995. DOI: 10.1016/0045-7949(94)00528-B.
  • S. Hatami, M. Azhari, and M.M. Saadatpour, Free vibration of moving laminated composite plates, Compos. Struct., vol. 80, no. 4, pp. 609–620, 2007. DOI: 10.1016/j.compstruct.2006.07.009.
  • B. Daraei, and S. Hatami, Free vibration analysis of variable stiffness composite laminates with flat and folded shapes, J. Solid Mech., vol. 8, pp. 662–678, 2016.
  • G.J. Hancock, and C.H. Pham, Buckling analysis of thin-walled sections under localized loading using the semi-analytical finite strip method, Thin-Walled Struct., vol. 86, pp. 35–46, 2015. DOI: 10.1016/j.tws.2014.09.017.
  • M.A. Rendall, G.J. Hancock, and K.J.R. Rasmussen, The generalised constrained finite strip method for thin-walled members in shear, Thin-Walled Struct., vol. 117, pp. 294–302, 2017. DOI: 10.1016/j.tws.2017.04.030.
  • E. Carrera, S. Brischetto, and P. Nali, Plates and Shells for Smart Structures: Classical and Advanced Theories for Modeling and Analysis, Wiley, New Delhi, 316p., 2011.
  • J.N. Reddy, Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, 2nd ed., CRC Press, Boca Raton, FL, 2004.
  • K.M. Liew, Solving the vibrations of thick symmetric laminates by Reissner/Mindlin plate theory and the p-Ritz method, J. Sound. Vib., vol. 198, no. 3, pp. 343–360, 1996. DOI: 10.1006/jsvi.1996.0574.
  • B. Liu, and Y. Xing, Exact solutions for free vibrations of orthotropic rectangular Mindlin plates, Compos. Struct., vol. 93, no. 7, pp. 1664–1464, 2011. DOI: 10.1016/j.compstruct.2011.01.014.

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