Geometric nonlinear dynamic analysis of MLC cylindrical shells with FGM core under impact load using by finite element method

Document Type : Research Note


Civil Engineering Department, Faculty of Engineering, Ferdowsi University of Mashhad. Mashhad. Iran


In recent decades, shells made of composite materials have been used in modern structures under impact load. Multi-Layer Composites (MLC) and Functionally Graded Materials (FGMs) are the upgrades of composites that have been considered due to their suitable mechanical properties such as high resistance to weight ratio, flexibility and impact resistance. In this research, geometric nonlinear dynamic behavior on multilayer composite cylindrical shells with FGM core under impact load has been analyzed; Because it is necessary to know how structures made of these materials behave under such loads. For this purpose, the effect of FGM core volume fraction index and the effective parameters of multi-layer composites such as the angles of the layers and the number of layers have been investigated. The results of this study show that by increasing the volume fraction index, the maximum displacement of the shell decreases. The maximum displacement occurs in the CFC (CFRP/FGM/CFRP) shell with pure metal FGM and the minimum displacement occurs in the GFG shell with pure ceramic FGM. Evaluation of the different positions of the layers shows that selecting a 15-degree positioning angle causes less displacement and also decreases the displacement as the number of layers increases.


  1. Bever, and P. Duwez, “Gradients in composite materials,” Materials Science and Engineering, vol. 10, no.7, pp. 1-8, 1972.
  2. Koizumi, “FGM activities in Japan,”Composites Part B: Engineering, vol. 28, no. 4, pp. 1-4, 1997.
  3. Horgan, and A. Chan, “The pressurized hollow cylinder or disk problem for functionally graded isotropic linearly elastic materials,” Journal of Elasticity, vol. 55, no. 1, pp. 43-59, 1999.
  4. Tutuncu, and M. Ozturk, “Exact solutions for stresses in functionally graded pressure vessels,” Composites Part B: Engineering, vol. 32, no. 8, pp. 683-686, 2001.
  5. Seidi, “Buckling analysis of Truncated conical Sandwich Shells with FGM Face sheets using Improved Higher-order Theory,”Journal of Mechanical Engineering, vol. 48, no. 4, pp. 337-340, 2019.
  6. Sheinman, and S. Greif, “Dynamic analysis of laminated shells of revolution,” Journal of Composite Materials, vol. 18, pp. 200-215, 1984.
  7. L. Ramkumar, and Y. R. Thakar, “Dynamic response of curved laminated plates subjected to low velocity impact,” ASME Journal of Engineering and Material  Technology, vol. 109, pp. 67-71, 1987.
  8. S. Johnson, and M. W. Hammond, “Crack growth behavior of internal titanium plies of a fiber metal laminate,” Composites: Part A, vol. 39, pp. 1705–1715, 2008.
  9. Christoforu, S. R. Swanson, S. C. Venterllo, and S. W. Beckwith, “Impact damage of carbon/epoxy composite cylinders,” Proceeding of the 32nd international SAMPE  symposium and exhibition, vol. 32, pp. 964-973, 1987.
  10. Christoforu, S. R. Swanson, and S. W. Beckwith, “Lateral impact of composite  cylinders,” Composite Materials: Fatigue and Fracture, vol. 2, pp. 373-386, 1989.
  11. Kumar, B. Nageswara Rao, and B. Pradhan, “Effect of impactor parameters and  laminate characteristics on impact response and damage in curved composite  laminates,” Journal of Reinforced Plastics and Composites, vol. 26, no. 13, pp.  1273-1290, 2007.
  12. C. Her, and Y.  C. Liang, “The finite element analysis of composite laminates and shellstructures subjected to low velocity impact,” Composite Structures, vol. 66,  no. 1, pp. 277-285, 2004.
  13. Kiratisaevee, and W. J. Cantwell, “The impact response of aluminum foam sandwich  structures based on a glass fiber-reinforced polypropylene fiber-metal laminate,” Polymer Composite, vol. 25, no. 5, pp. 499-509, 2004.
  14. W. Hutchinson, and M. Y. He, “Buckling of cylindrical sandwich shells with metal  foam cores,” International Journal of Solids and Structures, vol. 37, no. 46-47, pp. 6777-6794, 2000.
  15. Garg, R. K. Khare, and T. Kant, “Higher-order closed-form solutions for free vibration of laminated composite and sandwich shells,” Journal of Sandwich Structures & Materials, vol. 8, no. 3, pp. 205-235, 2006.
  16. Rahmani, S. M. R. Khalili, and K. Malekzadeh, “Free vibration response of  composite sandwich cylindrical shell with flexible core,” Composite Structures,  vol. 92, pp. 1269-1281, 2010.
  17. Yin, L. Sun, and G. H. Paulino, “Micromechanics-based elastic model for functionally graded materials with particle interactions,” Acta Materialia, vol. 52, no. 12, pp. 3535-  3543, 2004.
  18. S. Shen, Functionally graded materials: nonlinear analysis of plates and shells, CRC press, 2016. [E-book].
  19. Hajlaoui, E. Triki, A. Frikha, M. Wali, and F. Dammak, “Nonlinear dynamics analysis of FGM shell structures with a higher order shear strain enhanced solid-shell element,” Latin American Journal of Solids and Structures, vol. 14, no. 1, pp. 72-91, 2017.
  20. S. Hoo Fatt, and D. Sirivolu, “Dynamic Stability of Double-Curvature Composite Shells under External Blast,” International Journal of Non-Linear Mechanics, vol. 77, pp. 281-290, 2015.
  21. Vasilief, and V. Morozof, Advanced Mechanics of Composite Materials", Elservier, London, 1th ed, 2007. [E-book].
  22. Shahraki, F. Shahabian, and M. Koohestani, “The nonlinear dynamic analysis of elasto-plastic behaviour of the single-curved FGM shells under impact load,” AUT Journal of Civil Engineering, vol. 4, no. 3, 2020.
  23. Aksoylar, A. Ömerciko─člu, Z. Mecito─člu, and M. H. Omurtag, “Nonlinear transient analysis of FGM and FML plates under blast loads by experimental and mixed FE methods,” Composite Structures, vol. 94, no. 2, pp. 731-744, 2012.
  24. Gunes, M. Aydin, M. K. Apalak, and J. Reddy, “The elasto-plastic impact analysis of functionally graded circular plates under low-velocities,” Composite Structures, vol. 93, no. 2, pp. 860-869, 2011.
  25. T. Kaneko, S. Ujihashi, H. Yomoda and S. Inagi, “Finite element method failure analysis of a pressurized FRP cylinder under transverse impact loading. Thin-walled structures,” vol. 46, no. 7-9, pp. 898-904, 2008.