653
Views
26
CrossRef citations to date
0
Altmetric
Research Article

A finite element method for modal analysis of FGM plates

&
Pages 1111-1122 | Received 18 Jul 2019, Accepted 13 Mar 2020, Published online: 07 May 2020

References

  • Aboudi, J., M. J. Pindera, and S. M. Arnold. 1999. Higher-order theory for functionally graded materials. Composites Part B: Engineering 30 (8):777–832. doi:10.1016/S1359-8368(99)00053-0.
  • Alizadeh, M., and A. Alibeigloo. 2014. Static and free vibration analyses of functionally graded sandwich plates using three dimensional theory of elasticity. Modares Mechanical Engineering 14 (10):195–204.
  • Alizadeh, M., and A. M. Fattahi. 2019. Non‑classical plate model for FGMs. Engineering with Computers 35 (1):215–28. doi:10.1007/s00366-018-0594-6.
  • Amirpour, M., R. Das, and E. I. S. Flores. 2016. Analytical solutions for elastic deformation of functionally graded thick plates with in-plane stiffness variation using higher order shear deformation theory. Composites Part B: Engineering 94:109–21. doi:10.1016/j.compositesb.2016.03.040.
  • Amirpour, M., R. Das, and E. I. S. Flores. 2017. Bending analysis of thin functionally graded plate under in-plane stiffness variations. Applied Mathematical Modelling 44:481–96. doi:10.1016/j.apm.2017.02.009.
  • Amirpour, M., R. Das, and S. Bickerton. 2017. An elasto-plastic damage model for functionally graded plates with in-plane material properties variation: Material model and numerical implementation. Composite Structures 163:331–41. doi:10.1016/j.compstruct.2016.12.020.
  • Amirpour, M., S. Bickerton, E. Calius, B. R. Mace, and R. Das. 2018. Numerical and experimental study on free vibration of 3D-printed polymeric functionally graded plates. Composite Structures 189:192–205. doi:10.1016/j.compstruct.2018.01.056.
  • Amirpour, M., S. Bickerton, E. Calius, R. Das, and B. Mace. 2019. Numerical and experimental study on deformation of 3D-printed polymeric functionally graded plates: 3D-Digital Image Correlation approach. Composite Structures 211:481–9. doi:10.1016/j.compstruct.2019.01.014.
  • Asrari, R., F. Ebrahimi, M. M. Kheirikhah, and K. Hosseini Safari. 2020. Buckling analysis of heterogeneous magneto-electro-thermo-elastic cylindrical nanoshells based on nonlocal strain gradient elasticity theory. Mechanics Based Design of Structures and Machines. Advance online publication. doi:10.1080/15397734.2020.1728545.
  • Azizi, S., B. Safaei, A. M. Fattahi, and M. Tekere. 2015. Nonlinear vibrational analysis of nano-beams embedded in an elastic medium including surface stress effects. Advances in Materials Science and Engineering 2015:1–7. doi:10.1155/2015/318539.
  • Bendine, K., B. F. Boukhoulda, M. Nouari, and Z. Satla. 2016. Structural modeling and active vibration control of smart FGM plate through ANSYS. International Journal of Computational Methods 14 (2):1750042–1750059. doi:10.1142/S0219876217500426.
  • Chen, M. F., G. Y. Jin, Y. T. Zhang, F. L. Niu, and Z. G. Liu. 2019. Three-dimensional vibration analysis of beams with axial functionally graded materials and variable thickness. Composite Structures 207:304–22. doi:10.1016/j.compstruct.2018.09.029.
  • Chen, Y. K., G. Y. Jin, C. Y. Zhang, T. G. Ye, and Y. Q. Xue. 2018. Thermal vibration of FGM beams with general boundary conditions using a higher-order shear deformation theory. Composites Part B: Engineering 153:376–86. doi:10.1016/j.compositesb.2018.08.111.
  • Fattahi, A. M., and B. Safaei. 2017. Buckling analysis of CNT-reinforced beams with arbitrary boundary conditions. Microsystem Technologies 23 (10):5079–91. doi:10.1007/s00542-017-3345-5.
  • Fattahi, A. M., and S. Sahmani. 2017a. Non-local temperature-dependent postbuckling behavior of FG-CNT reinforced nanoshells under hydrostatic pressure combined with heat conduction. Microsystem Technologies 23 (10):5121–37. doi:10.1007/s00542-017-3377-x.
  • Fattahi, A. M., and S. Sahmani. 2017b. Size dependency in the axial postbuckling behavior of nanopanels made of functionally graded material considering surface elasticity. Arabian Journal for Science and Engineering 42 (11):4617–33. doi:10.1007/s13369-017-2600-5.
  • Fattahi, A. M., S. Sahmani, and N. A. Ahmed. 2019. Nonlocal strain gradient beam model for nonlinear secondary resonance analysis of functionally graded porous micro/nano-beams under periodic hard excitations. Mechanics Based Design of Structures and Machines. Advance online publication. doi:10.1080/15397734.2019.1624176.
  • Frikha, A., S. Zghal, and F. Dammak. 2018. Dynamic analysis of functionally graded carbon nanotubes-reinforced plate and shell structures using a double directors finite shell element. Aerospace Science and Technology 78:438–51. doi:10.1016/j.ast.2018.04.048.
  • Gasik, M. M. 1998. Micromechanical modelling of functionally graded materials. Computational Materials Science 13 (1–3):42–55. doi:10.1016/S0927-0256(98)00044-5.
  • Grujicic, M., and Y. Zhang. 1998. Determination of effective elastic properties of functionally graded materials using Voronoi cell finite element method. Materials Science and Engineering: Part A 251 (1–2):64–76. doi:10.1016/S0921-5093(98)00647-9.
  • Gupta, A., and M. Talha. 2015. Recent development in modeling and analysis of functionally graded materials and structures. Progress in Aerospace Sciences 79:1–14. doi:10.1016/j.paerosci.2015.07.001.
  • Hozhabrossadati, S. M., N. Challamel, M. Rezaiee-Pajand, and A. A. Sani. 2020. Free vibration of a nanogrid based on Eringen’s stress gradient model. Mechanics Based Design of Structures and Machines. Advance online publication. doi:10.1080/15397734.2020.1720720.
  • Jena, S. K., S. Chakraverty, M. Malikan, and F. Tornabene. 2019. Stability analysis of single-walled carbon nanotubes embedded in Winkler foundation placed in a thermal environment considering the surface effect using a new refined beam theory. Mechanics Based Design of Structures and Machines. Advance online publication. doi:10.1080/15397734.2019.1698437.
  • Koizmi, M. 1993. The concept of FGM. Ceramic Transactions and Function Gradient 34:3–10.
  • Markworth, A. J., and J. H. Saunders. 1995. A model of structure optimization for a functionally graded material. Materials Letters 22 (1–2):103–7. doi:10.1016/0167-577X(94)00238-X.
  • Parida, S., and S. Mohanty. 2019. Free vibration analysis of rotating functionally graded material plate under nonlinear thermal environment using higher order shear deformation theory. Proceedings of the Institution of Mechanical Engineers: Part C: Journal of Mechanical Engineering Science 233 (6):2056–73. doi:10.1177/0954406218777535.
  • Qin, Z., F. Chu, and Z. Jean. 2017. Free vibrations of cylindrical shells with arbitrary boundary conditions: a comparison study. International Journal of Mechanical Sciences 133:91–9. doi:10.1016/j.ijmecsci.2017.08.012.
  • Qin, Z., X. Pang, B. Safaei, and F. Chu. 2019. Free vibration analysis of rotating functionally graded CNT reinforced composite cylindrical shells with arbitrary boundary conditions. Composite Structures 220:847–60. doi:10.1016/j.compstruct.2019.04.046.
  • Qin, Z., Z. Yang, J. Zu, and F. Chu. 2018. Free vibration analysis of rotating cylindrical shells coupled with moderately thick annular plates. International Journal of Mechanical Sciences 142–143:127–39. doi:10.1016/j.ijmecsci.2018.04.044.
  • Ramu, I., and S. C. Mohanty. 2014. Modal analysis of functionally graded material plates using finite element method. Procedia Materials Science 6:460–7. doi:10.1016/j.mspro.2014.07.059.
  • Safaei, B., A. M. Fattahi, and F. Chu. 2018. Finite element study on elastic transition in platelet reinforced composites. Microsystem Technologies 24 (6):2663–71. doi:10.1007/s00542-017-3651-y.
  • Safaei, B., and A. M. Fattahi. 2017. Free vibrational response of single-layered graphene sheets embedded in an elastic matrix using different non-local plate models. Mechanics 23 (5):678–87. doi:10.5755/j01.mech.23.5.14883.
  • Safaei, B., N. A. Ahmed, and A. M. Fattahi. 2019. Free vibration analysis of polyethylene/CNT plates. The European Physical Journal Plus 134 (6):271. doi:10.1140/epjp/i2019-12650-x.
  • Safaei, B., R. Moradi-Dastjerdi, and F. Chu. 2018. Effect of thermal gradient load on thermo-elastic vibrational behavior of sandwich plates reinforced by carbon nanotube agglomerations. Composite Structures 192:28–37. doi:10.1016/j.compstruct.2018.02.022.
  • Safaei, B., R. Moradi-Dastjerdi, Z. Qin, K. Behdinan, and F. Chu. 2019b. Determination of thermoelastic stress wave propagation in nanocomposite sandwich plates reinforced by clusters of carbon nanotubes. Journal of Sandwich Structures and Materials. Advance online publication. doi:10.1177/1099636219848282.
  • Safaei, B., R. Moradi-Dastjerdi, Z. Qin, and F. Chu. 2019a. Frequency-dependent forced vibration analysis of nanocomposite sandwich plate under thermo-mechanical loads. Composites Part B: Engineering 161:44–54. doi:10.1016/j.compositesb.2018.10.049.
  • Sahmani, S., and A. M. Fattahi. 2017a. An anisotropic calibrated non-local plate model for biaxial instability analysis of 3D metallic carbon nanosheets using molecular dynamics simulations. Materials Research Express 4 (6):065001–14. doi:10.1088/2053-1591/aa6bc0.
  • Sahmani, S., and A. M. Fattahi. 2017b. Calibration of developed non-local anisotropic shear deformable plate model for uniaxial instability of 3D metallic carbon nanosheets using MD simulations. Computer Methods in Applied Mechanics and Engineering 322:187–207. doi:10.1016/j.cma.2017.04.015.
  • Sahmani, S., and A. M. Fattahi. 2017c. Development an efficient calibrated non-local plate model for nonlinear axial instability of zirconia nanosheets using molecular dynamics simulation. Journal of Molecular Graphics and Modelling 75:20–31. doi:10.1016/j.jmgm.2017.04.018.
  • Sahmani, S., and A. M. Fattahi. 2017d. Imperfection sensitivity of the size-dependent nonlinear instability of axially loaded FGM nanopanels in thermal environments. Acta Mechanica 228 (11):3789–810. doi:10.1007/s00707-017-1912-6.
  • Sahmani, S., A. M. Fattahi, and N. A. Ahmed. 2019. Radial postbuckling of nanoscaled shells embedded in elastic foundations based on Ru’s surface stress elasticity theory. Mechanics Based Design of Structures and Machines 47 (6):787–806. doi:10.1080/15397734.2019.1611447.
  • Sharma, A. K., P. Sharma, P. S. Chauhan, and S. S. Bhadoria. 2018. Study on harmonic analysis of functionally graded plates using FEM. International Journal of Applied Mechanics and Engineering 23 (4):941–61. doi:10.2478/ijame-2018-0053.
  • Talha, M., and B. N. Singh. 2010. Static response and free vibration analysis of FGM plates using higher order shear deformation theory. Applied Mathematical Modelling 34 (12):3991–4011. doi:10.1016/j.apm.2010.03.034.
  • Tornabene, F. 2009. Free vibration analysis of functionally graded conical, cylindrical shell and annular plate structures with a four-parameter power–law distribution. Computer Methods in Applied Mechanics and Engineering 198 (37–40):2911–35. doi:10.1016/j.cma.2009.04.011.
  • Tornabene, F., A. Liverani, and G. Caligiana. 2011. FGM and laminated doubly curved shells and panels of revolution with a free-form meridian: a 2-D GDQ solution for free vibrations. International Journal of Mechanical Sciences 53 (6):446–70. doi:10.1016/j.ijmecsci.2011.03.007.
  • Tornabene, F., and J. N. Reddy. 2013. FGM and laminated doubly-curved and degenerate shells resting on nonlinear elastic foundations: A GDQ solution for static analysis with a posteriori stress and strain recovery. World Journal of Mechanics 93 (4):635–88. doi:10.4236/wjm.2013.31001.
  • Tornabene, F., N. Fantuzzi, E. Viola, and R. C. Batra. 2015. Stress and strain recovery for functionally graded free-form and doubly-curved sandwich shells using higher-order equivalent single layer theory. Composite Structures 119:67–89. doi:10.1016/j.compstruct.2014.08.005.
  • Tornabene, F., N. Fantuzzi, M. Bacciocchi, and E. Viola. 2016. Effect of agglomeration on the natural frequencies of functionally graded carbon nanotube-reinforced laminated composite doubly-curved shells. Composites Part B: Engineering 89:187–218. doi:10.1016/j.compositesb.2015.11.016.
  • Trabelsi, S., A. Frikha, S. Zghal, and F. Dammak. 2019. A modified FSDT-based four nodes finite shell element for thermal buckling analysis of functionally graded plates and cylindrical shells. Engineering Structures 178:444–59. doi:10.1016/j.engstruct.2018.10.047.
  • Uymaz, B., and M. Aydogdu. 2007. Three-dimensional vibration analyses of functionally graded plates under various boundary conditions. Journal of Reinforced Plastics and Composites 26 (18):1847–63. doi:10.1177/0731684407081351.
  • Zarezadeh, E., V. Hosseini, and A. Hadi. 2019. Torsional vibration of functionally graded nano-rod under magnetic field supported by a generalized torsional foundation based on nonlocal elasticity theory. Mechanics Based Design of Structures and Machines. Advance online publication. doi:10.1080/15397734.2019.1642766.
  • Zghal, S., A. Frikha, and F. Dammak. 2018. Mechanical buckling analysis of functionally graded power-based and carbon nanotubes-reinforced composite plates and curved panels. Composites Part B: Engineering 150:165–83. doi:10.1016/j.compositesb.2018.05.037.
  • Zhang, N., Khan, T., Guo, H., Shi, S., Zhong, W. and Zhang, W. 2019. Functionally graded materials: an overview of stability, buckling, and free vibration analysis. Advances in Materials Science and Engineering. Advance online publication. doi:10.1155/2019/1354150.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.