Size-dependent analysis of FG-CNTRC microplates based on modified strain gradient elasticity theory

Chien H. Thai, A. J.M. Ferreira, T. Rabczuk, H. Nguyen-Xuan

Research output: Contribution to journalArticlepeer-review

71 Citations (Scopus)


We present in this study a size-dependent computational approach based on the modified strain gradient theory (MSGT) and higher-order shear deformation theory for static bending and free vibration analyses of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) microplates. Three material length scale parameters (MLSPs) are taken into account in MSGT to capture size effects of microplate behavior. The effective material properties of FG-CNTRC microplates are obtained by an extended rule of mixture. Four types of carbon nanotube distributions, which are either uniform or functionally graded (FG) through the plate thickness, are considered. The governing equations are derived from the principle of virtual work and are then solved by isogeometric analysis (IGA). The IGA is suitable for a numerical implementation of the size-dependent models since it requires higher-order gradients in the weak form. The inclusion of geometrical parameters, boundary conditions, distributed types of carbon nanotube and material length scale parameters are studied to evaluate the displacement and natural frequency of FG-CNTRC microplates. In addition, the present size-dependent model can be retrieved into the modified couple stress model or classical model when a few MLSPs are ignored.

Original languageEnglish
Pages (from-to)521-538
Number of pages18
JournalEuropean Journal of Mechanics, A/Solids
Publication statusPublished - 2018 Nov 1
Externally publishedYes

Bibliographical note

Funding Information:
This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 107.02-2016.19 .

Publisher Copyright:
© 2018 Elsevier Masson SAS


  • Carbon nanotube-reinforced composite materials
  • Higher-order shear deformation theory
  • Isogeometric analysis
  • Modified strain gradient theory
  • Size-dependent model

ASJC Scopus subject areas

  • General Materials Science
  • Mechanics of Materials
  • Mechanical Engineering
  • General Physics and Astronomy


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