A naturally stabilized nodal integration meshfree formulation for carbon nanotube-reinforced composite plate analysis

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

Research output: Contribution to journalArticlepeer-review

41 Citations (Scopus)


Naturally stabilized nodal integration (NSNI) meshfree formulations associated with the higher-order shear deformation plate theory (HSDT) are proposed to analyze bending and free vibration behaviors of carbon nanotube-reinforced composite (CNTRC) plates. An extended rule of mixture is used to compute the effective material properties of CNTRC plates. The uniform and functionally graded distributions of carbon nanotube (CNTs) via the plate thickness are studied. In the present approach, gradient strains are directly computed at nodes similar to the direct nodal integration (DNI). Outstanding features of the current approach are to alleviate instability solutions in the DNI and to significantly decrease computational cost as compared to the traditional high-order Gauss quadrature scheme. Discrete equations for bending and free vibration analyses are obtained by variational consistency in the Galerkin weak form. Enforcing essential boundary conditions is completely similar to the finite element method (FEM) due to satisfying the Kronecker delta function property of moving Kriging integration shape functions. Numerical validations with various complex geometries, stiffness ratios, volume fraction of CNTs and boundary conditions are given to show the efficiency of the present approach.

Original languageEnglish
Pages (from-to)136-155
Number of pages20
JournalEngineering Analysis with Boundary Elements
Publication statusPublished - 2018 Jul

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:
© 2017 Elsevier Ltd


  • Carbon nanotube-reinforced composite plates
  • Meshfree method
  • Moving Kriging interpolation
  • Naturally stabilized nodal integration

ASJC Scopus subject areas

  • Analysis
  • General Engineering
  • Computational Mathematics
  • Applied Mathematics


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