NURBS-based finite element analysis of functionally graded plates: Static bending, vibration, buckling and flutter

Navid Valizadeh, Sundararajan Natarajan, Octavio A. Gonzalez-Estrada, Timon Rabczuk, Tinh Quoc Bui, Stéphane P.A. Bordas

Research output: Contribution to journalArticlepeer-review

294 Citations (Scopus)


In this paper, a non-uniform rational B-spline based iso-geometric finite element method is used to study the static and dynamic characteristics of functionally graded material (FGM) plates. The material properties are assumed to be graded only in the thickness direction and the effective properties are computed either using the rule of mixtures or by Mori-Tanaka homogenization scheme. The plate kinematics is based on the first order shear deformation plate theory (FSDT). The shear correction factors are evaluated employing the energy equivalence principle and a simple modification to the shear correction factor is presented to alleviate shear locking. Static bending, mechanical and thermal buckling, linear free flexural vibration and supersonic flutter analysis of FGM plates are numerically studied. The accuracy of the present formulation is validated against available three-dimensional solutions. A detailed numerical study is carried out to examine the influence of the gradient index, the plate aspect ratio and the plate thickness on the global response of functionally graded material plates.

Original languageEnglish
Pages (from-to)309-326
Number of pages18
JournalComposite Structures
Publication statusPublished - 2013 May

Bibliographical note

Funding Information:
Sundararajan Natarajan would like to acknowledge the financial support of the School of Civil and Environmental Engineering, The University of New South Wales for his research fellowship since September 2012. Timon Rabczuk, Stéphane Bordas and Navid Valizadeh would like to acknowledge the financial support of the Framework Programme 7 Initial Training Network Funding under Grant No. 289361 “Integrating Numerical Simulation and Geometric Design Technology”. Stéphane Bordas and Octavio A González Estrada also thank partial funding provided by: (1) the EPSRC under Grant EP/G042705/1 Increased Reliability for Industrially Relevant Automatic Crack Growth Simulation with the eXtended Finite Element Method and (2) the European Research Council Starting Independent Research Grant (ERC Stg Grant Agreement No. 279578) entitled Towards real time multiscale simulation of cutting in non-linear materials with applications to surgical simulation and computer guided surgery”.


  • Finite elements
  • Functionally graded
  • Gradient index
  • Isogeometric analysis
  • Reissner Mindlin plate
  • Shear locking

ASJC Scopus subject areas

  • Ceramics and Composites
  • Civil and Structural Engineering


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