, Volume 49, Issue 1, pp 155–168 | Cite as

Static and vibration analysis of functionally graded beams using refined shear deformation theory

  • Thuc P. Vo
  • Huu-Tai Thai
  • Trung-Kien Nguyen
  • Fawad Inam


Static and vibration analysis of functionally graded beams using refined shear deformation theory is presented. The developed theory, which does not require shear correction factor, accounts for shear deformation effect and coupling coming from the material anisotropy. Governing equations of motion are derived from the Hamilton’s principle. The resulting coupling is referred to as triply coupled axial-flexural response. A two-noded Hermite-cubic element with five degree-of-freedom per node is developed to solve the problem. Numerical results are obtained for functionally graded beams with simply-supported, cantilever-free and clamped-clamped boundary conditions to investigate effects of the power-law exponent and modulus ratio on the displacements, natural frequencies and corresponding mode shapes.


Functionally graded beams Refined shear deformation theory Triply coupled response Finite element model 



The third author gratefully acknowledges financial support from Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 107.02-2012.07, and from University of Technical Education Ho Chi Minh City.


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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Thuc P. Vo
    • 1
    • 2
  • Huu-Tai Thai
    • 3
  • Trung-Kien Nguyen
    • 4
  • Fawad Inam
    • 2
  1. 1.School of EngineeringGlyndŵr UniversityWrexhamUK
  2. 2.Faculty of Engineering and EnvironmentNorthumbria UniversityNewcastle upon TyneUK
  3. 3.Department of Civil and Environmental EngineeringHanyang UniversitySeoulRepublic of Korea
  4. 4.Faculty of Civil Engineering and Applied MechanicsUniversity of Technical EducationHo Chi Minh CityVietnam

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