Efficient higher-order shear deformation theories for bending and free vibration analyses of functionally graded plates

Huu Tai Thai, Dong Ho Choi

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In this paper, various efficient higher-order shear deformation theories are presented for bending and free vibration analyses of functionally graded plates. The displacement fields of the present theories are chosen based on cubic, sinusoidal, hyperbolic, and exponential variations in the in-plane displacements through the thickness of the plate. By dividing the transverse displacement into the bending and shear parts and making further assumptions, the number of unknowns and equations of motion of the present theories is reduced and hence makes them simple to use. Equations of motion are derived from Hamilton's principle. Analytical solutions for deflections, stresses, and frequencies are obtained for simply supported rectangular plates. The accuracy of the present theories is verified by comparing the obtained results with the exact three-dimensional (3D) and quasi-3D solutions and those predicted by higher-order shear deformation theories. Numerical results show that all present theories can archive accuracy comparable to the existing higher-order shear deformation theories that contain more number of unknowns.

Original languageEnglish
Pages (from-to)1755-1771
Number of pages17
JournalArchive of Applied Mechanics
Issue number12
Publication statusPublished - 2013 Dec 1



  • Bending
  • Functionally graded plate
  • Higher-order plate theory
  • Vibration

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