Theories and analysis of functionally graded beams Articles uri icon

publication date

  • August 2021

start page

  • 1

end page

  • 24


  • 15


  • 11

International Standard Serial Number (ISSN)

  • 2076-3417


  • This is a review paper containing the governing equations and analytical solutions of the classical and shear deformation theories of functionally graded straight beams. The classical, first-order, and third-order shear deformation theories account for through-thickness variation of two-constituent functionally graded material, modified couple stress (i.e., strain gradient), and the von Karman nonlinearity. Analytical solutions for bending of the linear theories, some of which are not readily available in the literature, are included to show the influence of the material variation, boundary conditions, and loads.


  • analytical solutions; beams; classical theory; functionally graded structures; modified couple stress; numerical results; shear deformation theories