Modified Couple Stress-Based Third-Order Theory for Nonlinear Analysis of Functionally Graded Beams Academic Article uri icon


  • A microstructure-dependent nonlinear third-order beam theory which accounts for through-thickness power-law variation of a two-constituent material is developed using Hamilton's principle. The formulation is based on a modified couple stress theory, power- law variation of the material, and the von Kármán nonlinear strains. The modified couple stress theory contains a material length scale parameter that can capture the size effect in a functionally graded material beam. The influence of the material length scale parameter on linear bending is investigated. The finite element models are also developed to determine the effect of the geometric nonlinearity and microstructure-dependent constitutive relations on linear and nonlinear response.

author list (cited authors)

  • Arbind, A., Reddy, J. N., & Srinivasa, A. R.

citation count

  • 38

publication date

  • January 1, 2014 11:11 AM


  • Equations Of Motion
  • Functionally Graded Beam
  • General Third-order Beam Theory
  • Modified Couple Stress Theory
  • Nonlinear Finite Element Model
  • Von Karman Nonlinearity