Modified couple stress-based third-order theory for nonlinear analysis of functionally graded beams

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 ...