Nonlinear bending response of functionally graded nanobeams with material uncertainties

136To investigate the effect of material uncertainties on mechanical behaviors of nanobeam made of functionally graded (FG) materials, a non-probabilistic uncertainty modeling for the FG nanobeam is developed, which not only takes the uncertainties into account, but also can be degenerated into the deterministic model. Meanwhile, an iterative algorithm based interval analysis method (IA-IAM) with high accuracy is proposed for the numerical solution of the non-probabilistic uncertainty modeling. Furthermore, the combined effects of material uncertainties and size-dependent parameters as well as the power-law index of the FG material on the nonlinear bending response of the FG nanobeam are studied in detail. The non-probabilistic uncertainty modeling is appropriate to address uncertain material properties with limited measured data. And the proposed IA-IAM has the advantage of accurately predicting the lower and upper bounds (LB, UB) of the nonlinear bending deflection of the FG nanobeam.