A modified couple stress theory for buckling analysis of S-FGM nanoplates embedded in Pasternak elastic medium

摘要

Based on a modified couple stress theory, a model for sigmoid functionally graded material (S-FGM) nanoplates on elastic medium is developed. The two main advantages of the modified couple stress theory over the classical couple stress theory are the inclusion of asymmetric couple stress tensor and the involvement of only one material length scale parameter. Analytical solution for buckling analysis of S-FGM nanoplates on elastic medium is presented. The present models contain one material length scale parameter and can capture the size effect, and two-constituent material variation through the plate thickness. The governing equations are derived from minimum total potential energy principle based on a modified couple stress theory, and the power law variation of the material through the thickness of the plate. Material properties of functionally graded plate are assumed to vary according to two power law distribution of the volume fraction of the constituents. It is assumed that the elastic medium is modeled as Pasternak elastic medium. Buckling response of rectangular S-FGM nanoplates is derived, and the obtained results are compared well with reference solutions. The effects of power law index, small scale coefficient, aspect ratio, side-to-thickness ratio, loading types, and elastic medium parameter on the buckling load of S-FGM nanoplates have been discussed.