Postbuckling analysis of functionally graded nanoplates based on nonlocal theory and isogeometric analysis

Abstract This study aims to investigate the postbuckling response of functionally graded (FG) nanoplates by using the nonlocal elasticity theory of Eringen to capture the size effect. In addition, Reddy’s third-order shear deformation theory is adopted to describe the kinematic relations, while von Kaman’s assumptions are used to account for the geometrical nonlinearity. In order to calculate the effective material properties, the Mori-Tanaka scheme is adopted. Governing equations are derived based on the principle of virtual work. Isogeometric analysis (IGA) is employed as a discretization tool, which is able to satisfy the C 1 -continuity demand efficiently. The Newton-Raphson iterative technique with imperfections is employed to trace the postbuckling paths. Various numerical studies are carried out to examine the influences of gradient index, nonlocal effect, ratio of compressive loads, boundary condition, thickness ratio and aspect ratio on the postbuckling behaviour of FG nanoplates.