Nonlocal and surface effects on the buckling behavior of functionally graded nanoplates: An isogeometric analysis

Highlights: • Isogeometric buckling analysis of FGM nanoplates. • Considering different geometries including circular, elliptical and skew nanoplates. • Considering size influences based on the Eringen and Gurtin–Murdoch theories. • Developing a novel vector-matrix form of formulation with the capability of being easily used in the finite element method or isogeometric analysis. • Investigating nonlocal and surface effects on the buckling responses of nanoplates. The size-dependent static buckling responses of circular, elliptical and skew nanoplates made of functionally graded materials (FGMs) are investigated in this article based on an isogeometric model. The Eringen nonlocal continuum theory is implemented to capture nonlocal effects. According to the Gurtin–Murdoch surface elasticity theory, surface energy influences are also taken into account by the consideration of two thin surface layers at the top and bottom of nanoplate. The material properties vary in the thickness direction and are evaluated using the Mori–Tanaka homogenization scheme. The governing equations of buckled nanoplate are achieved by the minimum total potential energy principle. To perform the isogeometric analysis as a solution methodology, a novel matrix-vector form of formulation is presented. Numerical examples are given to study the effects of surface stress as well as other important parameters on the critical buckling loads of functionally graded nanoplates. It is found that the buckling configuration of nanoplates at small scales is significantly affected by the surface free energy.