Buckling analysis of non-uniform thickness nanoplates in an elastic medium using the isogeometric analysis

The paper presents a new numerical approach for buckling analysis of non-uniform thickness nanoplates in an elastic medium using the isogeometric analysis (IGA). By ignoring the van der Waals interaction between two adjacent plates, non-uniform thickness nanoplates are described as a single-layered graphene sheet. The governing differential equation of the nanoplates is derived by the nonlocal theory in which the nonlocal stress-strain relation is used to capture the nonlocal mechanics caused by small size effects. The governing equation is then discretized into algebraic equations and solved by using IGA procedure to determine the critical buckling load. By using the non-uniform rational B-splines, IGA easily satisfies the required continuity of the partial differential equations in buckling analysis. Several numerical examples are solved and compared with those of previous publications to illustrate the performance of IGA for buckling analysis of nanoplates.