Size-dependent isogeometric analysis of bi-directional functionally graded microbeams reinforced by graphene nanoplatelets

The size-dependent bending and free vibration of bi-directional functionally graded graphene nanoplatelets reinforced composite (BDFG-GPLRC) microbeams are investigated based on the Timoshenko beam theory and isogeometric analysis (IGA). The modified couple stress theory (MCST) is employed to describe the scale effect of microbeams. GPLs are distributed as power functions along the thickness and axis directions and four types of distribution patterns are taken into account. Employing the minimum potential energy principle and Hamilton’s principle, the government equations are established and solved by IGA. Correctness and accuracy of this method are verified by comparing with a published paper. By means of several numerical examples, the effects of GPL weight fraction, power-law indexes, boundary conditions and scale parameter on bending and free vibration behaviors of BDFG-GPLRC microbeams are studied in detail.