Size-dependent vibration and stability of moderately thick functionally graded micro-plates using a differential quadrature-based geometric mapping scheme

In this paper, we propose a novel differential quadrature-based geometric mapping scheme to address the C1-continuity requirements of the in-plane and out-of-plane kinematic quantities of a couple stress-based Mindlin–Reissner functionally graded (FG) plate model. This mapping scheme is combined with the minimum total potential energy principle to construct a four-node size-dependent plate element being free of shape functions with 20 degrees of...