Numerical nonlinear bending analysis of arbitrary-shaped FG-CNT-reinforced composite plates

A unified numerical framework is presented for the nonlinear bending analysis of plates with diverse geometric configurations made of FG CNT-reinforced composite (FGCNTC). The present scheme is based on the variational differential quadrature transform (VDQ-T) method in combination with Reddy’s refined shear-deformation model and incorporating von Kármán-type geometric nonlinearity. The transformation mapping embedded in the VDQ-T enables the same formulation to accommodate any plate geometry or boundary configuration without domain-specific modification. In addition, equations are obtained using a variational principle, and expressed in a compact matrix–vector form, which greatly facilitates numerical implementation and integration with other computational algorithms. The developed approach offers high efficiency and precise convergence relative to standard finite-element methodologies. Numerical results demonstrate the strong impact of CNT dispersion pattern and plate geometry parameters on the deflection and stiffness of FGCNTC plates; CNT‑rich outer surfaces or reduction in plate slenderness yields a noticeable stiffening effect. The present formulation therefore establishes a versatile platform applicable to a wide range of nonlinear analyses of nanocomposite plates with complex geometries.