Nonlinear Bending Behavior of Nano-scale Cylindrical Panels Made of FGM Using the VDQ Method

Abstract

In the context of strain gradient theory and 3D elasticity, the bending characteristics of circular cylindrical small-scale panels are studied in both linear and nonlinear regimes. It is considered that the panel is made of functionally graded (FG) material whose properties are estimated by power-law functions. An energy-based approach is presented to derive the governing equations including strain gradient effects and geometrical nonlinearity. The formulation is also presented in a novel matrix form which can be readily applied in numerical methods. The VDQ technique is utilized to directly discretize the energy functional using matrix operators. Then, an efficient numerical approach based on differential operators and the pseudo arc-length continuation algorithm is developed for solving the nonlinear bending problem. Numerical examples are given to investigate the effects of geometrical properties, length scale parameter, and material gradient index on the linear/nonlinear static behavior of FG small-scale panels under various boundary conditions. Besides, comparisons are presented between the results of various theories including MCST and MSGT. The results obtained from the linear and nonlinear models are also compared. © The Author(s), under exclusive licence to Shiraz University 2025.