Nonlinear bending and free vibration analyses of metal-ceramic functionally graded plates by 2-D natural element method

Abstract

Metal-ceramic functionally graded materials (FGMs) have attracted much attention in the recent years thanks to their excellent properties. Accordingly the intensive studies have focused on FGMs to investigate their thermo-mechanical behaviors. However, most of studies were restricted to the linear behavior with the assumption of small strain and small amplitude. Thus, the nonlinear deformation theory is prerequisite for the problems characterized by large deflection and large amplitude. In this context, this study intends to develop a nonlinear numerical method for solving the large deflection bending and free vibration problems. The proposed method is developed in the framework of 2-D natural element method (NEM) by adopting the von Kármán type nonlinearity and the (1, 1, 0) hierarchical model. A load incremental Newton-Raphson iterative equation system is derived for nonlinear bending problems, and a three-step direct iterative scheme is proposed to solve the nonlinear free vibration. The reliability of the proposed numerical method is verified by comparing with the reference methods. And, the nonlinear characteristics of bending deformation and free vibration of metal-ceramic FG plates are investigated by the proposed method. © 2021, The Korean Society of Mechanical Engineers and Springer-Verlag GmbH Germany, part of Springer Nature.