Quantification of various reduced order modelling computational methods to study deflection of size-dependent plates.

Methods of reduced order modelling (ROM) of nonlinear PDEs to ODEs based on investigation of flexible arbitrary geometry of the plan nano-plates have been reviewed, modified, and employed. The modified von Kármán equations serve as the paradigmatic object of investigation. They are derived in the framework of the modified coupled stress theory with the inclusion of the von Kármán geometric nonlinearity. The elliptic type PDEs are reduced to a system of ODEs using several methods, and the results are compared in order to quantify them for rectangular nano-plates. The following ROM methods have been used: Fourier method of separation of variables, the Kantorovich-Vlasov method (KVM), the variational iterations method (VIM) known as the extended Kantorovich method (EKM), the Agranovskii–Baglai–Smirnov method (ABSM) in combination with the KVM and VIM. We have found that the solutions obtained by combining VIM with the ABSM can be considered exact solutions of the von Kármán equations. The convergence of the developed iterative procedures is justified by a number of theorems for the static analysis of nanoplates on a rectangular plane. [ABSTRACT FROM AUTHOR]