Stress-strain state of a porous flexible rectangular FGM size-dependent plate subjected to different types of transverse loading: Analysis and numerical solution using several alternative methods

Abstract

In this study, a mathematical model of flexible porous functionally graded (PFG) Kirchhoff size-dependent plates on a rectangular plane is constructed. Hamilton's principle provides new size-dependent governing equations, taking into account geometrical nonlinearity according to the model of Theodor von Kármán, as well as boundary conditions and initial conditions for the displacement of the plates. Modified Coupled Stress Theory (MCST) is used to account for size-dependent effects. Numerical investigations analysing the stress-strain state of flexible Kirchhoff functionally graded size-dependent porous plates on a rectangular plane are based on the application of the Variational Iteration Method (VIM) or the Extended Kantorovich Method (EKM). The efficiency and high accuracy of the VIM method are demonstrated. The validity and reliability of the solutions obtained by VIM are discussed and compared with solutions obtained by other methods, such as the BGM in higher approximations, FDM of second-order accuracy and the FEM. Additionally, the solutions are compared with results obtained by other authors in the study of porous functionally graded macro, micro, and nanoplates. The solutions obtained are considered accurate. The results include an analysis of the influence of size-dependent parameters, type of material porosity, porosity index, functionally graded index, and different types of boundary conditions on the stress-strain state of plates under the action of different types of transverse loading.