Stress-strain State Analysis of Porous Elasto-plastic Size-dependent Plates Subjected to Hygro-Mechanical Loads Using the Variational Iterations Method

In this study, for the first time, a mathematical model of the stress-strain state of porous elasto-plastic size-dependent plates is constructed, taking into account hygro-mechanical loads. An original algorithm is proposed and developed. It uses the highly accurate Variational Iteration Method (VIM) or the Extended Kantorovich Method (EKM). This algorithm is applied to study stress-strain state of porous metallic Kirchhoff’s plates, taking into account elasto-plastic deformations, medium moisture and porosity. Modified Coupled Stress Theory (MCST) is used to account for size-dependent effects. The developed algorithm includes two nested one-to-one iteration procedures: the Variational Iteration Method and Birger’s method of variable elasticity parameter (MVEP). For each of these iterative methods there are theorems proving their convergence. Elasto-plastic deformations are considered using the deformation theory of plasticity. The proposed mathematical model and the developed algorithm provide high accuracy and computational speed in comparison to the results obtained by grid, variational and finite element methods. The effect of three porosity patterns and moisture accounting on the stress-strain state depending on the value of the size-dependent parameter is analysed.