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

IF 0.8 Q2 MATHEMATICS
A. D. Tebyakin, T. V. Yakovleva, A. V. Krysko
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Abstract

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.

Abstract Image

使用变量迭代法分析受水文机械荷载作用的多孔弹塑性尺寸相关板的应力应变状态
摘要 在本研究中,首次构建了多孔弹塑性尺寸相关板应力-应变状态的数学模型,并考虑了水文机械载荷。提出并开发了一种独创的算法。它采用了高精度的变异迭代法(VIM)或扩展康托洛维奇法(EKM)。考虑到弹塑性变形、介质湿度和孔隙率,该算法被用于研究多孔金属基尔霍夫板的应力应变状态。修正耦合应力理论(MCST)用于考虑尺寸效应。所开发的算法包括两个嵌套的一对一迭代程序:变量迭代法和伯杰弹性参数可变法(MVEP)。每种迭代法都有定理证明其收敛性。弹塑性变形是利用塑性变形理论来考虑的。与网格法、变分法和有限元法得出的结果相比,所提出的数学模型和所开发的算法精度高、计算速度快。分析了取决于尺寸参数值的三种孔隙率模式和水分含量对应力应变状态的影响。
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来源期刊
CiteScore
1.50
自引率
42.90%
发文量
127
期刊介绍: Lobachevskii Journal of Mathematics is an international peer reviewed journal published in collaboration with the Russian Academy of Sciences and Kazan Federal University. The journal covers mathematical topics associated with the name of famous Russian mathematician Nikolai Lobachevsky (Lobachevskii). The journal publishes research articles on geometry and topology, algebra, complex analysis, functional analysis, differential equations and mathematical physics, probability theory and stochastic processes, computational mathematics, mathematical modeling, numerical methods and program complexes, computer science, optimal control, and theory of algorithms as well as applied mathematics. The journal welcomes manuscripts from all countries in the English language.
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