Some boundary value problems for a micropolar porous elastic body

IF 1.1 4区工程技术 Q3 MATERIALS SCIENCE, CHARACTERIZATION & TESTING

Archives of Mechanics Pub Date : 2020-12-16 DOI:10.24423/AOM.3504

R. Janjgava, B. Gulua, S. Tsotniashvili

引用次数: 2

Abstract

The paper reviews the static equilibrium of a micropolar porous elastic material. We assume that the body under consideration is an elastic Cosserat media with voids, however, it can also be considered as an elastic microstretch solid, since the basic differential equations and mathematical formulations of boundary value problems in these two cases are actually identical. As regards the three-dimensional case, the existence and uniqueness of a weak solution of some boundary value problems are proved. The two-dimensional system of equations corresponding to a plane deformation case is written in a complex form and its general solution is presented with the use of two analytic functions of a complex variable and two solutions of the Helmholtz equations. On the basis of the constructed general representation, specific boundary value problems are solved for a circle and an infinite plane with a circular hole.

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微极多孔弹性体的若干边值问题

本文综述了微极性多孔弹性材料的静力平衡问题。我们假设所考虑的物体是具有空隙的弹性Cosserat介质，但它也可以被认为是弹性微拉伸固体，因为这两种情况下边值问题的基本微分方程和数学公式实际上是相同的。对于三维情况，证明了一些边值问题弱解的存在唯一性。利用两个复变量解析函数和两个亥姆霍兹方程的解，将平面变形情况对应的二维方程组写成复形式，给出了其通解。在构造的一般表示的基础上，求解了圆和带圆孔的无限平面的具体边值问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Archives of Mechanics 工程技术-材料科学：表征与测试

CiteScore

1.40

自引率

12.50%

发文量

审稿时长

>12 weeks

期刊介绍： Archives of Mechanics provides a forum for original research on mechanics of solids, fluids and discrete systems, including the development of mathematical methods for solving mechanical problems. The journal encompasses all aspects of the field, with the emphasis placed on: -mechanics of materials: elasticity, plasticity, time-dependent phenomena, phase transformation, damage, fracture; physical and experimental foundations, micromechanics, thermodynamics, instabilities; -methods and problems in continuum mechanics: general theory and novel applications, thermomechanics, structural analysis, porous media, contact problems; -dynamics of material systems; -fluid flows and interactions with solids. Papers published in the Archives should contain original contributions dealing with theoretical, experimental, or numerical aspects of mechanical problems listed above. The journal publishes also current announcements and information about important scientific events of possible interest to its readers, like conferences, congresses, symposia, work-shops, courses, etc. Occasionally, special issues of the journal may be devoted to publication of all or selected papers presented at international conferences or other scientific meetings. However, all papers intended for such an issue are subjected to the usual reviewing and acceptance procedure.