{"title":"Some boundary value problems for a micropolar porous elastic body","authors":"R. Janjgava, B. Gulua, S. Tsotniashvili","doi":"10.24423/AOM.3504","DOIUrl":null,"url":null,"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.","PeriodicalId":8280,"journal":{"name":"Archives of Mechanics","volume":"72 1","pages":"485-509"},"PeriodicalIF":1.1000,"publicationDate":"2020-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Archives of Mechanics","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.24423/AOM.3504","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATERIALS SCIENCE, CHARACTERIZATION & TESTING","Score":null,"Total":0}
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.
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.
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