{"title":"Determination of Elastoplastic State of an Anisotropic Medium Weakened by a Horizontal Elliptic Cavity under Mass Forces","authors":"S. V. Matveev, A. N. Matveeva, A. H. Alexandrov","doi":"10.1134/S002565442560179X","DOIUrl":null,"url":null,"abstract":"<p>The paper studies the stress state of a heavy anisotropic space weakened by a horizontal cavity. The problem is solved using the small parameter method. In the initial zero approximation, the material is considered to be ideally plastic, not possessing anisotropy properties. Such problem parameters as hole ellipticity and mass forces, and material anisotropy are taken into account in the first approximation.</p><p>During the study, analytical expressions were obtained for the stress components in the elastic and plastic regions, and the boundary of the elastic-plastic zone was also determined. The influence of anisotropy and material mass forces on the stress state of the medium is shown.</p><p>The obtained solutions can be used to assess the stability of underground structures, calculate the stress state of rock massifs and other problems of continuum mechanics.</p>","PeriodicalId":697,"journal":{"name":"Mechanics of Solids","volume":"60 3","pages":"1707 - 1712"},"PeriodicalIF":0.9000,"publicationDate":"2025-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mechanics of Solids","FirstCategoryId":"5","ListUrlMain":"https://link.springer.com/article/10.1134/S002565442560179X","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MECHANICS","Score":null,"Total":0}
引用次数: 0
Abstract
The paper studies the stress state of a heavy anisotropic space weakened by a horizontal cavity. The problem is solved using the small parameter method. In the initial zero approximation, the material is considered to be ideally plastic, not possessing anisotropy properties. Such problem parameters as hole ellipticity and mass forces, and material anisotropy are taken into account in the first approximation.
During the study, analytical expressions were obtained for the stress components in the elastic and plastic regions, and the boundary of the elastic-plastic zone was also determined. The influence of anisotropy and material mass forces on the stress state of the medium is shown.
The obtained solutions can be used to assess the stability of underground structures, calculate the stress state of rock massifs and other problems of continuum mechanics.
期刊介绍：
Mechanics of Solids publishes articles in the general areas of dynamics of particles and rigid bodies and the mechanics of deformable solids. The journal has a goal of being a comprehensive record of up-to-the-minute research results. The journal coverage is vibration of discrete and continuous systems; stability and optimization of mechanical systems; automatic control theory; dynamics of multiple body systems; elasticity, viscoelasticity and plasticity; mechanics of composite materials; theory of structures and structural stability; wave propagation and impact of solids; fracture mechanics; micromechanics of solids; mechanics of granular and geological materials; structure-fluid interaction; mechanical behavior of materials; gyroscopes and navigation systems; and nanomechanics. Most of the articles in the journal are theoretical and analytical. They present a blend of basic mechanics theory with analysis of contemporary technological problems.
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