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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>

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Determination of Elastoplastic State of an Anisotropic Medium Weakened by a Horizontal Elliptic Cavity under Mass Forces

  • 期刊论文

  • 发表日期：

    2025年6月1日

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  • S. V. Matveev,
  • A. N. Matveeva,
  • A. H. Alexandrov

摘要

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.