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Abstract <p>This paper is dedicated to the equations obtained through a self-similar transformation of variables under axisymmetric conditions from the general three-dimensional equations of the mathematical theory of plasticity with the Tresca yield condition and the associated flow rule for the stress states corresponding to an edge of the yield surface. It has been shown that some self-similar solutions can be derived from a single ordinary differential equation involving a root-type irrational term on the right-hand side. Proper substitutions transform this equation to an irrationality-free form, which is classified as the Abel equation of the first kind, that makes it possible to represent its integrals by applying the results of the analytical theory of differential equations.</p>

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On the Canonical Forms of Self-Similar Equations in the Axisymmetric Problem of Plasticity Theory

  • 期刊论文

  • 发表日期：

    2025年9月1日

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  • Y. N. Radayev

摘要

Abstract

This paper is dedicated to the equations obtained through a self-similar transformation of variables under axisymmetric conditions from the general three-dimensional equations of the mathematical theory of plasticity with the Tresca yield condition and the associated flow rule for the stress states corresponding to an edge of the yield surface. It has been shown that some self-similar solutions can be derived from a single ordinary differential equation involving a root-type irrational term on the right-hand side. Proper substitutions transform this equation to an irrationality-free form, which is classified as the Abel equation of the first kind, that makes it possible to represent its integrals by applying the results of the analytical theory of differential equations.