Scholarlink

<p>A&#xa0;linear model of the theory of thermoelasticity for an isotropic body in the cylindrical coordinate system is considered. The stationary temperature satisfies a&#xa0;three-dimensional Laplace equation. The general solution of the system of Navier’s differential equations, which describes the thermoelastic stress state of the body, is presented as a&#xa0;sum of homogeneous and partial solutions. The partial solution, which does not contain elastic displacements, is called the temperature solution. The theorem states that the sum of normal temperature stresses is zero. To solve the Navier’s equations, the temperature is presented as a&#xa0;Fourier-Bessel series, according to which properties the temperature solution of the Navier’s equations is constructed. Analytical formulas for the description of temperature displacements and stresses in explicit form are given. The general solution of the equations of the theory of thermoelasticity in terms of four harmonic functions is presented.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Construction of three-dimensional solutions of equations of the theory of thermoelasticity in the cylindrical coordinate system

  • 期刊论文

  • 发表日期：

    2025年3月1日

查看全文
  • V. P. Revenko

摘要

A linear model of the theory of thermoelasticity for an isotropic body in the cylindrical coordinate system is considered. The stationary temperature satisfies a three-dimensional Laplace equation. The general solution of the system of Navier’s differential equations, which describes the thermoelastic stress state of the body, is presented as a sum of homogeneous and partial solutions. The partial solution, which does not contain elastic displacements, is called the temperature solution. The theorem states that the sum of normal temperature stresses is zero. To solve the Navier’s equations, the temperature is presented as a Fourier-Bessel series, according to which properties the temperature solution of the Navier’s equations is constructed. Analytical formulas for the description of temperature displacements and stresses in explicit form are given. The general solution of the equations of the theory of thermoelasticity in terms of four harmonic functions is presented.