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<p>We derive a closed-form solution to the two-dimensional thermoelastic problem of an insulated compressible liquid inclusion of arbitrary shape embedded in an infinite isotropic elastic matrix subjected to uniform remote heat flux. When the mapping function which maps the exterior of the liquid inclusion onto the exterior of the unit circle in the image plane contains an arbitrary number <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(N+1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>N</mi> <mo>+</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation> of terms, a modified form of analytic continuation leads to a set of <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(2N-1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>2</mn> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation> coupled linear algebraic equations with quite simple structure. Solving this set of equations allows us to completely determine the internal uniform hydrostatic stress field within the liquid inclusion and the thermoelastic field in the matrix. We apply our results to a variety of different inclusion shapes including two types of deloid, an equilateral triangle, a square and a rectangle to examine the influence of geometry, liquid compressibility, direction of heat flux and the number of terms used in the mapping function on the resulting stress distributions.</p>

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An insulated compressible liquid inclusion of arbitrary shape under uniform heat flux

  • 期刊论文

  • 发表日期：

    2025年12月14日

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  • Romina Ardeshiri Jouneghani,
  • Xu Wang,
  • Peter Schiavone

摘要

We derive a closed-form solution to the two-dimensional thermoelastic problem of an insulated compressible liquid inclusion of arbitrary shape embedded in an infinite isotropic elastic matrix subjected to uniform remote heat flux. When the mapping function which maps the exterior of the liquid inclusion onto the exterior of the unit circle in the image plane contains an arbitrary number \(N+1\) N + 1 of terms, a modified form of analytic continuation leads to a set of \(2N-1\) 2 N - 1 coupled linear algebraic equations with quite simple structure. Solving this set of equations allows us to completely determine the internal uniform hydrostatic stress field within the liquid inclusion and the thermoelastic field in the matrix. We apply our results to a variety of different inclusion shapes including two types of deloid, an equilateral triangle, a square and a rectangle to examine the influence of geometry, liquid compressibility, direction of heat flux and the number of terms used in the mapping function on the resulting stress distributions.