The temperature-dependent thermoelastic problem of an elliptic inhomogeneity embedded in an infinite matrix

Xie, Kunkun; Song, Haopeng; Gao, Cun‐Fa

doi:10.1016/j.ijengsci.2021.103523

Cited by 7 publications

(3 citation statements)

References 22 publications

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“…Assuming that a and b satisfy the condition 22 1 ab  , the Laplace equation above can be simplified as:…”

Section: General Solution Of Three-dimensional Temperature-dependent ...mentioning

confidence: 99%

“…More rigorous calculation has been carried out by some simulation and numerical methods, such as finite element methods [19], 3D J-integral [20], variational method [21], floating random walk Monte-Carlo method and differential transform method , wherein strict analytical derivation is not required. Only very recently, 2D temperature-dependent problem have been analyzed using generalized complex variable method [22]. It is thus highly desirable if closed-form solutions for 3D temperaturedependent problem can be derived.…”

Section: Introductionmentioning

confidence: 99%

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The 3-D problem of temperature and thermal flux distribution around defects with temperature-dependent material properties

2023

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The analytical solution of three-dimensional heat conduction problem, including the temperature and thermal flux fields, is one of the important problems that have not been completely solved in solid mechanics. Considering the temperature dependence of material parameters makes the problem more difficult. In this paper, we first reduce the three-dimensional temperature-dependent heat conduction problem to the solution of three-dimensional Laplace equation by introducing the intermediate function. Then, the generalized ternary function is proposed, and the general solution of three-dimensional Laplace equation is given. Finally, the analytical solutions of three specific problems are obtained and the corresponding temperature-thermal flux fields are discussed. The results show that the thermal flux field of three-dimensional temperature dependent problem is the same as the classical constant thermal conductivity approach result, while the temperature field is different from the classical result. Thermal flux at a planar defect boundary has r-1/2 singularity, and its intensity is proportional to the fourth root of defect width. On the other hand, when blocked by a planar defect, the thermal flux distribution will re-adjusted so that it overflows at the same rate from all parts of the planar defect boundary.

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“…Assuming that a and b satisfy the condition 22 1 ab  , the Laplace equation above can be simplified as:…”

Section: General Solution Of Three-dimensional Temperature-dependent ...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The 3-D problem of temperature and thermal flux distribution around defects with temperature-dependent material properties

2023

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“…Several authors have addressed the problem concerning the deformations of an infinite elastic matrix into which is embedded an isotropic or anisotropic elastic elliptical inhomogeneity (including the two limiting cases in which the inhomogeneity takes the form of an elliptical hole or an elliptical rigid inclusion) and is subjected to prescribed remote uniform heat flux (see, for example, previous works [1][2][3][4][5][6][7][8]). In the context of thermo-anisotropic elasticity, however, certain issues remain.…”

Section: Introductionmentioning

confidence: 99%

Real-form solution for an anisotropic elastic elliptical inhomogeneity under uniform heat flux

Wang

Schiavone

2022

Mathematics and Mechanics of Solids

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We use the extended Stroh sextic formalism for thermo-anisotropic elasticity to present an elegant solution of the problem of an anisotropic elastic elliptical inhomogeneity embedded in an infinite anisotropic elastic matrix subjected to uniform remote heat flux. We prove rigorously that the remote thermal stresses cannot be set to zero in a generally anisotropic elastic matrix. In particular, a real-form solution is derived for the internal thermoelastic field describing stresses, strains, and displacements within the elliptical inhomogeneity.

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Analytical results describing plane thermoelastic fields and effective thermal expansion under the assumption of temperature dependency

Xie,

Song,

Schiavone

et al. 2024

Acta Mech

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The temperature-dependent thermoelastic problem of an elliptic inhomogeneity embedded in an infinite matrix

Cited by 7 publications

References 22 publications

The 3-D problem of temperature and thermal flux distribution around defects with temperature-dependent material properties

The 3-D problem of temperature and thermal flux distribution around defects with temperature-dependent material properties

Real-form solution for an anisotropic elastic elliptical inhomogeneity under uniform heat flux

Analytical results describing plane thermoelastic fields and effective thermal expansion under the assumption of temperature dependency

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