Determination of the stationary temperature field and stresses in the vicinity of a slit possessing heat resistance

Кіт, Г. С.; Podstrigach, Ya. S.

doi:10.1007/bf00714662

Cited by 12 publications

(3 citation statements)

References 1 publication

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“…where h c is defined as the heat conductance coefficient of the crack surfaces [26,27]. The thermally conductive and insulated crack models can be retrieved by letting l r ! '…”

Section: Introductionmentioning

confidence: 99%

Thermoelastic analysis of a cracked orthotropic strip under heat conduction effect of crack interior

Zhong

Wu²,

Liao

2019

Mathematics and Mechanics of Solids

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The problem of a Griffith crack embedded in an orthotropic strip is investigated under a combination of thermal and mechanical loadings. The extended thermal-medium crack model is used to address the effects of thermal conductivity of crack interior on the fracture parameters of concerns. Using the Fourier transform technique, the boundary-value problem is reduced to solving singular integral equations with Cauchy kernel. The closed-form solutions of temperature fields are determined. In solving the elastic fields, the Lobatto–Chebyshev integration formula is applied to discretize the obtained singular integral equations as a system of algebraic equations, which is solved by elaborating an algorithm. Numerical results are reported to illustrate the effects of the thermal conductivity inside crack and the thickness of orthotropic strip on the partial insulation coefficient, the thermal stress intensity factor, and the strain energy density factor. The crack initiation behavior is analyzed according to the normalized strain energy density factor. The observations reveal that the crack-tip thermoelastic fields in an orthotropic strip are dependent on the combined effects of the thermoelastic loadings, the physical and geometrical properties of the material and crack. Some comparisons with the existing works are offered to show the novelty and applicability of the obtained results.

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“…where h c is defined as the heat conductance coefficient of the crack surfaces [26,27]. The thermally conductive and insulated crack models can be retrieved by letting l r ! '…”

Section: Introductionmentioning

confidence: 99%

Thermoelastic analysis of a cracked orthotropic strip under heat conduction effect of crack interior

Zhong

Wu²,

Liao

2019

Mathematics and Mechanics of Solids

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“…In these studies, heat transfer across the crack gap was modelled by the boundary conditions of imperfect thermal contact between crack faces involving the constant thermal conductance of the filler. The same boundary conditions at crack faces were utilized by Kit and Podstrigach [20], Thangjitham and Choi [21] and Zhou et al [22], but the source of the thermal resistance was not mentioned in these works. Kit and Krivtsun [18] and Martynyak et al [23] modelled the effect of a heat-conducting filler of a crack by the thermal resistance R ( x ) = R ( 0 ) 1 − x 2 / c 2 , where c is the semi-width of the crack, x is the coordinate of a point at the crack line and x = 0 is the central point of the crack.…”

Section: Introductionmentioning

confidence: 99%

The thermoelastic contact problem for wavy surfaces with a heat-conducting medium in interface gaps

Chumak

2017

Mathematics and Mechanics of Solids

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This paper presents a study on the thermoelastic contact between a wavy surface and a flat surface in the presence of a heat-conducting interstitial medium in interface gaps. The influence of applied mechanical and thermal loads on the deformation of the gaps is taken into account. The contact problem is reduced to a system of singular integro-differential equations for a temperature jump across the gaps and the height of the gaps. Solutions are obtained for the cases of thermoinsulated and heat-conducting gaps. It is shown that, in contrast to the thermoinsulated gap model, the use of the heat-conducting gap model makes it possible to construct a physically correct solution of the contact problem. It is revealed that the wavy interface with heat-conducting gaps exhibits thermal rectification. The effects of the medium’s thermal conductivity, the pressure and heat flow magnitudes and the waviness amplitude on the effective thermal contact resistance and the level of thermal rectification are analysed.

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“…To take account of the fact that the physical and mechanical properties of the surface layers of bodies may be quite different from such properties in their interior, Ya. S. Pidstryhach proposed modeling these transition zones by intermediate layers [2,5,28,29] and then regarding them as having the properties of transition zones of a thin shell, whose theory is quite well-developed. One could then take account of the influence of these shells on the thermodynamic state of the system of media in contact under general mixed boundary conditions.…”

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confidence: 99%

Characteristics of the creative work of Yaroslav Stepanovych Pidstryhach, member of the Ukrainian National Academy of Sciences

Кіт¹,

Burak²,

Shevchuk³

1999

J Math Sci

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Academician Yaroslav Stepanovych Pidstryhach was a noted scholar and specialist in mechanics, the founder of theoretical modeling in the mechanics of deformable media taking account of their structure and the linking of mechanical and nonmechanical processes. He devoted particular attention to the rote of classical and modern branches of mathematics that are of vital importance in constructing mathematical models for computing, incorporating in those models the latest results in the mechanics of solid media, nonequilibrium thermodynamics, condensed-matter physics and chemistry, electrodynamics, and other related areas. To revive the mathematical schools in L'viv and the Zakhid region of the Ukraine, the L'viv branch of mathematical physics of the Institute of Mathematics was founded and became the basis for the Institute of Applied Problems of Mechanics and Mathematics of the Ukrainian National Academy of Sciences. These institutions became the pillars of the Academy of Sciences in mathematics and mechanics in the region. He invited a number of distinguished scholars in the area of mathematics to work at the Institute.Ya. S. Pidstryhach understood that the high demands of rapid scientific and engineering progress could no longer be satisfied by the results of mechanical studies based on the classical Hooke's law, that the physicomechanical state of individual mechanical structures is determined not only by the mechanical load, but also by a wide range of external actions and interconnected internal processes caused by these actions. As a scholar who reached the intellectual summit of his time, he realized that a more profound knowledge of the hidden laws of nature would require that all scientific researchers understand not just the problems of their own narrow specialties, but also those of related areas and at least the "idiom" of very distant branches of knowledge. This does not mean, of course, that a scientist is required to be a professional in each of these areas; but he must be sufficiently erudite

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Determination of the stationary temperature field and stresses in the vicinity of a slit possessing heat resistance

Cited by 12 publications

References 1 publication

Thermoelastic analysis of a cracked orthotropic strip under heat conduction effect of crack interior

Thermoelastic analysis of a cracked orthotropic strip under heat conduction effect of crack interior

The thermoelastic contact problem for wavy surfaces with a heat-conducting medium in interface gaps

Characteristics of the creative work of Yaroslav Stepanovych Pidstryhach, member of the Ukrainian National Academy of Sciences

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