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Plane thermal stresses around holes under steady distribution of temperature

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Summary

A method for determining the plane thermal stress distribution in a multiply connected region under steady distribution of temperature is presented. The analysis is based on the complex variable approach and permits, if the thermal field is known, the simple determination of theKolosoff functions. The method is illustrated using two examples.

Zusammenfassung

Es wird eine Methode zur Bestimmung des ebenen Wärmespannungszustandes in einem mehrfach zusammenhängenden Bereich unter stationärer Temperaturverteilung angegeben. Die Analyse benützt die komplexe Darstellung und erlaubt die einfache Bestimmung derKolosoff-Funktionen, wenn das Temperaturfeld bekannt ist. Die Methode wird anhand von zwei Beispielen illustriert.

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Abbreviations

c :

constant which take valuesc=αE/(1−ν) for plane strain and

c :

αE for plane stress

Re{}:

real part of

u, v :

components of displacement vector

T :

temperature

z :

complex variable (x+i y)

α:

coefficient of thermal expansion

ζ:

complex variable in a mapped plane

η:

boundary value ofz or ζ

κ:

Kolosoffs constant which takes values κ=3−4ν for plane strain and κ=(3−ν)/(1+ν) for plane stress

μ:

shear modulus of elasticity

ν:

Poissons ratio

σxx,σyy,σxy :

components of stress tensor

ω (ζ):

mapping function

References

  1. Ugodtschikov, A. G.: A Method of Solving the Plane Problem of Thermoelasticity. Prikladnaja Mechanica, Vol. III,2, 99–105 (1967) (Russian).

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  2. Muskhelishvili, N. I.: Some Basic Problems of the Theory of Elasticity. Moscow, Nauka, 1966 (Russian).

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  3. Florence, A. L. andJ. N. Goodier: Thermal Stresses Due to Disrurbance of Uniform Heat Flow by an Insulated Ovaloid Hole. J. Appl. Mech.27, 635–639 (1960).

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  4. Deresiewicz, H.: Thermal Stresses in a Plate Due to Disturbance and Uniform Heat Flow by a Hole of General Shape. J. Appl. Mech.28, 147–149 (1961).

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Authors and Affiliations

  1. Technical University Prague, Faculty of Technical and Nuclear Physics, Křemencova 10, Prague 1, ČSSR

    M. Svoboda

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  1. M. Svoboda
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Svoboda, M. Plane thermal stresses around holes under steady distribution of temperature. Acta Mechanica 6, 232–238 (1968). https://doi.org/10.1007/BF01170387

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  • DOI: https://doi.org/10.1007/BF01170387

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