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Stresses due to a nucleus of thermo-elastic strain (i) in an infinite elastic solid with spherical cavity and (ii) in a solid elastic sphere

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Abstract

In this paper solutions in series form for the stresses due to a nucleus of thermo-elastic strain in an infinite elastic solid in the presence of a spherical cavity and also in an elastic solid sphere have been found.

Zusammenfassung

Die thermischen Spannungen in einem festen Körper unendlicher Ausdehnung, welcher einen sphärischen Hohlraum enthält, sind bei einer Temperatur von 0°C in Gegenwart eines erhitzten Elementes, das sich in endlichem Abstand vom Hohlraum befindet, hergeleitet worden, wobei zahlenmässige Angaben für die Spannungen und Verschiebungen an der Oberfläche des Hohlraums gemacht werden können. Die Ergebnisse sind mit den entsprechenden, für den zweidimensionalen Fall gültigen Zahlenwerten verglichen worden. Ferner was es möglich, auch für das Problem einer festen Kugel von der Temperatur 0°C und einem erhitzten Kern in ihrem Innern eine Lösung zu finden.

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Abbreviations

x, y, z :

Cartesian coordinates;

r, θ, ϕ:

spherical polar coordinates;

u x ,u y ,u z :

components of displacement in Cartesian coordinates;

u r ,u θ,u ϕ :

components of displacement in spherical coordinates;

σ r , σ θ , σ ϕ , τ ϕθ , τ rϕ , τ θϕ :

components of stress in spherical coordinates;

E :

coefficient of elasticity in stress;

G :

coefficient of elasticity in shear;

α:

coefficient of linear expansion;

ν:

Poisson's ration

References

  1. J. N. Goodier, Phil. Mag.23, 1017 (1937).

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  2. E. Stenberg, R. A. Eubanks, andM. A. Sadowasky,On Axisymmetric Problem of Elasticity Theory for Region Bounded by Two Concentric Spheres, Proc. First nat. Congr. Appl. Mech., June 1951 (The American Society of Mechanical Engineers, 1952), p 209–215.

  3. R. A. Eubanks,Stress Concentrations Due to a Hemispherical Pit on a Free Surface, J. appl. Mech.21, No. 1 (March), 57 (1954).

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Authors and Affiliations

  1. Birla College, Pilani, Rajasthan, India

    Brahma Dev Sharma

Authors
  1. Brahma Dev Sharma
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The following nomenclature has been used in this paper:

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Dev Sharma, B. Stresses due to a nucleus of thermo-elastic strain (i) in an infinite elastic solid with spherical cavity and (ii) in a solid elastic sphere. Journal of Applied Mathematics and Physics (ZAMP) 8, 142–150 (1957). https://doi.org/10.1007/BF01590609

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  • DOI: https://doi.org/10.1007/BF01590609

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