Thermal shock in an elastic body with a spherical cavity
Authors:
Eli Sternberg and J. G. Chakravorty
Journal:
Quart. Appl. Math. 17 (1959), 205-218
MSC:
Primary 73.00
DOI:
https://doi.org/10.1090/qam/107424
MathSciNet review:
107424
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Abstract: This investigation aims at the dynamic thermoelastic response of an infinite medium with a spherical cavity to a sudden uniform change in the temperature of its internal boundary. By means of the Laplace transform, a closed solution to this problem—exact within classical elastokinetics—is obtained in terms of error functions of real and complex arguments. The ensuing temperature stresses are compared with the corresponding quasi-static results.
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T. Mura, Thermal strain and stresses in transient state, Proc. Second Japan Congr. Appl. Mech. 9 (1952)
- V. I. Danilovskaya, On a dynamical problem of thermo-elasticity, Akad. Nauk SSSR. Prikl. Mat. Meh. 16 (1952), 341–344 (Russian). MR 0048273
- Eli Sternberg and J. G. Chakravorty, On inertia effects in a transient thermoelastic problem, J. Appl. Mech. 26 (1959), 503–509. MR 0118104
B. A. Boley, Thermally induced vibrations of beams, J. Aero. Sci. 23, 2, 179 (1956)
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H. Jeffreys, On the cause of oscillatory movement in seismograms, Monthly Notices, Roy. Astron. Soc., Geo-phys. Suppl. 2, 8, 410 (1931)
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V. I. Danilovskaya, Thermal stresses in an elastic half-space due to a sudden heating of its boundary (in Russian), Prikl. Mat. Mekh. 14, 316 (1950)
T. Mura, Thermal strain and stresses in transient state, Proc. Second Japan Congr. Appl. Mech. 9 (1952)
V. I. Danilovskaya, On a dynamical problem of thermoelasticity (in Russian), Prikl. Mat. Mekh. 16, 3,341 (1952)
Eli Sternberg and J. G. Chakravorty, On inertia effects in a transient thermoelastic problem, Technical Report, Office of Naval Research, Contract Nonr 562(25), Brown University, May 1958. To appear in a future issue of the J. Appl. Mech.
B. A. Boley, Thermally induced vibrations of beams, J. Aero. Sci. 23, 2, 179 (1956)
B. A. Boley and A. D. Barber, Dynamic response of beams and plates to rapid heating, J. Appl. Mech. 24, 3, 413 (1957)
W. Nowacki, A dynamical problem of thermoelasticity, Nadb. Arch. Mech. Stos. 9, 325 (1957)
J. Ignaczak, Thermal displacements in an elastic semi-space due to a sudden heating of the boundary plane, Nadb. Arch. Mech. Stos. 9, 4, 395 (1957)
Eli Sternberg, Transient thermal stresses in an infinite medium with a spherical cavity, Proc., Koninkl. Nederl. Akad. Wet., Ser. B, 60, 5, 396 (1957)
H. Jeffreys, On the cause of oscillatory movement in seismograms, Monthly Notices, Roy. Astron. Soc., Geo-phys. Suppl. 2, 8, 410 (1931)
H. S. Carslaw and J. C. Jaeger, Conduction of heat in solids, Clarendon Press, Oxford, 1947
Staff of the Bateman Manuscript Project, Higher transcendental functions, vol. 2, McGraw-Hill, New York, 1953
Staff of the Bateman Manuscript Project, Tables of integral transforms I, McGraw-Hill, New York, 1954
G. Grünberg, Über den in einer isotropen Kugel durch ungleichförmige Erwärmung erregten Spannungszustand, Z. Physik 35, 7, 548 (1926)
E. Melan, Mitteilung, Sitzungsbericht der math.-naturwiss. Klasse, Oesterr. Akad. Wiss., Oct. 13, 1955
E. Melan, Wärmespannungen bei der Abkühlung einer Kugel, Acta Physica Austriaca 10, 1-2, 81 (1956)
R. Trostel, Instationäre Wärmespannungen in einer Hohlkugel, Ingenieur-Archiv 24, 6, 373 (1956)
S. Timoshenko and J. N. Goodier, Theory of elasticity, 2nd. ed. McGraw-Hill, New York, 1951
E. L. McDowel and E. Sternberg, Axisymmetric thermal stresses in a spherical shell of arbitrary thickness, J. Appl. Mech. 24, 3, 376 (1957)
Tables of probability functions, vol. 1, New York W.P.A., 1941
J. B. Rosser, Theory and application of
J. B. Rosser, Theory and application of $\int _0^z {{e^{ - {x^2}}}} dx$ and $\int _0^z {e - {p^2}{y^2}dy\int _0^y {{e^{ - x}}^2dx} }$, Mapleton House, New York, 1948.
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Article copyright:
© Copyright 1959
American Mathematical Society