On variational principles in thermoelasticity and heat conduction
Author:
G. Herrmann
Journal:
Quart. Appl. Math. 21 (1963), 151-155
DOI:
https://doi.org/10.1090/qam/161512
MathSciNet review:
161512
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Abstract: The variational principles for displacements, for stresses and for both displacements and stresses in isothermal elasticity are extended to the coupled processes of thermoelasticity and heat conduction in a three-dimensional, anisotropic body. The character of these principles is examined and it is established that in a stable system one is concerned with a minimum, a maximum and a stationary value problem, respectively.
- Eric Reissner, On variational principles in elasticity, Calculus of variations and its applications. Proceedings of Symposia in Applied Mathematics, Vol. VIII, McGraw-Hill Book Co., Inc., New orl-Toronto-London, for the American Mathematical Society, Providence, R.I., 1958, pp. 1–6. MR 0096419
- Eric Reissner, On a variational theorem in elasticity, J. Math. Physics 29 (1950), 90–95. MR 0037702
- M. A. Biot, Thermoelasticity and irreversible thermodynamics, J. Appl. Phys. 27 (1956), 240–253. MR 77441
- G. Herrmann, On a complementary energy principle in linear thermoelasticity, J. Aero. Sci. 25 (1958), 660. MR 102263
G. Herrmann, Energy methods for the analysis of temperature distributions and thermal stresses in structures, Prel. publ. Sixth Congress, Intern. Assoc. Bridge and Structural Eng., Leemann, Zürich, 1960
- M. A. Biot, Variational principles in irreversible thermodynamics with application to viscoelasticity, Phys. Rev. (2) 97 (1955), 1463–1469. MR 70514
- M. A. Biot, Linear thermodynamics and the mechanics of solids, Proceedings of the Third U.S. National Congress of Applied Mechanics, Brown University, Providence, R.I., June 11-14, 1958, American Society of Mechanical Engineers, New York, 1958, pp. 1–18. MR 0102941
E. Reissner, On variational principles in elasticity, Symposium on the calculus of variations and its applications, Proc. Symposia Appl. Math. 8, McGraw-Hill Book Co., New York, 1958
E. Reissner, On a variational theorem in elasticity, J. Math. Phys. 29, 90-95 (1950)
M. A. Biot, Thermoelasticity and irreversible thermodynamics, J. Appl. Phys. 27, 240–253 (1956)
G. Herrmann, On a complementary energy principle in linear thermoelasticity, J. Aero/Space Sciences 25, 660 (1958)
G. Herrmann, Energy methods for the analysis of temperature distributions and thermal stresses in structures, Prel. publ. Sixth Congress, Intern. Assoc. Bridge and Structural Eng., Leemann, Zürich, 1960
M. A. Biot, Variational principles in irreversible thermodynamics with application to viscoelasticity, Physical Review 97, 1463-1469 (1955)
M. A. Biot, Linear thermodynamics and the mechanics of solids, Proc. Third U. S. National Congress Appl. Mechanics, ASME, New York, 1958, pp. 1-18
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Article copyright:
© Copyright 1963
American Mathematical Society
