Variational principles for linear coupled thermoelasticity
Authors:
R. E. Nickell and J. L. Sackman
Journal:
Quart. Appl. Math. 26 (1968), 11-26
MSC:
Primary 73.49
DOI:
https://doi.org/10.1090/qam/231576
MathSciNet review:
231576
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Abstract: Several variational principles are derived for the initial-boundary-value problem of fully coupled linear thermoelasticity for an inhomogeneous, anisotropic continuum. A consistent set of field variables is employed and a method based on the Laplace transform is used to incorporate the initial conditions explicitly into the formulation. These principles lend themselves readily to numerical solutions based on an extended Ritz method.
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A. E. H. Love, A treatise on the mathematical theory of elasticity, 4th Ed., Cambridge University Press, 1927
M. A. Biot, Thermoelasticity and irreversible thermodynamics, J. Appl. Phys. 27, 3, 240 (1956)
G. Herrmann, On variational principles in thermoelasticity and heat conduction, Q. Appl. Math. 21, 2, 151 (1963)
Bao-Lian’, Fu, The generalized variational principles of thermoelasticity, Scientia Sinica 13, 9, 1507 (1964) (in Russian)
M. Ben-Amoz, On a variational theorem in coupled thermoelasticity, Trans. ASME, J. Appl. Mech. 32, 4, 943 (1965).
M. E. Gurtin, Variational principles for linear elastodynamics, Arch Rat. Mech. Anal. 16, 1, 34 (1964)
M. E. Gurtin, Variational principles for linear initial-value problems, Q. Appl. Math. 22, 3, 252 (1964)
J. Mikusinski, Operational calculus, Pergamon Press, New York, 1959
O. D. Kellogg, Foundations of potential theory, F. Ungar Publishing Co., New York, 1929
E. C. Titchmarsh, The zeros of certain integral functions, Proc. London Math. Soc. 25, 4, 283 (1926)
J. Ignaczak, A completeness problem for stress equations of motion in the linear elasticity theory, Arch. Mech. Stos. 15, 2, 225 (1963)
Hai-Chang Hu, On some variational principles in the theory of elasticity and the theory of plasticity, Scientia Sinica 4, 1, 33 (1955)
K. Washizu, On the variational principles of elasticity and plasticity, ASRL TR 25-18, Massachusetts Institute of Technology
E. Hellinger, Die allgemeinen ansätze der Mechanik der Kontinua, Encyclopädie der Mathematischen Wissenschaften, 4, parts 4 and 5, 654 (1914)
E. Reissner, On a variational theorem in elasticity, J. Math. Phys. 29, 2, 90 (1950)
A. E. H. Love, A treatise on the mathematical theory of elasticity, 4th Ed., Cambridge University Press, 1927
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© Copyright 1968
American Mathematical Society
