Variational principles in anisotropic and nonhomogeneous elastokinetics
Author:
M. Ben-Amoz
Journal:
Quart. Appl. Math. 24 (1966), 82-86
MSC:
Primary 73.49
DOI:
https://doi.org/10.1090/qam/195329
MathSciNet review:
195329
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Abstract: Variational principles are formulated in terms of polarization stresses and strains in anisotropic and nonhomogeneous elastokinetics. The principles correspond to the well-known principles of Reissner and Washizu and are shown to produce, under suitable subsidiary conditions, functional which are a generalization to elastokinetics of the Hashin-Shtrikman functional in elastostatics.
- Z. Hashin and S. Shtrikman, On some variational principles in anisotropic and non-homogeneous elasticity, J. Mech. Phys. Solids 10 (1962), 335–342. MR 147031, DOI https://doi.org/10.1016/0022-5096%2862%2990004-2
- R. Hill, New derivations of some elastic extremum principles, Progress in Applied Mechanics, Macmillan, New York, 1963, pp. 99–106. MR 0160359
- Eric Reissner, On a variational theorem in elasticity, J. Math. Physics 29 (1950), 90–95. MR 0037702
- 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
K. Washizu, On the variational principles of elasticity and plasticity, Aeroelastic and Structure Res. Lab., MIT, 1955
Z. Hashin and S. Shtrikman, On some variational principles in anisotropic and nonhomogeneous elasticity, J. Mech. Phys. Solids, 10 (1962), pp. 335–342
R. Hill, New derivations of some elastic extremum principles, Progress in Appl. Mech., The Prager Anniversary Vol., Macmillan Co., 1963, p. 99
E. Reissner, On a variational theorem in elasticity, J. Math. Phys. 29 (1950), pp. 90–95
E. Reissner, On variational principles in elasticity, Proc. Symposia Appl. Math., vol.8, Mc Graw-Hill Book Co., New York, 1958, p. 1
K. Washizu, On the variational principles of elasticity and plasticity, Aeroelastic and Structure Res. Lab., MIT, 1955
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Article copyright:
© Copyright 1966
American Mathematical Society
