Korn’s constant for a spherical shell
Authors:
Elias Andreou, George Dassios and Demosthenes Polyzos
Journal:
Quart. Appl. Math. 46 (1988), 583-591
MSC:
Primary 73C20; Secondary 49G05, 73L20
DOI:
https://doi.org/10.1090/qam/963592
MathSciNet review:
963592
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Abstract: Upon invoking the variational characterization of Korn’s constant and Dafermos’ technique to reduce it to a boundary value problem, the Korn constant of a spherical shell of arbitrary thickness has been evaluated. The classical result of Payne and Weinberger for the sphere is recovered as the special case of vanishing interior radius, while as the thickness of the shell tends to zero, Korn’s constant tends to infinity in a nonuniform sense.
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M. Gurtin, The linear theory of elasticity, in Handbuch der Physik, Band VIa/2, Berlin, 1972
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- L. E. Payne and H. F. Weinberger, On Korn’s inequality, Arch. Rational Mech. Anal. 8 (1961), 89–98. MR 158312, DOI https://doi.org/10.1007/BF00277432
B. Bernstein and R. A. Toupin, Korn inequalities for the sphere and circle, Arch. Rat. Mech. Anal. 6, 51–64 (1960)
C. Dafermos, Some remarks on Korn’s inequality, Z. Angew. Math. Phys. 19, 913–920 (1968)
R. A. Eubanks and E. Sternberg, On the completeness of the Boussinesq—Papkovich stress functions, J. Rat. Mech. Anal. 5, 735–746 (1956)
M. Gurtin, The linear theory of elasticity, in Handbuch der Physik, Band VIa/2, Berlin, 1972
E. W. Hobson, The theory of spherical and ellipsoidal harmonics, Chelsea, 1955
C. O. Horgan and J. K. Knowles, Eigenvalue problems associated with Korn’s inequalities, Arch. Rat. Mech. Anal. 40, 384–402 (1971)
C. O. Horgan, On Korn’s inequality for incompressible media, SIAM J. Appl. Math. 28, 419–430 (1975)
C. O. Horgan, Inequalities of Korn and Friedrichs in elasticity and potential theory, Z. Angew. Math. Phys. 26, 155–164 (1975)
C. O. Horgan and L. E. Payne, On inequalities of Korn, Friedrichs and Babuška-Aziz, Arch. Rat. Mech. Anal. 82, 165–179 (1983)
L. E. Payne and H. F. Weinberger, On Korn’s inequality, Arch. Rat. Mech. Anal. 8, 89–98 (1961)
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Article copyright:
© Copyright 1988
American Mathematical Society
