Decay estimates for the constrained elastic cylinder of variable cross section
Authors:
J. N. Flavin, R. J. Knops and L. E. Payne
Journal:
Quart. Appl. Math. 47 (1989), 325-350
MSC:
Primary 73C02; Secondary 73C10, 73C20
DOI:
https://doi.org/10.1090/qam/998106
MathSciNet review:
998106
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Y. Biollay, First boundary value problem in elasticity: Bounds for the displacement in Saint-Venant’s principle, ZAMP 31, 556–567 (1980)
H. D. Block, A class of inequalities, Proc. Amer. Math. Soc. 8, 853–859 (1957)
J. H. Bramble and L. E. Payne, Bounds for solutions of second order partial differential equations, Contribution to Differential Equations 1, 95–127 (1963)
H. Brezis and J. A. Goldstein, Liouville theorems for some improperly posed problems. Improperly Posed Boundary Value Problems. (Conf. Univ. New Mexico, Albuquerque N.M., 1974.) Res. Notes in Math. 1, Pitman, London, 1975, pp. 65–75
L. Cesari, Asymptotic Behaviour and Stability Problems in Ordinary Differential Equations, Springer-Verlag, Berlin, 1971
G. Fichera, Remarks on Saint-Venant’s principle, The I. N. Vekua Anniversary Volume, 1977
G. Fichera, Il principio di Saint-Venant: Intuizone dell’ingegnere e rigore del matematico, Rend. di Matematica 10 (VI), 1–24 (1977)
J. N. Flavin and R. J. Knops, Some spatial decay estimates in continuum mechanics, J. Elast. 17, 249–264 (1987)
J. N Flavin and R. J. Knops, Some decay and other estimates in two-dimensional linear elastostatics, Quart. J. Mech. Appl. Math. 41, 223–238 (1988)
J. N. Flavin and R. J. Knops, Some convexity considerations for a two-dimensional traction problem, ZAMP 39, 166–176 (1988)
G. P. Galdi, R. J. Knops, and S. Rionero, Asymptotic behaviour in the nonlinear elastic beam, Arch. Rat. Mech. Anal. 87, 305–318 (1985)
J. A. Goldstein and A. Lubin, On bounded solutions of nonlinear differential equations in a Hilbert space, SIAM J. Math. Anal. 5, 837–840 (1974)
J. K. Hale, Ordinary Differential Equations, Wiley-Interscience, New York, 1969
E. Hille, Lectures on Ordinary Differential Equations, Addison-Wesley, New York, 1969
C. O. Horgan and J. K. Knowles, Recent developments concerning Saint-Venant’s principle, Advances in Applied Mechanics 23 (1983)
D. S. Kinderlehrer, A relation between semi-inverse and Saint-Venant solutions for prisms, SIAM J. Math. Anal. 17, 626–640 (1986)
K. Kirchgässner and J. Scheurle, Saint-Venant’s principle from a dynamical point of view, Preprint, Stuttgart, 1987
R. J. Knops and L. E. Payne, A Saint-Venant principle for nonlinear elasticity, Arch. Rat. Mech. Anal. 81, 1–12 (1983)
J. K. Knowles, An energy estimate for the biharmonic equation and its application to Saint-Venant’s principle in plane elastostatics, Indian J. Pure Appl. Math. 14, 791–805 (1983)
P. Ladeveze, Sur le principle de Saint-Venant en élasticité, J. de Mécanique Théorique et Appliquée 1, 161–184 (1983)
H. A. Levine, On the uniqueness of bounded solutions to $u’\left ( t \right ) = A\left ( t \right )u\left ( t \right ) and u”\left ( t \right ) = A\left ( t \right )u\left ( t \right )$ in Hilbert space, SIAM J. Math. Anal. 4, 250–259 (1973)
V. G. Maz’ya and B. A. Plamenevskiǐ, On properties of solutions of three-dimensional problems of elasticity theory and hydrodynamics in domains with isolated singular points, Dinamika Sploshnoi Sredi Vyp. 50, 99–120 (1981). English transl. in Amer. Math. Soc. Transl. (2), 123, 109–123 (1984)
O. A. Oleinik and G. A. Yosifian, On the asymptotic behaviour at infinity of solutions of linear elasticity, Arch. Rat. Mech. Anal. 78, 29–53 (1982)
M. Protter and H. F. Weinberger, Maximum Principles in Differential Equations, Prentice-Hall, New Jersey, 1967
R. A Toupin, Saint-Venant’s principle, Arch. Rat. Mech. Anal. 18, 83–96 (1965)
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© Copyright 1989
American Mathematical Society
