Buckling and barrelling instabilities on non-linearly elastic columns
Author:
Penny J. Davies
Journal:
Quart. Appl. Math. 49 (1991), 407-426
MSC:
Primary 73H05; Secondary 73G05, 73V25
DOI:
https://doi.org/10.1090/qam/1121674
MathSciNet review:
MR1121674
Full-text PDF Free Access
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Additional Information
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S. Agmon, A. Douglis, and L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I, Comm. Pure Appl. Math. 12, 623–727 (1959)
S. Agmon, A. Douglis, and L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. II, Comm. Pure Appl. Math. 17, 35–92 (1964)
G. Aubert and R. Tahraoui, Sur la faible fermeture de certains ensembles de contraintes an elasticite non-lineaire plane, Arch. Rational Mech. Anal. 97, 33–58 (1987)
J. M. Ball, Discontinuous equilibrium solutions and cavitation in nonlinear elasticity, Philos. Trans. Roy. Soc. Lond. Ser. A 306, 557–611 (1982)
J. M. Ball, Differentiability properties of symmetric and isotropic functions, Duke Math. J. 51, 699–728 (1984)
M. F. Beatty and P. Dadras, Some experiments on the elastic stability of some highly elastic bodies, Internat. J. Engrg. Sci. 14, 233–238 (1976)
M. F. Beatty and D. E. Hook, Some experiments on the stability of circular rubber bars under end thrust, Internat. J. Solids and Stuctures 4 623–635 (1968)
P. J. Davies, Buckling and barrelling instabilities in finite elasticity, J. Elasticity 21, 147–192 (1989)
P. J. Davies, A simple derivation of necessary and sufficient conditions for the strong ellipticity of isotropic hyperelastic materials in plane strain, to appear in J. Elasticity
L. HÖrmander, On the regularity of the solutions of boundary problems, Acta. Math. 99, 225–264 (1958)
L. van Hove, Sur la signe de la variation seconde des integrales multiple a plusieurs fonctions inconnues, Mem. Acad. Roy. Belg. (5) 24 (1949)
J. K. Knowles and E. Sternberg, On the failure of ellipticity of the equations for finite elastostatic plane strain, Arch. Rational Mech. Anal. 63, 321–336 (1977)
J. K. Knowles and E. Sternberg, On the failure of ellipticity and the emergence of discontinuous deformation gradients in plane finite elastostatics, J. Elasticity 8, 329–379 (1978)
M. Levinson, Stability of a compressed neo-Hookean rectangular parallelepiped, J. Mech. Phys. Solids 16, 403–415 (1968)
R. W. Ogden, Non-linear Elastic Deformations, Ellis-Horwood Series: Mathematics and its Applications, Ellis-Horwood Ltd., Chichester, 1984
H. C. Simpson and S. J. Spector, On barrelling instabilities in finite elasticity, J. Elasticity 14, 103–125 (1984)
H. C. Simpson and S. J. Spector, Some monotonicity results for ratios of modified Bessel functions, Quart. Appl. Math. 42, 95–98 (1984)
H. C. Simpson and S. J. Spector, On barrelling for a special material in finite elasticity, Quart. Appl. Math. 42, 99–111 (1984)
H. C. Simpson and S. J. Spector, On the positivity of the second variation in finite elasticity, Arch. Rational Mech. Anal. 98, 1–94 (1987)
H. C. Simpson and S. J. Spector, On bifurcation in finite elasticity: buckling of a rectangular rod, written communication
G. N. Watson, A Treatise on the Theory of Bessel Functions, Cambridge Univ. Press, London, 1922
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Article copyright:
© Copyright 1991
American Mathematical Society
