Buckling problems in finite plane elasticity-harmonic materials
Authors:
Chien H. Wu and Guang Zhong Cao
Journal:
Quart. Appl. Math. 41 (1984), 461-474
MSC:
Primary 73H05
DOI:
https://doi.org/10.1090/qam/724057
MathSciNet review:
724057
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Abstract: Bucklings of biaxially deformed annular, rectangular and arbitrary regions are considered. It is found that for many different configurations the buckling conditions are governed by the same equation $\chi = 0$, where $\chi$ is merely a material function. Furthermore, the buckling solutions are completely unrelated to the buckling loads.
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M. A. Biot, Mechanics of incremental deformations, Wiley, 1965
C. H. Wu, Plane-strain buckling of a crack in a harmonic solid subjected to crack-parallel compression, J. Appl. Mech. 46, 597–604 (1979)
C. H. Wu, Plane-strain buckling of cracks in incompressible elastic solids, J. Elasticity 10, 163–177 (1980)
F. John, Plane-strain problems for a perfectly elastic material of harmonic type, Comm. Pure Appl. Math. 13, 239–296 (1960)
J. K. Knowles and E. Sternberg, On the singularity induced by certain mixed boundary conditions in linearized and nonlinear elastostatics, Internat. J. Solids Struc. 11, 1173–1201 (1975)
J. K. Knowles and E. Sternberg, On the failure of ellipticity of the equations for finite elastostatic plane strains, Arch. Rational Mech. Anal. 63, 321–336 (1977)
J. K. Knowles and E. Sternberg, An asymptotic finite-deformation analysis of the elastostatic field near the tip of a crack, J. Elasticity 3, 67–107 (1973)
R. S. Rivlin, Stability of pure homogeneous deformations of an elastic cube under dead loading, Quart. Appl. Math. 32, 265–271 (1974)
C. B. Sensenig, Instability of thick elastic solids, Comm. Pure Appl. Math. 17, 451–491 (1964)
J. J. Stoker, Topics on nonlinear elasticity, Lecture Notes, Courant Inst. Math. Sci., New York University, 1964
E. Bromberg, Buckling of a very thick rectangular block, Comm. Pure Appl. Math. 23, 511–528 (1970)
R. S. Rivlin, Large elastic deformations of isotropic materials. II. Some uniqueness theorems for pure homogeneous deformation, Philos. Trans. Roy. Soc. London Ser. A 240, 491–508 (1948)
K. N. Sawyers, Stability of an elastic cube under dead loading, Internat. J. Non-linear Mech. 11, 11–23 (1976)
K. N. Sawyers, Material stability and bifurcation in finite elasticity, Finite Elasticity, AMD 27, ASME, 1977
E. J. Brunelle, Surface instability due to initial compressive stress, Bulletin of the Seismological Society of America 63, 1885–1893 (1973)
J. W. Hutchinson and V. Tvergaard, Surface instabilities on statically strained plastic solids, Internat. J. Mech. Sci. 22, 339–354 (1980)
J. F. Dorris and S. Nemat-Nasser, Instability of a layer on a half space, J. Appl. Mech. 102, 304–312 (1980)
N. Triantafyllidis and R. Abeyaratne, Instabilities of a finitely deformed fiber reinforced elastic material, to be published
J. B. Keller and S. Antman, Bifurcation theory and nonlinear eigenvalue problems, Benjamin, New York, 1969
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© Copyright 1984
American Mathematical Society