Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

  • [1] M. A. Biot, Mechanics of incremental deformations, Wiley, 1965 MR 0185873
  • [2] 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)
  • [3] C. H. Wu, Plane-strain buckling of cracks in incompressible elastic solids, J. Elasticity 10, 163-177 (1980) MR 576165
  • [4] F. John, Plane-strain problems for a perfectly elastic material of harmonic type, Comm. Pure Appl. Math. 13, 239-296 (1960) MR 0118022
  • [5] 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) MR 0388930
  • [6] 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) MR 0431861
  • [7] 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) MR 0475148
  • [8] R. S. Rivlin, Stability of pure homogeneous deformations of an elastic cube under dead loading, Quart. Appl. Math. 32, 265-271 (1974)
  • [9] C. B. Sensenig, Instability of thick elastic solids, Comm. Pure Appl. Math. 17, 451-491 (1964) MR 0169453
  • [10] J. J. Stoker, Topics on nonlinear elasticity, Lecture Notes, Courant Inst. Math. Sci., New York University, 1964
  • [11] E. Bromberg, Buckling of a very thick rectangular block, Comm. Pure Appl. Math. 23, 511-528 (1970) MR 0270598
  • [12] 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) MR 0026534
  • [13] K. N. Sawyers, Stability of an elastic cube under dead loading, Internat. J. Non-linear Mech. 11, 11-23 (1976)
  • [14] K. N. Sawyers, Material stability and bifurcation in finite elasticity, Finite Elasticity, AMD 27, ASME, 1977
  • [15] E. J. Brunelle, Surface instability due to initial compressive stress, Bulletin of the Seismological Society of America 63, 1885-1893 (1973)
  • [16] J. W. Hutchinson and V. Tvergaard, Surface instabilities on statically strained plastic solids, Internat. J. Mech. Sci. 22, 339-354 (1980)
  • [17] J. F. Dorris and S. Nemat-Nasser, Instability of a layer on a half space, J. Appl. Mech. 102, 304-312 (1980)
  • [18] N. Triantafyllidis and R. Abeyaratne, Instabilities of a finitely deformed fiber reinforced elastic material, to be published
  • [19] J. B. Keller and S. Antman, Bifurcation theory and nonlinear eigenvalue problems, Benjamin, New York, 1969 MR 0241213

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 73H05

Retrieve articles in all journals with MSC: 73H05

Additional Information

DOI: https://doi.org/10.1090/qam/724057
Article copyright: © Copyright 1984 American Mathematical Society

American Mathematical Society