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
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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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  • [1] Maurice A. Biot, Mechanics of incremental deformations. Theory of elasticity and viscoelasticity of initially stressed solids and fluids, including thermodynamic foundations and applications to finite strain, John Wiley & Sons, Inc., New York-London-Sydney, 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] Chien H. Wu, Plane-strain buckling of cracks in incompressible elastic solids, J. Elasticity 10 (1980), no. 2, 163–177. MR 576165, https://doi.org/10.1007/BF00044501
  • [4] Fritz John, Plane strain problems for a perfectly elastic material of harmonic type, Comm. Pure Appl. Math. 13 (1960), 239–296. MR 0118022, https://doi.org/10.1002/cpa.3160130206
  • [5] J. K. Knowles and Eli Sternberg, On the singularity induced by certain mixed boundary conditions in linearized and nonlinear elastostatics, Internat. J. Solids and Structures 11 (1975), no. 11, 1173–1201. MR 0388930
  • [6] J. K. Knowles and Eli Sternberg, On the failure of ellipticity of the equations for finite elastostatic plane strain, Arch. Rational Mech. Anal. 63 (1976), no. 4, 321–336 (1977). MR 0431861, https://doi.org/10.1007/BF00279991
  • [7] J. K. Knowles and Eli Sternberg, An asymptotic finite-deformation analysis of the elastostatic field near the tip of a crack, J. Elasticity 3 (1973), no. 2, 67–107 (English, with German summary). MR 0475148, https://doi.org/10.1007/BF00045816
  • [8] R. S. Rivlin, Stability of pure homogeneous deformations of an elastic cube under dead loading, Quart. Appl. Math. 32, 265-271 (1974)
  • [9] Chester B. Sensenig, Instability of thick elastic solids, Comm. Pure Appl. Math. 17 (1964), 451–491. MR 0169453, https://doi.org/10.1002/cpa.3160170406
  • [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 (1970), 511–528. MR 0270598, https://doi.org/10.1002/cpa.3160230315
  • [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 (1948), 491–508. MR 0026534, https://doi.org/10.1098/rsta.1948.0003
  • [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] Bifurcation theory and nonlinear eigenvalue problems, Edited by Joseph B. Keller and Stuart Antman, W. A. Benjamin, Inc., New York-Amsterdam, 1969. MR 0241213

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

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