Symmetry and bifurcation in three-dimensional elasticity. I. (English) Zbl 0509.73018


74B20 Nonlinear elasticity
74G60 Bifurcation and buckling
74A99 Generalities, axiomatics, foundations of continuum mechanics of solids
74G99 Equilibrium (steady-state) problems in solid mechanics
74H99 Dynamical problems in solid mechanics
Full Text: DOI


[1] J. M. Ball [1977]. Convexity Conditions and Existence Theorems in Nonlinear Elasticity, Ar · Zbl 0368.73040 · doi:10.1007/BF00279992
[2] J. M. Ball, R. J. Knops & J. E. Marsden [1978]. Two examples in nonlinear elasticity, Springer Lecture Notes in Math. # 466, 41–49. · doi:10.1007/BFb0061796
[3] G. Capriz & P. Podio Guidugli [1974]. On Signorini’s Perturbation Method in Nonlinear Elasticity, Ar · Zbl 0315.73062 · doi:10.1007/BF00287095
[4] G. Fichera [1972]. Existence theorems in elasticity, Handbuch der Physik, Bd. V1 a/2, 347–389, Springer-Verlag.
[5] T. Frankel [1965]. Critical submanifolds of the classical groups and Stiefel manifolds, in Differential and Combinatorial Topology, S. S. Cairns (ed.), Princeton University Press. · Zbl 0134.42602
[6] M. Golubitsky & V. Guillemin [1973]. Stable Mappings and Their Singularities, Graduate Texts in Math. # 14, Springer-Verlag. · Zbl 0294.58004
[7] M. Golubitsky & J. Marsden [1982]. The Morse lemma in infinite dimensions via singularity theory (preprint). · Zbl 0525.58013
[8] M. Golubitsky & D. Schaeffer [1979a]. A theory for imperfect bifurcation via singularity theory, Comm. Pure Appl. Math., 32, 21–98. · Zbl 0409.58007 · doi:10.1002/cpa.3160320103
[9] M. Golubitsky & D. Schaeffer [1979b]. Imperfect bifurcation in the presence of symme · Zbl 0467.58019 · doi:10.1007/BF01238845
[10] G. Grioli [1962]. Mathematical Theory of Elastic Equilibrium, Ergebnisse der Ang. Mat. # 67, Springer. · Zbl 0102.17004
[11] J. K. Hale [1977]. Bifurcation near families of solutions, Proc. Int. Conf. on Differential Equations, Uppsala, 91–100.
[12] J. K. Hale & P. Z. Taboas [1980]. Bifurcation near degenerate families, Jou · Zbl 0441.34033 · doi:10.1080/00036818008839316
[13] M. Hirsch [1976]. Differential Topology, Graduate Texts in Math. # 33, Springer-Verlag.
[14] R. Knops & E. Wilkes [1973]. Theory of elastic stability, Handbuch der Physik V1 a/3, C. Truesdell (ed.), Springer-Verlag. · Zbl 0377.73060
[15] J. Marsden & T. Hughes [1978]. Topics in the Mathematical Foundations of Elasticity, in Nonlinear Analysis and Mechanics, Volume II, R. J. Knops (ed.), Pitman.
[16] J. Mather [1969]. Stability of C mappings: II. Ann. of Math. (2) 89, 254–291. · Zbl 0177.26002 · doi:10.2307/1970668
[17] R. Ogden [1977]. Inequalities associated with the inversion of elastic stress-deformation relations and their implications. Math · Zbl 0354.73023 · doi:10.1017/S030500410005338X
[18] R. Palais [1968]. Foundations of Global Non-linear Analysis, Benjamin. · Zbl 0164.11102
[19] S. Ramanujam [1969]. Morse Theory of Certain Symmetric S · Zbl 0196.25006 · doi:10.4310/jdg/1214428826
[20] M. Reeken [1973]. Stability of critical points under small perturba · Zbl 0248.58004 · doi:10.1007/BF01317578
[21] A. Signorini [1930]. Sulle deformazioni termoelastiche finite, Proc. 3r
[22] F. Stoppelli [1958]. Sull’esistenza di soluzioni delle equazioni dell’elastostatica isoterma nel caso di sollecitazioni dotate di assi di e · Zbl 0097.17301
[23] A. J. Tromba [1976]. Almost Riemannian structures on Banach manifolds, the Morse lemma and the Darbou · Zbl 0345.58005 · doi:10.4153/CJM-1976-064-x
[24] C. Truesdell & W. Noll [1965]. The Nonlinear Field Theories of Mechanics, Handbuch der Physik III/3, S. Flügge (ed.), Springer-Verlag.
[25] W. van Buren [1968]. On the Existence and Uniqueness of Solutions to Boundary Value Problems in Finite Elasticity, Thesis, Carnegie-Mellon University; Westinghouse Research Laboratories Report 68-107-MEKMARI.
[26] C. C. Wang & C. Truesdell [1973]. Introduction to Rational Elasticity, Nordhoff.
[27] R. Wasserman [1974]. Stability of Unfoldings. Springer Lecture Notes in Mathematics, # 393.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.