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Symmetry and bifurcation in three-dimensional elasticity

Part III: Stressed reference configurations

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References

  • J. Ball & D. Schaeffer [1982]. Bifurcation and stability of homogeneous equilibrium configurations of an elastic body under dead-load tractions (preprint).

  • S. Bharatha & M. Levinson [1978]. Signorini's perturbation scheme for a general reference configuration in finite elastostatics, Arch. Rational Mech. Anal. 67, 365–394.

    Google Scholar 

  • G. Capriz & P. Podio Guidugli [1979]. The role of Fredholm conditions in Signorini's Perturbation Method, Arch. Rational Mech. Anal. 70, 261–288.

    Google Scholar 

  • D. Chillingworth, J. Marsden & Y. Wan [1982]. Symmetry and bifurcation in three dimensional elasticity, Part I. Arch. Rational Mech. Anal. 80, 295–331.

    Google Scholar 

  • D. Chillingworth, J. Marsden & Y. Wan [1983]. Symmetry and bifurcation in three dimensional elasticity, Part II. Arch. Rational Mech. Anal. 83, 362–395.

    Google Scholar 

  • D. Ebin & J. Marsden [1970]. Groups of diffeomorphisms and the motion of an incompressible fluid, Ann. of Math. 92, 102–163.

    Google Scholar 

  • G. Fichera [1972]. Existence theorems in elasticity, Handbuch der Physik, VIa/2, 347–389, C. Truesdell, ed., Springer-Verlag.

  • T. Fraenkel [1965]. Critical manifolds of the classical groups and Stiefel manifolds, in Differential and Combinatorial Topology, S. S. Cairns, ed., Princeton University Press.

  • M. Golubitsky & J. Marsden [1983]. The Morse lemma in infinite dimensions via singularity theory, SIAM J. Math. Anal. (to appear).

  • M. Golubitsky & D. Schaeffer [1979]. Imperfect bifurcation in the presence of symmetry, Commun. Math. Phys. 67, 205–232.

    Google Scholar 

  • G. Grioli [1962]. Mathematical Theory of Elastic Equilibrium, Ergebnisse der Angew. Math. 7, Springer-Verlag.

  • M. Gurtin [1972]. The linear theory of elasticity, in Handbuch der Physik VIa/2, 1–295. C. Truesdell, ed., Springer-Verlag.

  • W. Y. Hsiang [1975]. Cohomology theory of topological transformation groups, Springer-Verlag.

  • J. Marsden & T. Hughes [1983]. The Mathematical Foundations of Elasticity, Prentice-Hall.

  • J. Marsden & Y. H. Wan [1983]. Linearization stability and Signorini series for the traction problem in elastostatics, Proc. Roy. Soc. Edinburgh (to appear).

  • V. Poénaru [1976]. Singularités C en Présence de Symétrie. Lecture Notes in Math. 510, Springer-Verlag.

  • S. Ramanujam [1969]. Morse theory of certain symmetric spaces. J. Diff. Geometry 3, p. 213–229.

    Google Scholar 

  • D. H. Sattinger [1979]. Group theoretic methods in bifurcation theory. Lecture Notes in Math. 762, Springer-Verlag.

  • A. Signorini [1930]. Sulle deformazioni termoelastiche finite, Proc. 3rd Int. Cong. Appl Mech. 2, 80–89.

    Google Scholar 

  • F. Stoppelli [1958]. Sulla esistenza di soluzioni delle equazioni dell'elastostatica isoterma nel caso di sollecitazioni dotate di assi di equilibrio. Richerche Mat. 6 (1957), pp. 241–287, 7, (1958), 71–101, 138–152.

    Google Scholar 

  • A. Tromba [1976]. Almost Riemannian structure on Banach manifolds, the Morse lemma and the Darboux theorem, Can. J. Math. 28, 640–652.

    Google Scholar 

  • C. Truesdell & W. Noll [1965]. The non-linear field theories of mechanics, Handbuch der Physik III/3, S. Flügge, ed., Springer.

  • Y. H. Wan [1983]. Symmetry and bifurcation in incompressible elasticity (preprint).

  • C.-C. Wang & C. Truesdell [1973]. Introduction to Rational Elasticity, Noordhoff.

  • G. Wasserman [1974]. Stability of unfoldings, Springer Lecture Notes in Math. 393.

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Communicated by S. Antman

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Wan, Y.H., Marsden, J.E. Symmetry and bifurcation in three-dimensional elasticity. Arch. Rational Mech. Anal. 84, 203–233 (1983). https://doi.org/10.1007/BF00281519

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