In this paper some problems of finite elastic deformation of thin circular plates are studied. For the problem of a plate without bending stiffness subjected to lateral pressure p and a radial edge force fO, it is shown that there exists a unique solution for all fo>O (tension). In the case fO>O (compression), the solutions are not necessarily unique and branching of solutions takes place. The more complex problem of a plate with bending stiffness is briefly discussed for p = O and fO>O, generalizing a result of small finite deflection theory concerning branching of solutions near the classical buckling loads.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Reissner, E.: On finite deflections of circular plates. Proc.Sympos.Applied Mathematics 1 (1949), 213–219.CrossRefGoogle Scholar
  2. 2.
    Adkins, J.E. and Rivlin, R.S.: Large elastic deformations of isotropic materials, IX. The deformation of thin shells. Phil.Trans.Roy. Soc.Lond. A 244 (1952), 505–531.CrossRefGoogle Scholar
  3. 3.
    Spencer, A.J.M.: The static theory of elasticity. J.Inst.Maths.Applies. 6 (1970), 164–200.CrossRefGoogle Scholar
  4. 4.
    Clark, R.A. and Narayanaswamy, O.S.: Nonlinear membrane problems for elastic shells of revolution. Seventieth Anniversary Symposium on the Theory of Shells to honor Lloyd Hamilton Donnell, Houston, Texas, (1967), 79-110.Google Scholar
  5. 5.
    Dickey, R.W.: The plane circular elastic surface under normal pressure. Arch.Rat.Mech.Anal. 26 (1967), 219–236.CrossRefGoogle Scholar
  6. 6.
    Weinitschke, H.J.: Existenz-und Eindeutigkeitssätze für die Gleichungen der kreisförmigen Membran. Meth.u.Verf.d.math.Phys. 3. (1970), 117–139.Google Scholar
  7. 7.
    Collatz, L.: Funktionalanalysis und Numerische Mathematik. Berlin-Göttingen-Heidelberg, Springer-Verlag 1964.CrossRefGoogle Scholar
  8. 8.
    Weinitschke, H.J.: Endliche Deformationen elastischer Membranen. ZAMM 53 (1973), 89–91.Google Scholar
  9. 9.
    Callegari, A.J., Reiss, E.L. and Keller, H.B.: Membrane buckling: a study of solution multiplicity. Comm.Pure Appl.Math. 24 (1971),499–527.CrossRefGoogle Scholar
  10. 10.
    Dickey, R.W.: Bifurcation problems in nonlinear elasticity. Research Notes in Mathematics 3. London-San Francisco-Melbourne, Pitman Publishing 1976.Google Scholar
  11. 11.
    Keller, J.B., Keller, H.B. and Reiss, E.L.: Buckled states of circular plates. Quart. Appl.Math. 20 (1962), 55–65.Google Scholar

Copyright information

© Springer Basel AG 1977

Authors and Affiliations

  • Hubertus J. Weinitschke
    • 1
  1. 1.Institut für Mathematische Methoden der IngenieurwissenschaftenTechnische Universität BerlinBerlin 12Deutschland

Personalised recommendations