Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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



Stretching the circular cylindrical elastic sheet

Author: B. F. Bowman
Journal: Quart. Appl. Math. 38 (1980), 313-322
MSC: Primary 73C20
DOI: https://doi.org/10.1090/qam/592198
MathSciNet review: 592198
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The theory of thin elastic sheets, neglecting bending, is applied to many thin surface problems. The classical theory for these surfaces is inadequate when the strains are small, the surface is unstressed before deformation, and boundary displacements are prescribed. The equations in this case are degenerate. Attempts to solve the exact equations for these elastic membranes have failed for small strains. The purpose of this paper is to determine the behavior of the solution to the exact equations for the elastic surface which is initially a circular cylinder and which is deformed by a uniform pull at the ends keeping the end radii fixed. A resolution of the small-strain behavior both analytically and numerically is of particular importance.

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

  • [1] B. Bowman, Stretching the circular cylindrical elastic sheet, Ph.D. Thesis, Math. Dept., University of Wisconsin (1979) MR 2628675
  • [2] E. Bromberg and J. J. Stoker, Nonlinear theory of curved elastic sheets, Quart. Appl. Math. 3 (1945) MR 0013355
  • [3] A. J. Callegari, H. B. Keller and E. L. Reiss, Membrane buckling: A study of solution multiplicity, Communications on Pure and Appl. Math. 24 (1971) MR 0290638
  • [4] A. J. Callegari and E. L. Reiss, Nonlinear boundary value problems for the circular membrane, Arch, for Rational Mech. and Anal. 31 (1960) MR 0233538
  • [5] A. H. Corneliussen and R. T. Shield, Finite deformation of elastic membranes with application to the stability of an inflated and extended tube, Arch, for Rational Mech. and Anal. 7 (1961) MR 0126993
  • [6] R. Courant and D. Hilbert, Methods of mathematical physics, 1, Intersc. Publ. Inc., New York (1953) MR 0065391
  • [7] T. V. Davies and E. M. James, Nonlinear differential equations, Addison, Wesley Publishing Co. (1966) MR 0199482
  • [8] R. W. Dickey, The plane circular elastic surface under normal pressure, Arch, for Rational Mech. and Anal. 26 (1967) MR 1553496
  • [9] B. Ecke, Z Angew. Mathematica und Mechanik, 7 (1927)
  • [10] A. Foppl, Vorlesungen über technische Mechanik, Bd. 5, G. Teubner, Leipzig (1907)
  • [11] Martin A. Goldberg, An iterative solution for rotationally symmetric nonlinear membrane problems, Inter. J. of Nonlinear Mech. 1 (1966)
  • [12] H. Hencky, Uber den Spannungszustand in kreisrunden Platten, Zeitung Math. Phys. 63 (1915)
  • [13] V. V. Novozhilov, Theory of elasticity, Pergamon Student Ed. (1961) MR 0129194
  • [14] E. Reissner, Rotationally symmetric problems in the theory of thin elastic shells, Third U.S. Nat. Con. of Appl. Mech. (1958) MR 0101672
  • [15] J. J. Stoker, Topics in nonlinear elasticity, Courant Inst, of Math. Sci. Lecture Notes (1964)
  • [16] F. Tricomi, Integral equations, Inter. Publ. Inc., New York (1957) MR 0094665
  • [17] Chien-Heng Wu, On certain integrable nonlinear membrane solutions, Quart, of Appl. Math. 28 (1970)
  • [18] Chien-Heng Wu, On the solutions of a nonlinear membrane problem, SIAM J. of Appl. Math. 18 (1970) MR 0286346

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 73C20

Retrieve articles in all journals with MSC: 73C20

Additional Information

DOI: https://doi.org/10.1090/qam/592198
Article copyright: © Copyright 1980 American Mathematical Society

American Mathematical Society