Minimum energy solution for the spherical shell
Author:
R. W. Dickey
Journal:
Quart. Appl. Math. 48 (1990), 321-339
MSC:
Primary 73K15; Secondary 73H05
DOI:
https://doi.org/10.1090/qam/1052139
MathSciNet review:
MR1052139
Full-text PDF Free Access
Abstract |
References |
Similar Articles |
Additional Information
Abstract: A Galerkin procedure is used to prove the existence of a minimum energy solution for the problem of the spherical shell under constant normal pressure. It is shown that if the pressure is sufficiently small the trivial solution is the minimum energy solution and if the pressure is sufficiently large a nontrivial solution furnishes the minimum energy solution. Bounds are obtained on these critical pressures.
- J. J. Stoker, Nonlinear elasticity, Gordon and Breach Science Publishers, New York-London-Paris, 1968. MR 0413654
- Stuart S. Antman, Existence and nonuniqueness of axisymmetric equilibrium states of nonlinearly elastic shells, Arch. Rational Mech. Anal. 40 (1970/71), 329–372. MR 277152, DOI https://doi.org/10.1007/BF00251796
- Louis Bauer, Edward L. Reiss, and Herbert B. Keller, Axisymmetric buckling of hollow spheres and hemispheres, Comm. Pure Appl. Math. 23 (1970), 529–568. MR 278605, DOI https://doi.org/10.1002/cpa.3160230402
- Charles G. Lange and Gregory A. Kriegsmann, The axisymmetric branching behavior of complete spherical shells, Quart. Appl. Math. 39 (1981/82), no. 2, 145–178. MR 625467, DOI https://doi.org/10.1090/S0033-569X-1981-0625467-4
- Ke-Gang Shih and Stuart S. Antman, Qualitative properties of large buckled states of spherical shells, Arch. Rational Mech. Anal. 93 (1986), no. 4, 357–384. MR 829834, DOI https://doi.org/10.1007/BF00280513
- R. W. Dickey, Nonlinear bending of circular plates, SIAM J. Appl. Math. 30 (1976), no. 1, 1–9. MR 403377, DOI https://doi.org/10.1137/0130001
- N. N. Lebedev, Special functions and their applications, Revised English edition, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1965. Translated and edited by Richard A. Silverman. MR 0174795
- R. Courant and D. Hilbert, Methods of mathematical physics. Vol. I, Interscience Publishers, Inc., New York, N.Y., 1953. MR 0065391
- A. N. Kolmogorov and S. V. Fomin, Elements of the theory of functions and functional analysis. Vol. 1. Metric and normed spaces, Graylock Press, Rochester, N. Y., 1957. Translated from the first Russian edition by Leo F. Boron. MR 0085462
R. A. Askey, Orthogonal polynomials and special function, Regional Conference Series in Applied Math, Vol. 21., SIAM, Philadelphia
J. J. Stoker, Nonlinear Elasticity, Gordon and Breach, New York, 1968
S. S. Antman, Existence and nonuniqueness of axisymmetric equilibrium states of nonlinearly elastic shells, Arch. Rational Mech. Anal 40, 329–373 (1981)
L. Bauer, E. L. Reiss, and H. B. Keller, Axisymmetric buckling of hollow spheres and hemispheres, Comm. Pure and Appl. Math 23, 529–568 (1970)
C. G. Lange and G. A. Kriegsmann, The axisymmetric branching behavior of complete spherical shells, Quart. Appl. Math. 39, 145–178 (1981)
K. G. Shih and S. S. Antman, Qualitative properties of large buckled states of spherical shells, Arch. Rational Mech. Anal. 93, 357–384 (1986)
R. W. Dickey, Nonlinear bending of circular plates, SIAM J. Appl. Math. 30, 1–9 (1976)
N. N. Lebedev, Special Functions and Their Applications, Prentice-Hall, Englewood Cliffs, N.J., 1965
R. Courant and D. Hilbert, Methods of Mathematical Physics, Vol 1., Interscience, New York, 1953
A. N. Kolmogorov and S. V. Fomin, Elements of the Theory of Functions and Functional Analysis, Vol 1., Graylock Press, Rochester, N.Y., 1957
R. A. Askey, Orthogonal polynomials and special function, Regional Conference Series in Applied Math, Vol. 21., SIAM, Philadelphia
Similar Articles
Retrieve articles in Quarterly of Applied Mathematics
with MSC:
73K15,
73H05
Retrieve articles in all journals
with MSC:
73K15,
73H05
Additional Information
Article copyright:
© Copyright 1990
American Mathematical Society
