Unsymmetric wrinkling of circular plates
Authors:
L. S. Cheo and Edward L. Reiss
Journal:
Quart. Appl. Math. 31 (1973), 75-91
DOI:
https://doi.org/10.1090/qam/99710
MathSciNet review:
QAM99710
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Abstract: The branching of unsymmetric equilibrium states from axisymmetric equilibrium states for clamped circular plates subjected to a uniform edge thrust and a uniform lateral pressure is analyzed in this paper. The branching process is called wrinkling and the loads at which branching occurs are called wrinkling loads. The nonlinear von Kármán plate theory is employed. The wrinkling loads are determined by solving numerically the eigenvalue problem obtained by linearizing about a symmetric equilibrium state. The post-wrinkling behavior is studied by a perturbation expansion in the neighborhood of the wrinkling loads.
T. von Kármán, Festigkeitsprobleme in Maschinenbau, Ency. Math. Wiss. 4, 348–352, Teubner, Leipzig, 1910
- Michael Yanowitch, Non-linear buckling of circular elastic plates, Comm. Pure Appl. Math. 9 (1956), 661–672. MR 88200, DOI https://doi.org/10.1002/cpa.3160090403
- Nai-Chien Huang, Unsymmetrical buckling of thin shallow spherical shells, Trans. ASME Ser. E. J. Appl. Mech. 31 (1964), 447–457. MR 171437
- 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
- K. O. Friedrichs and J. J. Stoker, Buckling of the circular plate beyond the critical thrust, J. Appl. Mech. 9 (1942), A-7–A-14. MR 0006323
N. F. Morozov, Investigation of a circular symmetric compressible plate with a large boundary load, Izv. Vyssh. Ucheb. Zav. 34, 95–97 (1963)
- Herbert B. Keller and Edward L. Reiss, Iterative solutions for the non-linear bending of circular plates, Comm. Pure Appl. Math. 11 (1958), 273–292. MR 98504, DOI https://doi.org/10.1002/cpa.3160110302
- Edward L. Reiss, A uniqueness theorem for the nonlinear axisymmetric bending of circular plates, AIAA J. 1 (1963), 2650–2652. MR 189330, DOI https://doi.org/10.2514/3.2142
T. von Kármán, E. E. Sechler and L. H. Donnell, The strength of thin plates in compression, Trans. A.S.M.E. 54, APM 53–57 (1932)
- D. Yu. Panov and V. I. Feodos′ev, On the equilibrium and instability of sloping shells with large deflections, Akad. Nauk SSSR. Prikl. Mat. Meh. 12 (1948), 389–406 (Russian). MR 0026896
- W. Piechocki, On the existence of solutions for heated non-linear orthotropic and non-homogeneous shallow shells, Arch. Mech. Stos. 21 (1969), 813–825 (English, with Russian and Polish summaries). MR 262668
T. von Kármán, Festigkeitsprobleme in Maschinenbau, Ency. Math. Wiss. 4, 348–352, Teubner, Leipzig, 1910
M. Yanowitch, Non-linear buckling of circular plates, Comm. Pure Appl. Math. 9, 661–672 (1956)
N. C. Huang, Unsymmetrical buckling of thin shallow spherical shells, J. Appl. Mech. 31, 447–457 (1964)
L. Bauer, E. L. Reiss and H. B. Keller, Axisymmetric buckling of hollow spheres and hemispheres, Comm. Pure Appl. Math. 23, 529–568 (1970)
K. O. Friedrichs and J. J. Stoker, Buckling of the circular plate beyond the critical thrust, J. Appl. Mech. 9, A7-A14 (1942)
N. F. Morozov, Investigation of a circular symmetric compressible plate with a large boundary load, Izv. Vyssh. Ucheb. Zav. 34, 95–97 (1963)
H. B. Keller and E. L. Reiss, Iterative solutions for the non-linear bending of circular plates, Comm. Pure Appl. Math. 11, 273–292; Non-linear bending and buckling of circular plates, Proc. 3rd U. S. Nat. Cong. of Appl. Mech. 375–385 (1958)
E. L. Reiss, A uniqueness theorem for the non-linear axisymmetric bending of circular plates, AIAA Jour. 1, 2650–2652 (1963)
T. von Kármán, E. E. Sechler and L. H. Donnell, The strength of thin plates in compression, Trans. A.S.M.E. 54, APM 53–57 (1932)
D. Panov and V. Feodosev, Equilibrium and loss of stability of shallow shells with large deflections, P.M.M. 12, 389–406 (1948)
W. Piechocki, On the non-linear theory of thin elastic spherical shells, Arch. Mech. Stos. 21, 81–101 (1969)
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Article copyright:
© Copyright 1973
American Mathematical Society
