Wrinkling of pre-stressed annular thin films under azimuthal shearing

Mathematics and Mechanics of Solids

Volumn 13, Issue 6, 2008, Pages 513-531

  Coman, Ciprian D ^a   Bassom, Andrew P ^b  

^a UNIVERSITY OF GLASGOW   (United Kingdom)

^b UNIVERSITY OF WESTERN AUSTRALIA   (Australia)

Author keywords

Azimuthal shearing; Singular perturbations; Thin films; WKB techniques; Wrinkling

Indexed keywords

ASYMPTOTIC STABILITY; BIFURCATION (MATHEMATICS); COMPUTER SIMULATION; DIFFERENCE EQUATIONS; DIFFERENTIAL EQUATIONS; DIRECT NUMERICAL SIMULATION; EIGENVALUES AND EIGENFUNCTIONS; LINEAR EQUATIONS; MOLECULAR BEAM EPITAXY; PARAMETER ESTIMATION; SHEARING; THICK FILMS; THIN FILMS; VAPOR DEPOSITION;

AZIMUTHAL SHEARING; BENDING STIFFNESS; BIFURCATION EQUATIONS; DIRECT NUMERICAL SIMULATIONS; EIGEN VALUE PROBLEMS; EIGEN-MODES; GEOMETRICAL FEATURES; LOCALIZED DEFORMATIONS; NEUTRAL STABILITY CURVES; PRE STRESSING; QUALITATIVE BEHAVIOR; SINGULAR PERTURBATION; SINGULAR PERTURBATIONS; THIN PLATES; VARIABLE CO-EFFICIENT; WKB TECHNIQUES; WRINKLING;

DIFFERENTIATION (CALCULUS);

EID: 48349132373     PISSN: 10812865     EISSN: 17413028     Source Type: Journal    
DOI: 10.1177/1081286507077107     Document Type: Article

References (32)

1. Mansfield, E.H. The Bending and Stretching of Plates, Cambridge University Press, Cambridge, 1989.
2. Danielson, D.A. and Natarajan, S. Tension field theory and the stress in stretched skin. Journal of Biomechanics, 8, 135-142 (1975).
3. Friedl, N., Rammerstorfer, F.G. and Fischer, F.D. Buckling of stretched strips. Computers and Structures, 78, 185-190 (2000).
4. Cerda, E. and Mahadevan, L. Geometry and physics of wrinkling. Physical Review Letters, 90, 1-4 (2003).
5. Burton, K. and Taylor, D.L. Traction forces of cytokinesis measured using optically modified elastic substrata. Nature, 385, 450-454 (1997).
6. Géminard, J.C., Bernal, R. and Melo, F. Wrinkle formations in axis-symmetrically stretched membranes. The European Physical Journal E, 15, 117-126 (2004).
7. Wagner, H. Flat sheet metal girders with very thin metal web. Zeitschrift für Flugtechnik Motorluftshiffahrt, 20, 200-207, 227-233, 256-262, 279-284 (1929).
8. Reissner, E. On tension field theory. In Proceedings of the 5th International Congress of Applied Mechanics, pp. 88-92, 1938.
9. Coman, C.D. Edge-buckling in stretched thin films under in-plane bending. Zeitschrift für angewandte Mathematik und Physik (in press).
10. Stein, M. and Hedgepeth, J.M. Analysis of partly wrinkled membranes. Technical Note NASA-TN D-813 (1961).
11. Mikulas, M.M. Behaviour of a flat stretched membrane wrinkled by the rotation of an attached hub. Technical Note NASA-TN D-2456 (1964).
12. Steigmann, D.J. Tension field theory. Proceedings of the Royal Society of London, A429, 141-173 (1990).
13. Pipkin, A.C. The relaxed energy density for isotropic elastic membranes. IMA Journal of Applied Mathematics, 36, 85-89 (1986).
14. Iwasa, T., Natori, M.C. and Higuchi, K. Evaluation of tension field theory for wrinkling analysis with respect to the post-buckling study. ASME Journal of Applied Mechanics, 71, 532-540 (2004).
15. Rimrott, F.P.J. and Cvercko, M. Wrinkling in thin plates due to in-plane body forces, in Inelastic Behaviour of Plates and Shells, pp. 19-48, ed. L. Bevilacqua, R. Feijoo, & R. Valid, Springer, Berlin, 1986.
16. Mansfield, E.H. Gravity-induced wrinkle lines in vertical membranes. Proceedings of the Royal Society of London, A375, 307-325 (1981).
17. Coman, C.D. and Haughton, D.M. Localised wrinkling instabilities in radially stretched annular thin films. Acta Mechanica, 185, 179-200 (2006).
18. Coman, C.D. and Bassom, A.P. On the wrinkling of a pre-stressed annular thin film in tension. Journal of the Mechanics and Physics of Solids (in press).
19. Dean, W.R. The elastic stability of an annular plate. Proceedings of the Royal Society of London, A268, 268-284 (1924).
20. Durban, D. and Stavsky, Y. Elastic buckling of polar-orthotropic annular plates in shear. International Journal of Solids and Structures, 18, 51-58 (1982).
21. Hamada, M. and Harima, T. In-plane buckling of an annular plate. Bulletin of JSME, 29, 1089-1095 (1986).
22. Chang-jun, C. and Xiao-an, L. Buckling and post-buckling of annular plates in shearing (Parts I & II). Computer Methods in Applied Mechanics and Engineering, 92, 157-172, 172-191 (1991).
23. Miyamura, T. Wrinkling on stretched circular membrane under in-plane torsion: Bifurcation analyses and experiments. Engineering Structures, 22, 1407-1425 (2000).
24. Li, X. and Steigmann, D.J. Finite plane twist of an annular membrane. Quarterly Journal of Mechanics and Applied Mathematics, 46, 601-625 (1993).
25. Novozhilov, V.V. The Theory of Thin Shells, Noordhoff, Gröningen, 1959.
26. Freund, L.B. and Suresh, S. Thin Film Materials, Cambridge University Press, Cambridge, 2003.
27. Slaughter, W.S. The Linearized Theory of Elasticity, Birkhäuser, Boston, 2002.
28. Alfutov, N.A. Stability of Elastic Structures, Springer, Berlin, 2000.
29. Collatz, L. Eigenwertprobleme und Ihre Numerische Behandlung, Chelsea Publishing Company, New York, 1948.
30. Drazin, P. and Reid, W. Hydrodynamic Stability, Cambridge University Press, Cambridge, 1981.
31. Lindsay, K.A. and Rooney, C.E. A note on compound matrices. Journal of Computational Physics, 133, 472-477 (1992).
32. Jeffreys, H. Asymptotic Approximations, Clarendon, Oxford, 1968.