The Localised Wrinkling of a Stretched Bi-Annular Thin Plate
The wrinkling of a thin elastic bi-annular plate with piecewise-constant mechanical properties, subjected to radial stretching, is considered. The critical wrinkling stretching loading and the corresponding wrinkling patterns are extensively investigated, together with the roles played by both the geometrical and mechanical parameters.
[1] U. Ascher and R. D. Russell. Reformulation of Boundary Value
Problems into "Standard" Form. SIAM Review, 23(2):238-254, 1981.
[2] Winfried Auzinger, Gnter Kneisl, Othmar Koch, and Ewa Weinmller.
Sbvp 1.0 - a matlab solver for singular boundary value problems.
Technical report, Institute for Applied Mathematics and Numerical
Analysis, http://www.math.tuwien.ac.at/ ewa/, 2002.
[3] Winfried Auzinger, Gnter Kneisl, Othmar Koch, and Ewa Weinmller.
A collocation code for singular boundary value problems in ordinary
differential equations. Numerical Algorithms, 33:27-39, 2003.
10.1023/A:1025531130904.
[4] C.D. Coman and A.P. Bassom. On the wrinkling of a pre-stressed
annular thin film in tension. Journal of the Mechanics and Physics
of Solids, 55:1601-1617, 2007.
[5] C.D. Coman and D.M. Haughton. Localised wrinkling instabilities in
radially stretched annular thin films. Acta Mech., 185:179-200, 2006.
[6] C.D. Coman and X. Liu. Buckling-resistant thin annular plates in
tension. 2012. (submitted for publications 2012).
[7] C.D. Coman and X. Liu. Semi-analytical approximations for a class
of multi-parameter eigenvalue problems related to tensile buckling. Z.
angew. Math. Phys., 2012. (accepted, May 2012).
[8] Y Frostig and GJ Simitses. Buckling of multi-annular plates. Computers
& Structures, 24(3):443-454, 1986.
[9] Y Frostig and GJ Simitses. Buckling of ring-stiffened multi-annular
plates. Computers & Structures, 29(3):519-526, 1988.
[10] J. C. G'eminard, R. Bernal, and F. Melo. Wrinkle formations in axissymmetrically
stretched membranes. The European Physical Journal E,
15:117-126, 2004.
[11] Henry Louis Langhaar. Energy methods in applied mechanics. Wiley,
1962.
[12] K. A Lindsay. The application of compound matrices to convection
problems in multi-layered continua. Mathematical Models and Methods
in Applied Sciences, 2(2):121-141, 1992.
[13] X. Liu. On some eigenvalue problems for elastic instabilities in tension.
PhD thesis, University of Glasgow, 2012.
[14] GJ Simitses. Effect of boundary conditions and rigidities on the buckling
of annular plates. Thin-Walled Structures, 5, 1987.
[15] O. Koch W. Auzinger, E. Karner and E. Weinm¨uller. Collocation
methods for the solution of eigenvalue problems for singular ordinary
differential equations. Opuscula Math., 26(2):pp. 229-241, 2006.
[1] U. Ascher and R. D. Russell. Reformulation of Boundary Value
Problems into "Standard" Form. SIAM Review, 23(2):238-254, 1981.
[2] Winfried Auzinger, Gnter Kneisl, Othmar Koch, and Ewa Weinmller.
Sbvp 1.0 - a matlab solver for singular boundary value problems.
Technical report, Institute for Applied Mathematics and Numerical
Analysis, http://www.math.tuwien.ac.at/ ewa/, 2002.
[3] Winfried Auzinger, Gnter Kneisl, Othmar Koch, and Ewa Weinmller.
A collocation code for singular boundary value problems in ordinary
differential equations. Numerical Algorithms, 33:27-39, 2003.
10.1023/A:1025531130904.
[4] C.D. Coman and A.P. Bassom. On the wrinkling of a pre-stressed
annular thin film in tension. Journal of the Mechanics and Physics
of Solids, 55:1601-1617, 2007.
[5] C.D. Coman and D.M. Haughton. Localised wrinkling instabilities in
radially stretched annular thin films. Acta Mech., 185:179-200, 2006.
[6] C.D. Coman and X. Liu. Buckling-resistant thin annular plates in
tension. 2012. (submitted for publications 2012).
[7] C.D. Coman and X. Liu. Semi-analytical approximations for a class
of multi-parameter eigenvalue problems related to tensile buckling. Z.
angew. Math. Phys., 2012. (accepted, May 2012).
[8] Y Frostig and GJ Simitses. Buckling of multi-annular plates. Computers
& Structures, 24(3):443-454, 1986.
[9] Y Frostig and GJ Simitses. Buckling of ring-stiffened multi-annular
plates. Computers & Structures, 29(3):519-526, 1988.
[10] J. C. G'eminard, R. Bernal, and F. Melo. Wrinkle formations in axissymmetrically
stretched membranes. The European Physical Journal E,
15:117-126, 2004.
[11] Henry Louis Langhaar. Energy methods in applied mechanics. Wiley,
1962.
[12] K. A Lindsay. The application of compound matrices to convection
problems in multi-layered continua. Mathematical Models and Methods
in Applied Sciences, 2(2):121-141, 1992.
[13] X. Liu. On some eigenvalue problems for elastic instabilities in tension.
PhD thesis, University of Glasgow, 2012.
[14] GJ Simitses. Effect of boundary conditions and rigidities on the buckling
of annular plates. Thin-Walled Structures, 5, 1987.
[15] O. Koch W. Auzinger, E. Karner and E. Weinm¨uller. Collocation
methods for the solution of eigenvalue problems for singular ordinary
differential equations. Opuscula Math., 26(2):pp. 229-241, 2006.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:61350", author = "Xiang Liu and Ciprian Coman", title = "The Localised Wrinkling of a Stretched Bi-Annular Thin Plate", abstract = "The wrinkling of a thin elastic bi-annular plate with piecewise-constant mechanical properties, subjected to radial stretching, is considered. The critical wrinkling stretching loading and the corresponding wrinkling patterns are extensively investigated, together with the roles played by both the geometrical and mechanical parameters.
", keywords = "bi-annular plate, wrinkling pattern, critical stretching
loading.", volume = "6", number = "11", pages = "1596-6", }
