A comparative study of two representative wrinkling theories, a bifurcation theory and a tension field theory, is carried out for quantitative evaluation of the tension field theory regarding wrinkling analysis. Results obtained from the bifurcation theory show the limitations of tension field theory on the wrinkling analysis. Existence of compressive stresses caused by wrinkling phenomena, which is not accounted for tension field theory, is quantitatively presented. Considering strain energy due to these compressive stresses and geometrical boundary constraints, it is clarified that there are regions, in which the tension field theory is not properly applied.
Issue Section:
Technical Papers
1.
Johnston, J., and Lienard, S., 2001, “Modeling and Analysis of Structural Dynamics for a One-Tenth Scale Model NSGT Sunshield,” Paper No. AIAA-2001-1407.
2.
Murphey, T. W., Murphey, D. W., Mikulas, M. M., and Adler, A. L., 2002, “A Method to Quantify the Thrust Degradation Effects of Structural Wrinkles in Solar Sails,” Paper No. AIAA-2002-1560.
3.
Johnston, J., 2002, “Finite Element Analysis of Wrinkled Membrane Structures for Sunshield Applications,” Paper No. AIAA-2002-1456.
4.
Blandino, J. R., Johnston, J. D., Miles, J. J., and Soplop, J. S., 2001, “Thin Film Membrane Wrinkling due to Mechanical and Thermal Loads,” Paper No. AIAA-2001-1345.
5.
Roddeman
, D. G.
, Drukker
, J.
, Oomens
, C. W. J.
, and Janssen
, J. D.
, 1987
, “Wrinkling of Thin Membranes: Part I—Theory; Part II—Numerical Analysis
,” ASME J. Appl. Mech.
, 54
, pp. 884
–892
.6.
Adler, A. L., Mikulas, M. M., and Hedgepeth, J. M., 2000, “Static and Dynamic Analysis of Partially Wrinkled Membrane Structures,” Paper No. AIAA-2000-1810.
7.
Kang
, S.
, and Im
, S.
, 1997
, “Finite Element Analysis of Wrinkling Membrane
,” ASME J. Appl. Mech.
, 64
, pp. 263
–269
.8.
Kang
, S.
, and Im
, S.
, 1999
, “Finite Element Analysis of Dynamic Response of Wrinkling Membranes
,” ASME J. Appl. Mech.
, 173
, pp. 227
–240
.9.
Yang, B., and Ding, H., 2002, “A Two-Viable Parameter Membrane Model for Wrinkling Analysis of Membrane Structures,” Paper No. AIAA-2002-1460.
10.
Wu
, C. H.
, 1974
, “The Wrinkled Axisymmetric Air Bags Made of Inextensible Membrane
,” ASME J. Appl. Mech.
, 41
, pp. 963
–968
.11.
Stein, M. S., and Hedgepeth, J. M., 1961, “Analysis of Partly Wrinkled Membrane,” NASA TN D-813.
12.
Mikulas, M. M., 1964, “Behavior of a Flat Stretched Membrane Wrinkled by the Rotation of an Attached Hub,” NASA TN D-2456.
13.
Li
, X. Li
, and Steigmann
, D. J.
, 1993
, “Finite Plane Twist of an Annular Membrane
,” Q. J. Mech. Appl. Math.
, 46
, pp. 601
–625
.14.
Miyamura
, T.
, 2000
, “Wrinkling of Stretched Circular Membrane Under In-Plane Torsion: Bifurcation Analysis and Experiments
,” Eng. Struct.
, 20
, pp. 1407
–1425
.15.
Miyamura, T., 1995, “Bifurcation Analysis and Experiment for Wrinkling on Stretched Membrane,” Doctoral dissertation, Univ. of Tokyo (in Japanese).
16.
Iwasa, T., Natori, M. C., Noguchi, H., and Higuchi, K., 2003, “Geometrically Nonlinear Analysis on Wrinkling Phenomena of a Circular Membrane,” The Membrane Structures Association of Japan, Research Report on Membrane Structures, (16), pp. 7–14 (in Japanese); also International Conference on Computational Experimental Engineering Sciences (ICCES’03), Corfu, Greece.
17.
Iwasa
, T.
, Natori
, M. C.
, and Higuchi
, K.
, 2003
, “Numerical Study on Wrinkling Properties of a Circular Membrane
,” Journal of JSASS
, 51
(591
591
) (in Japanese).18.
Iwasa
, T.
, Natori
, M. C.
, and Higuchi
, K.
, 2003
, “Comparative Study on Bifurcation Theory and Tension Field Theory for Wrinkling Analysis
,” J Struct. Eng.
, 49B
, pp. 319
–326
(in Japanese).19.
Dean
, W. R.
, 1924
, “The Elastic Stability of an Annular Plate
,” Proc. R. Soc. London, Ser. A
, 106
, pp. 268
–284
.20.
Bucciarelli
, L. L.
, 1969
, “Torsional Stability of Shallow Shells of Revolution
,” AIAA J.
, 7
, pp. 648
–653
.21.
Bathe
, K.-J.
, and Dvorkin
, E. N.
, 1986
, “A Formation of General Shell Elements–The Use of Mixed Interpolation of Tensorial Components
,” Int. J. Numer. Methods Eng.
, 22
, pp. 697
–722
.22.
Bathe
, K.-J.
, and Dvorkin
, E. N.
, 1985
, “Short Communication a Four-Node Plate Bending Element Based on Mindlin/Reissner Plate Theory and a Mixed Interpolation
,” Int. J. Numer. Methods Eng.
, 21
, pp. 367
–383
.23.
Bucalem
, M. L.
, and Bathe
, K.-J.
, 1993
, “Higher-Order MITC General Shell Elements
,” Int. J. Numer. Methods Eng.
, 36
, pp. 3729
–3754
.24.
Chapell
, D.
, and Bathe
, K.-J.
, 1998
, “Fundamental Considerations for the Finite Element Analysis of Shell Structures
,” Comput. Struct.
, 66
(1
), pp. 19
–36
.25.
Bathe
, K.-J.
, Iosilevich
, A.
, and Chapelle
, D.
, 2000
, “An Evaluation of the MITC Shell Elements
,” Comput. Struct., 75.26.
Taylor, R. L., “FEAP-A Finite Element Analysis Program Version 7.3 User Manual,” http://www.ce.berkeley.edu/∼rlt/.
27.
Noguchi
, H.
, and Hisada
, T.
, 1992
, “An Efficient Formulation for a Shell Element Considering Finite Rotation Increments and Its Assessment
,” Trans. Jpn. Soc. Mech. Eng.
, 58
(550
550
) (in Japanese).28.
Libai, A., and Simmonds, J. G., 1998, The Nonlinear Theory of Elastic Shells, 2nd Ed., Cambridge University Press, New York, pp. 276–280, 431–441.
Copyright © 2004
by ASME
You do not currently have access to this content.