Buckling of unilaterally constrained plates: Applications to the study of delaminations in layered structures

Journal of the Franklin Institute

Volumn 335, Issue 6, 1998, Pages 1009-1039

  Shahwan, Khaled W ^a   Waas, Anthony M ^b  

^a Automated Analysis Corporation   (United States)

^b UNIVERSITY OF MICHIGAN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; BUCKLING; CONSTRAINT THEORY; DEFORMATION; DELAMINATION; FOUNDATIONS; GALERKIN METHODS; MATHEMATICAL MODELS; NONLINEAR EQUATIONS; STIFFNESS; STRUCTURAL ANALYSIS;

CLASSICAL PLATE THEORY; KIRCHHOFF-LOVE HYPOTHESIS; MOIRE METHOD;

PLATES (STRUCTURAL COMPONENTS);

EID: 0032137867     PISSN: 00160032     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0016-0032(97)00053-7     Document Type: Article

References (29)

1. Allan, T., One-way buckling of a compressed strip under lateral loading. J. Mech. Engrg. Sci., 1968, Vol. 10(2), 173-181.
2. Anderson, W. F., Buckling of a strip on a rigid half-space with a transverse pressure: Wrinkling of non-bonded cladding. In Proceedings of the First International Conference on Structural Mechanics in Reactor Technology, Berlin, Germany, 1972, Vol. 2, Part C, pp. 123-144.
3. Yun, H. D. and Kyriakides, S., Localized buckling of a heavy beam on a contacting surface: A model for beam mode buckling of buried pipelines. Engineering Mechanics Research Laboratory, EMRL report No. 83/5, Dept. of Aerospace Engineering and Engineering Mechanics, University of Texas, Austin, TX, 1983.
4. Wang, C. Y., Buckling and postbuckling of the lying sheet. Internat. J. Solids Structures, 1984, Vol. 20(4), 351-358.
5. Hobbs, R. E., Discussion of: 'Buckling and postbuckling of the lying sheet (by C. Y. Wang)'. Internat. J. Solids Structure, 1985, 21(4), 423-424; Author's reply to R. E. Hobbs, Internat. J. Solids Structure, 1985, 21(4), 425.
6. Hobbs, R. E., Discussion of: 'Buckling and postbuckling of the lying sheet (by C. Y. Wang)'. Internat. J. Solids Structure, 1985, 21(4), 423-424; Author's reply to R. E. Hobbs, Internat. J. Solids Structure, 1985, 21(4), 425.
7. Roorda, J., Buckles, bulges and blow-ups. In Applied Solid Mechanics-2, ed. A. S. Tooth and J. Spence. Elsevier, London, 1988, pp. 347-380.
8. Plaut, R. H. and Mróz, Z., Uni-directional buckling of a pinned elastica with external pressure. Internat. J. Solids Structures, 1992, Vol. 29(16), 2091-2100.
9. Villaggio, P., Buckling under unilateral constraints. Internat. J. Solids Structures, 1979, 15, 193-201.
10. Benson, R., Plate tenting with a one-sided constraint. J. Appl. Mech., 1991, 58, 484-492.
11. Naumann, J., On some unilateral boundary value problems for the von Kármán equations, Part I: The coercive case. Aplikace Matematiky, 1975, 20, 96-125.
12. Naumann, J., On some unilateral boundary value problems in nonlinear plate theory. Beitr. Anal., 1977, 10, 119-134.
13. Chai, H. and Babcock, C., Two dimensional modeling of compressive failure in delaminated laminates. J. Composite Materials, 1985, 19, 67-98.
14. Chai, H., Buckling and post-buckling behavior of elliptical plates: Part I - Analysis. J. Appl. Mech., 1990, 57, 981-988. See also Part II - Results. J. Appl. Mech., 1990, 57, 989-994.
15. Chai, H., Buckling and post-buckling behavior of elliptical plates: Part I - Analysis. J. Appl. Mech., 1990, 57, 981-988. See also Part II - Results. J. Appl. Mech., 1990, 57, 989-994.
16. Do, C., The buckling of a thin elastic plate subjected to unilateral Conditions. In Applications of Methods of Functional Analysis to Problems of Mechanics, ed. P. Germain and B. Naijroles. Lecture Notes in Mathematics, Vol. 503, Springer, Berlin, 1976.
17. Do, C., Bifurcation theory for elastic plates subjected to unilateral conditions. J. Math. Anal. Appl., 1977, 60, 435-448.
18. Kubrusly, R. S. and Oden, J. T., Nonlinear eigenvalue problems characterized by variational inequalities with applications to the postbuckling of unilaterally-supported plates. Nonlinear Anal., 1981, Vol. 5(12), 1265-1284.
19. Ohtake, K., Oden, J. T. and Kikuchi, N., Analysis of certain unilateral problems in von Kármán plate theory by a penalty method, Part 2: Approximation and numerical analysis. Comput. Meth. Appl. Mech. Engrg., 1980, 24, 317-337.
20. Burgess, I. W., The buckling of a radially constrained imperfect circular ring. Internat. J. Mech. Sci., 1971, 13, 741-753.
21. Celep, Z., Rectangular plates resting on tensionless elastic foundation. J. of Engrg. Mech. Proc. ASCE, 1988, Vol. 114(12), 2083-2092.
22. Farshad, M. and Shahinpoor, M., Beams on bilinear elastic foundations. Internat. J. Mech. Sci., 1972, 14, 441-445.
23. Tsai, N. and Westmann, R., Beams on tensionless foundation. J. Engrg. Mech. Div. Proc. ASCE, 1967, 93, 1-12.
24. Ohtake, K., Oden, J. T. and Kikuchi, N., Analysis of certain unilateral problems in von Kármán plate theory by a penalty method, Part 1: A variational principle with penalty. Comput. Methods Appl. Mech. Engrg., 1980, 24, 187-213.
25. Seide, P., Compressive buckling of a long simply supported plate on an elastic foundation. J. Aeronaut. Sci., 1958, 25, 382-392.
26. Shahwan, K. and Waas, A., Elastic buckling of infinitely long specially orthotropic plates on tensionless foundations. Trans ASME J. Engrg. Mater. Technol., 1991, 113, 396-403 (Errata in Vol. 114, pp. 124-125).
27. Powell, M. J. D., A hybrid method for nonlinear equations. In Numerical Methods for Nonlinear Algebraic Equations, ed. P. Rabinowitz. Gordon and Breach, New York, 1970, Ch. 6.
28. Gerard, G. and Becker, H., Handbook of Structural Stability. I: Buckling of Flat Plates. NACA TN 3781, 1957.
29. Comiez, J., Waas, A. M. and Shahwan, K. W., Delamination buckling; experiment and analysis. Int. J. Solids Structures, 1995, 32(6/7), 767-782.