On the solution of mode jumping phenomena in thin-walled shell structures

Computer Methods in Applied Mechanics and Engineering

Volumn 136, Issue 1-2, 1996, Pages 59-92

  Riks, Eduard ^a   Rankin, Charles C ^b   Brogan, Francis A ^b  

^a DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

^b LOCKHEED MARTIN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPACTION; COMPOSITE STRUCTURES; COMPUTER SIMULATION; INTEGRATION; NUMERICAL METHODS; PLATES (STRUCTURAL COMPONENTS); PROBLEM SOLVING;

COMPOSITE CYLINDER; MATCHING CONDITIONS; MODE JUMPING PROBLEM; PATH FOLLOWING METHODS; PLATE STRIP; QUASISTATIC PARTS; THIN WALLED SHELL STRUCTURES; TRANSIENT INTEGRATION METHOD;

SHELLS (STRUCTURES);

EID: 0030247003     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/0045-7825(95)00970-1     Document Type: Article

References (24)

1. M. Stein, Loads and deformations of buckled rectangular plates, NASA Technical Report R-40, National Aeronautics and Space Administration, 1959.
2. M. Stein, The phenomenon of change of buckling patterns in elastic structures, NASA Technical Report R-39, National Aeronautics and Space Administration, 1959.
3. W.J. Supple, Changes of wave-form of plates in the post-buckling range, Int. J. Solids Struct. 6 (1970) 1243-1258.
4. T. Nakamura and K. Uetani, The secondary buckling and post-buckling behaviours of rectangular plates, Int. J. Mech. Sci. 21 (1979) 265-286.
5. H. Suchy, H. Troger and R. Weiss, A numerical study of mode jumping of rectangular plates, ZAMM Z. Angew. Math. u. Mech. 65(2) (1985) 71-78.
6. D. Schaeffer and M. Golubitsky, Boundary conditions and mode jumping in the buckling of a rectangular plate, Commun. Math. Phys. 69 (1979) 209-236.
7. M. Golubitsky and D. Schaeffer, Singularities and Groups in Bifurcation Theory, Volume I, Applied Mathematical Sciences (Springer Verlag, New York, Heidelberg, Tokyo, 1985).
8. W.T. Koiter, On the stability of elastic equilibrium (H.J. Paris Publ., Amsterdam 1945), English translation: Report No. AFFDL-TR-70-25, Air Force Flight Dynamics Lab., Wright Patterson AFB, OH, 1970.
9. W.T. Koiter, Elastic stability and post-buckling behavior, in: R.E. Langer ed., Proc. Symp. on Nonlinear Problems, University of Wisconsin Press, 1963, p. 257.
10. J.M.T. Thompson and G.W. Hunt, A General Theory of Elastic Stability (John Wiley, Chichester, New York, 1973).
11. B. Budiansky, Theory of buckling and postbuckling of elastic structures, in: C.S. Yih, ed., Advances in Applied Mechanics Vol. 14 (Academic Press, New York, 1974).
12. E. Riks, F.A. Brogan and C.C. Rankin, Aspects of the stability analysis of shells, International Conference of Computational Engineering Science, April 10-14, 1988, Atlanta, in: W. B. Krätzig and E. Oñate, eds., Static and Dynamic Stability of Shells, Springer Series in Computational Mechanics (Springer Verlag, Heidelberg, 1990).
13. E. Riks, Progress in collapse analysis, J. Pressure Vessel Technol. 109 (1987) 27-41.
14. E. Riks, Some computational aspects of the stability analysis of nonlinear structures, Comput. Methods Appl. Mech. Engrg. 47 (1984) 219-259.
15. C. Rankin et al., The STAGS user's manual, NASA CONTRACTOR REPORT, to be published.
16. K.C. Park, Evaluating time integration methods for nonlinear dynamic analysis, in: T. Belytschko, J.R. Osias and P.V. Marcal, eds., Finite Element Analysis for Transient Nonlinear Behavior, Applied Mechanics Symposia Series (ASME, New York, 1975).
17. C.C. Rankin, E. Riks, J.H. Starnes and W. Allen Waters, Jr., An experimental and numerical verification of the postbuckling behavior of a composite cylinders in compression, NASA CONTRACTOR REPORT, to be published.
18. D. Shilkrut, Investigation of axisymmetric deformation of geometrically non-linear, rotationally, orthotropic, circular plates, Int. J. Non-Linear Mech. 18(2) (1983) 95-118.
19. D. Shilkrut, Stability and vibration of geometrically nonlinear cylindrically orthotropic circular plates, J. Appl. Mech. 51 (1984) 345-360.
20. D. Shilkrut, The influence of the paths of multiparametrical conservative loading on the behaviour of a geometrically nonlinear deformable elastic body, in: I. Elishakoff, J. Arbocz, C.D. Babcock, Jr. and A. Libai, eds., Buckling of Structures; Theory and Experiment. The Joseph Singer Anniversary Volume (Elsevier, 1988).
21. B.H. Kröplin and D. Dinkler, A creep type strategy used for tracing the load path in elastoplastic postbuckling analysis, Comput. Methods Appl. Mech. Engrg. 32 (1982) 365-376.
22. B.H. Kröplin and D. Dinkler, Eine Methode zur directen Berechnung von Gleichgewichtslagen im Nachbeul-bereich, Ingenieur Archiv 51 (1982) 415-420.
23. C. Petiau and C. Cornuault, Efficient algorithms for post buckling computations, in: R. Glowinsky and J.L. Lions, eds., Computing Methods in Applied Science and Engineering (Elsevier, North Holland, Amsterdam, 1984).
24. V.I. Feodos'ev, On a method of solution of the nonlinear problems of stability of deformable systems, PPM (2) (1963) 265-274.