Computation of localized post buckling in long axially compressed cylindrical shells

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 355, Issue 1732, 1997, Pages 2137-2150

  Lord, G J ^a   Champneys, A R ^a   Hunt, G W ^b  

^a UNIVERSITY OF BRISTOL   (United Kingdom)

^b University of Bath   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 3142520144     PISSN: 1364503X     EISSN: None     Source Type: Journal    
DOI: 10.1098/rsta.1997.0114     Document Type: Article

References (25)

1. Beyn, W.-J. 1990 The numerical computation of connecting orbits in dynamical systems. IMA J. Numer. Analys. 9, 379-405.
2. Champneys, A. R. & Toland, J. F 1993 Bifurcation of a plethora of multi-modal homoclinic orbits fo autonomous Hamiltonian sytems. Nonlinearity 6, 665-772.
3. Devaney, R. L. 1976 Homoclinic orbits in Hamiltonian systems. J. Differ. Equat. 21, 431-438.
4. Doedel, E. & Kernevez, J. P. 1986 AUTO: Software for continuation problems in ordinary differential equations with applications. California Institute of Technology Applied Mathematics Technical Report.
5. Donnell, L. H. 1934 A new theory for buckling of thin cylinders under axial compression and bending. Trans. ASME Aero. Engng 56, 795-806.
6. Donnell, L. H. & Wan, C. C. 1950 Effect of imperfections on buckling of thin cylinders and columns under axial compression. J. Appl. Mech. 49, 73-83.
7. Friedman, M. J. & Doedel, E. J. 1994 Numerical computational of invariant manifolds connecting fixed points. SIAM J. Numer. Analys. 28, 789-808.
8. Golubitsky, M., Marsden, J. & Schaeffer, D. 1984 Bifurcation problems with hidden symmetries. In Partial differential equations and dynamical systems (ed. W. Fitzgibbon), pp. 181-210. Boston, MA: Pitman.
9. Gottlieb, D & Orszag, S. A. 1977 Numerical analysis of spectral methods: theory and applications. Philadelphia, PA: SIAM.
10. Hagstrom, T. M. & Keller, H. B. 1987 Asymptotic boundary conditions and numerical methods for nonlinear elliptic problems on unbounded domains. Math. Comp. 48, 449-470.
11. Hoff, N., Madsen, W. A. & Mayers, J. 1966 Post-buckling equilibrium of axially compressed circular cylindrical shells. AIAA Jl 4, 126-133.
12. Hunt, G. W. 1986 Hidden (a)symmetries of elastic and plastic bifurcation. Appl. Mech. Rev. 39, 1165-1186.
13. Hunt, G. W. & Lucena Neto, E. 1991 Localized buckling in long axially loaded cylindrical shells. J. Mech. Phys. Solids 39, 881-894.
14. Hunt, G. W. & Lucena Neto, E. 1993 Maxwell critical loads for axially loaded cylindrical shells. Trans. ASME 60, 702-706.
15. Hunt, G. W., Bolt, H. M. & Thompson, J. M. T. 1989 Structural localisation phenomena and the dynamical phase-space analogy. Proc. R. Soc. Lond. A 425, 245-267.
16. Hunt, G. W. Lawther, R. & Providência e Costa, P. 1997 Finite element modelling of spatially chaotic structures. Int. J. Numer. Meth. Engng. 40, 2237-2256.
17. Hunt, G. W., Williams, K. A J. & Cowell, R. G. 1986 Hidden symmetry concepts in the elastic buckling of axially loaded cylinders. Int. J. Solids Structures 22, 1501-1515.
18. Kirchgässner, K. 1982 Wave solutions of reversible systems and applications. J. Differ. Equat. 45, 113-127.
19. Koiter, W. T. 1945 On the stability of elastic equilibrium. Ph.D. thesis, University of Delft. (Engl. Transl. Tech. Rep. AFFDL-TR-70-25 Air Force Flight Dyn. Lab. 1970.)
20. Mielke, A. 1991 Hamiltonian and Lagrangian flows on center manifolds: with applications to elliptic variational problems. Springer Lecture Notes in Mathematics, vol. 1489. Berlin: Springer.
21. Sandstede, B. 1997 Convergence estimates for the numerical approximation of homoclinic solutions. IMA J. Numer. Analysis 17, 437-462.
22. Schecter, S. 1993 Numerical computation of saddle - node homoclinic bifurcation points. SIAM J. Numer. Analysis 30, 1155-1178.
23. Wohlever, J. C. & Healey, T. J. 1995 A group theoretic approach to the global-bifurcation analysis of an axially compressed cylindrical-shell. Comp. Meth. Appl. Mech. Engng 122, 315-349.
24. Yamaki, N. 1984 Elastic stability of circular cylindrical shells. Applied Mathematics and Mechanics Series, vol. 27. New York: Elsevier.
25. Yoshimura, Y. 1930 On the mechanism of buckling of a circular clindrical shell under axial compression. NACA Technical Memorandum.