Asymmetric bifurcations of thick-walled circular cylindrical elastic tubes under axial loading and external pressure

International Journal of Solids and Structures

Volumn 45, Issue 11-12, 2008, Pages 3410-3429

  Zhu, Y ^a   Luo, X Y ^a   Ogden, R W ^a  

^a UNIVERSITY OF GLASGOW   (United Kingdom)

Author keywords

Bifurcation; Elastic stability; Elastic tube; Finite deformation

Indexed keywords

ELASTICITY; MATHEMATICAL MODELS; NUMERICAL METHODS; PRESSURE EFFECTS;

ELASTIC MATERIALS; ELASTIC STABILITY; ELASTIC TUBES;

AXIAL LOADS;

EID: 41649090333     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijsolstr.2008.02.005     Document Type: Article

References (38)

1. Amabili M., and Pai{dotless}̈doussis M.P. Review of studies on geometrically nonlinear vibrations and dynamics of circular cylindrical shells and panels, with and without fluid-structure intersection. Applied Mechanics Reviews 56 (2003) 349-381
2. Bardi F.C., and Kyriakides S. Plastic buckling of circular tubes under axial compression - Part I: Experiments. International Journal of Mechanical Sciences 48 (2006) 830-841
3. Bardi F.C., Kyriakides S., and Yun H.D. Plastic buckling of circular tubes under axial compression - Part II: Analysis. International Journal of Mechanical Sciences 48 (2006) 842-854
4. Batdorf, S.B., 1947. A simplified method of elastic stability analysis for thin cylindrical shells. NACA Report 874.
5. Bertram C.D. Two modes of instability in a thick-walled collapsible tube conveying a flow. Journal of Biomechanics 15 (1982) 223-224
6. Bertram C.D. The effects of wall thickness, axial strain and end proximity on the pressure-area relation of collapsible tubes. Journal of Biomechanics 20 (1987) 863-876
7. Bertram C.D., Raymond C.J., and Pedley T.J. Mapping of instabilities for flow through collapsed tubes of differing length. Journal of Fluids and Structures 4 (1990) 125-153
8. Bertram C.D. The dynamics of collapsible tubes. In: Ellington C.P., and Pedley T.J. (Eds). Biological Fluid Dynamics (1995), The Company of Biologists Limited, Cambridge, UK 253-264
9. Bertram C.D., and Elliot N.S.J. Flow-rate limitation in a uniform thin-walled collapsible tube, with comparison to a uniform thick-walled tube and a tube of tapering thickness. Journal of Fluids and Structures 17 (2003) 541-559
10. Flaherty J.E., Keller J.B., and Rubinow S.I. Post buckling behavior of elastic tubes and rings with opposite sides in contact. SIAM Journal of Applied Mathematics 23 (1972) 446-455
11. Flügge W. Stresses in Shells. Second ed. (1973), Springer, Berlin
12. Gerald C.F., and Wheatley P.O. Applied Numerical Analysis (1984), Addison Wesley, New York
13. Green A.E., Rivilin R.S., and Shield R.T. General theory of small elastic deformations superposed on finite elastic deformations. Proceedings of the Royal Society of London A 211 (1952) 128-154
14. Haughton D.M., and Ogden R.W. On the incremental equations in non-linear elasticity - I. Membrane theory. Journal of the Mechanics and Physics of Solids 26 (1978) 93-110
15. Haughton D.M., and Ogden R.W. On the incremental equations in non-linear elasticity - II. Bifurcation of pressured spherical shells. Journal of the Mechanics and Physics of Solids 26 (1978) 111-138
16. Haughton D.M., and Ogden R.W. Bifurcation of inflated circular cylinders of elastic material under axial loading - I. Membrane theory for thin-walled tubes. Journal of the Mechanics and Physics of Solids 27 (1979) 179-212
17. Haughton D.M., and Ogden R.W. Bifurcation of inflated circular cylinders of elastic material under axial loading - II. Exact theory for thick-walled tubes. Journal of the Mechanics and Physics of Solids 27 (1979) 489-512
18. Heil M. The stability of cylindrical shells conveying viscous flow. Journal of Fluids and Structures 10 (1996) 173-196
19. Heil M., and Pedley T.J. Large post-buckling deformations of cylindrical shells conveying viscous flow. Journal of Fluids and Structures 10 (1996) 565-599
20. Ho B.P.C., and Cheng S. Some problems in stability of heterogeneous aeolotropic cylindrical shells under combined loading. AIAA Journal 1 (1963) 1603-1607
21. Kounadis A.N. Recent advances on postbuckling analyses of thin-walled structures: beams, frames and cylindrical shells. Journal of Constructional Steel Research 62 (2006) 1101-1115
22. Luo X.Y., and Pedley T.J. A numerical simulation of unsteady flow in a 2D collapsible channel. Journal of Fluid Mechanics 314 (1996) 191-225
23. Luo X.Y., and Pedley T.J. The effects of the wall inertia on the 2D collapsible channel flow. Journal of Fluid Mechanics 363 (1998) 253-280
24. Luo X.Y., and Pedley T.J. Flow limitation and multiple solutions in 2D collapsible channel flow. Journal of Fluid Mechanics 420 (2000) 301-324
25. Luo X.Y., Cai Z.X., Li W.G., and Pedley T.J. The cascade structure of linear stabilities of flow in collapsible channels. Journal of Fluid Mechanics 600 (2008) 45-76
26. Marzo A., Luo X.Y., and Bertram C.D. Three-dimensional collapse and steady flow in thick-walled flexible tubes. Journal of Fluids and Structures 20 (2005) 817-835
27. Nash W.A. Buckling of thin cylindrical shells subject to hydrostatic pressure. Journal of the Aeronautical Sciences 21 (1954) 354-355
28. Nowinski J.L., and Shahinpoor M. Stability of an elastic circular tube of arbitrary wall thickness subjected to an external pressure. International Journal of Non-linear Mechanics 4 (1969) 143-158
29. Ogden R.W. Large deformation isotropic elasticity - on the correlation of theory and experiment for incompressible rubberlike solids. Proceedings of the Royal Society of London A 326 (1972) 565-584
30. Ogden R.W. On stress rates in solid mechanics with application to elasticity theory. Proceedings of the Cambridge Philosophical Society 75 (1974) 303-319
31. Ogden R.W. Non-linear Elastic Deformations (1997), Dover Publications, New York
32. Sobel L.H. Effects of boundary conditions on the stability of cylinders subject to lateral and axial pressure. AIAA Journal 2 (1964) 1437-1440
33. von Mises R. Der kritische Außendruck zylindrischer Rohre. VDI Zeitschrift 58 (1914) 750-755
34. Wang A.S.D., and Ertepinar A. Stability and vibrations of elastic thick-walled cylindrical and spherical shells subjected to pressure. International Journal of Non-linear Mechanics 7 (1972) 539-555
35. Weissman M., and Mockros L. The mechanics of a collapsing tube heart pump. International Journal of Mechanical Sciences 9 (1967) 113-121
36. Yamaki N. Buckling of circular cylindrical shells under external pressure. Reports of the Institute of High Speed Mechanics 20 (1969) 35-55
37. Yamaki N. Influence of prebuckling deformation on the buckling of circular cylindrical shells under external pressure. Reports of the Institute of High Speed Mechanics 21 (1970) 81-104
38. Yamaki N. Elastic Stability of Circular Cylindrical Shells (1984), North-Holland, Amsterdam