Three-dimensional non-linear buckling of thick-walled elastic tubes under pressure

International Journal of Non-Linear Mechanics

Volumn 48, Issue , 2013, Pages 1-14

  Zhu, Y ^a   Luo, X Y ^a   Wang, H M ^b   Ogden, R W ^c   Berry, C ^d  

^a UNIVERSITY OF GLASGOW   (United Kingdom)

^b XI'AN JIAOTONG UNIVERSITY   (China)

^c UNIVERSITY OF ABERDEEN   (United Kingdom)

^d UNIVERSITY OF GLASGOW   (United Kingdom)

Author keywords

Elastic tubes; Finite deformation; Large strain; Non linear elasticity; Tube buckling

Indexed keywords

AXISYMMETRIC; COMMERCIAL PACKAGES; ELASTIC TUBES; EXTERNAL PRESSURES; FINITE DEFORMATIONS; FINITE ELEMENT; GOVERNING EQUATIONS; LAGRANGIAN MESH; LARGE STRAINS; NEO-HOOKEAN MATERIAL; NEWTON ITERATIONS; NONLINEAR ELASTICITY; NUMERICAL CONVERGENCE; NUMERICAL SCHEME; OBJECT ORIENTED; PHYSIOLOGICAL SYSTEMS; POST BUCKLING DEFORMATION; POTENTIAL APPLICATIONS; SYSTEM OF EQUATIONS; WALL THICKNESS; WEIGHTED RESIDUALS;

ABAQUS; GALERKIN METHODS; ITERATIVE METHODS; JACOBIAN MATRICES; THREE DIMENSIONAL;

TUBES (COMPONENTS);

EID: 84865841549     PISSN: 00207462     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijnonlinmec.2012.06.013     Document Type: Article

References (51)

1. W.A. Conrad Pressure-flow relationships in collapsible tubes IEEE Transactions on Biomedical Engineering 16 1969 284 295
2. A.I. Katz, Y. Chen, and A.H. Moreno Flow through a collapsible tube experimental analysis and mathematical model Biophysical Journal 9 1969 1261 1279
3. K. Ishizaka, and J.L. Flanagan Synthesis of voiced sounds from a two-mass model of the vocal cords Bell System Technical Journal 51 1972 1233 1268
4. A.H. Shapiro Steady flow in collapsible tubes Journal of Biomechanical Engineering 99 1977 126 147
5. R.D. Kamm, and A.H. Shapiro Unsteady flow in a collapsible tube subjected to external pressure or body forces The Journal of Fluid Mechanics 95 1979 1 78
6. C.D. Bertram, and T.J. Pedley A mathematical model of unsteady collapsible tube behaviour Journal of Biomechanics 15 1982 39 50 (Pubitemid 12184211)
7. C. Cancelli, and T.J. Pedley A separated-flow model for collapsible-tube oscillations The Journal of Fluid Mechanics 157 1985 375 404
8. O.E. Jensen Instabilities of flow in a collapsed tube The Journal of Fluid Mechanics 220 1990 623 659
9. X.Y. Luo, and T.J. Pedley A numerical simulation of steady flow in a 2-D collapsible channel Journal of Fluids and Structures 9 1995 149 174
10. X.Y. Luo, and T.J. Pedley A numerical simulation of unsteady flow in a two-dimensional collapsible channel The Journal of Fluid Mechanics 314 1996 191 225 (Pubitemid 126467321)
11. X.Y. Luo, and T.J. Pedley The effects of wall inertia on flow in a two-dimensional collapsible channel The Journal of Fluid Mechanics 363 1998 253 280 (Pubitemid 128488628)
12. X.Y. Luo, and T.J. Pedley Multiple solutions and flow limitation in collapsible channel flows The Journal of Fluid Mechanics 420 2000 301 324
13. T.J. Pedley, and X.Y. Luo Modelling flow and oscillations in collapsible tubes Theoretical and Computational Fluid Dynamics 10 1998 277 294
14. O.E. Jensen, and M. Heil High-frequency self-excited oscillations in a collapsible-channel flow The Journal of Fluid Mechanics 481 2003 235 268 (Pubitemid 36632357)
15. X.Y. Luo, Z.X. Cai, W.G. Li, and T.J. Pedley The cascade structure of linear stabilities of flow in collapsible channels The Journal of Fluid Mechanics 600 2008 45 76 (Pubitemid 351460720)
16. P.S. Stewart, M. Heil, S.L. Waters, and O.E. Jensen Sloshing and slamming oscillations in collapsible channel flow The Journal of Fluid Mechanics 662 2010 288 319
17. H.F. Liu, X.Y. Luo, and Z.X. Cai Stability and energy budget of pressure-driven collapsible channel flows Journal of Fluid Mechanics 705 2012 348 370
18. A.L. Hazel, and M. Heil Steady finite-Reynolds-number flows in three-dimensional collapsible tubes The Journal of Fluid Mechanics 486 2003 79 103 (Pubitemid 36882117)
19. A. Marzo, X.Y. Luo, and C.D. Bertram Three-dimensional collapse and steady flow in thick-walled flexible tubes Journal of Fluids and Structures 20 2005 817 835 (Pubitemid 41149341)
20. M. Heil, and S.L. Waters How rapidly oscillating collapsible tubes extract energy from a viscous mean flow The Journal of Fluid Mechanics 601 2008 199 227 (Pubitemid 351552435)
21. R.J. Whittaker, S.L. Waters, O.E. Jensen, J. Boyle, and M. Heil The energetics of flow through a rapidly oscillating tube. Part I general theory The Journal of Fluid Mechanics 648 2010 83 121
22. R.J. Whittaker, M. Heil, J. Boyle, O.E. Jensen, and S.L. Waters The energetics of flow through a rapidly oscillating tube. Part II application to an elliptical tube The Journal of Fluid Mechanics 648 2010 123 153
23. M. Heil, and T.J. Pedley Large post-buckling deformations of cylindrical shells conveying viscous flow Journal of Fluids and Structures 10 1996 565 599
24. N. Yamaki Buckling of circular cylindrical shells under external pressure Reports of the Institute of High Speed Mechanics 20 1969 35 55
25. N. Yamaki Elastic Stability of Circular Cylindrical Shells 1984 North-Holland Amsterdam
26. M. Amabili, and M.P. Païdoussis Review of studies on geometrically nonlinear vibrations and dynamics of circular cylindrical shells and panels, with and without fluid-structure interaction Applied Mechanics Reviews 56 2003 349 381
27. A.N. Kounadis Recent advances on postbuckling analyses of thin-walled structures beams, frames and cylindrical shells Journal of Constructional Steel Research 62 2006 1101 1115 (Pubitemid 44442404)
28. F.C. Bardi, and S. Kyriakides Plastic buckling of circular tubes under axial compression - Part I experiments International Journal of Mechanical Sciences 48 2006 830 841 (Pubitemid 44226366)
29. F.C. Bardi, S. Kyriakides, and H.D. Yun Plastic buckling of circular tubes under axial compression - Part II analysis International Journal of Mechanical Sciences 48 2006 842 854 (Pubitemid 44226367)
30. W.T. Koiter, Purpose and achievements of research in elastic stability, in: Recent Advances in Engineering Sciences, Proceedings of the 4th Technical Conference of the Society for Engineering Science, Raleigh, NC, 1966, pp. 197-218.
31. W.T. Koiter, Elastic stability, buckling and post-buckling behaviour, in: Proceedings of the IUTAM Symposium on Finite Elasticity, Lehigh University, 1980, 1981, pp. 13-24.
32. G.J. Simitses Buckling of moderately thick laminated cylindrical shells a review Composites B Engineering 27 1996 581 587 (Pubitemid 126350829)
33. J.W. Hutchinson, and W.T. Koiter Postbuckling theory Applied Mechanics Reviews 23 1974 1353 1366
34. Y. Zhu, X.Y. Luo, and R.W. Ogden Asymmetric bifurcations of thick-walled circular cylindrical elastic tubes under axial loading and external pressure International Journal of Solids and Structures 45 2008 3410 3429
35. J. Chróścielewski, W. Pietraszkiewicz, and W. Witkowski On shear correction factors in the non-linear theory of elastic shells International Journal of Solids and Structures 47 2010 3537 3545
36. A. Libai, and J.G. Simmonds The Nonlinear Theory of Elastic Shells second ed. 1998 Cambridge University Press Cambridge, UK
37. Y. Goto, and C. Zhang Plastic buckling transition modes in moderately thick cylindrical shells Journal of Engineering Mechanics 125 1999 426 434
38. C.D. Bertram Two modes of instability in a thick-walled collapsible tube conveying a flow Journal of Biomechanics 15 1982 223 224 (Pubitemid 12156624)
39. C.D. Bertram 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
40. C.D. Bertram, C.J. Raymond, and T.J. Pedley Mapping of instabilities for flow through collapsed tubes of differing length Journal of Fluids and Structures 4 1990 125 153
41. C.D. Bertram, and N.S.J. Elliott 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 (Pubitemid 36678819)
42. J.L. Nowinski, and M. Shahinpoor 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
43. Y. Zhu, X.Y. Luo, and R.W. Ogden Nonlinear axisymmetric deformations of an elastic tube under external pressure European Journal of Mechanics A/Solids 29 2010 216 229
44. B. Kirk, J.W. Peterson, R.H. Stogner, and G.F. Carey LibMesh a C library for parallel adaptive mesh refinement/coarsening simulations Engineering with Computers 22 2006 237 254
45. Abaqus 6.10 Documentation, 2010.
46. E. Riks An incremental approach to the solution of snapping and buckling problems International Journal of Solids and Structures 15 1979 529 551 (Pubitemid 9477358)
47. M.A. Crisfield A fast incremental/iterative solution procedure that handles snap-through Computers & Structures 13 1981 55 62 (Pubitemid 11504717)
48. R.W. Ogden Non-linear Elastic Deformations 1997 Dover Publications New York
49. S. Balay, K. Buschelman, V. Eijkhout, W.D. Gropp, D. Kaushik, M.G. Knepley, L.C. McInnes, B.F. Smith, H. Zhang, PETSc Users Manual. Technical Report ANL-95/11 - Revision 3.0.0, Argonne National Laboratory, 2008.
50. O.C. Zienkiewicz, and J.Z. Zhu The superconvergent patch recovery and a posteriori error estimates. Part 1 the recovery technique International Journal of Numerical Methods in Engineering 33 1992 1331 1364
51. A.S.D. Wang, and A. Ertepinar Stability and vibrations of elastic thick-walled cylindrical and spherical shells subjected to pressure International Journal of Non-Linear Mechanics 7 1972 539 555