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Shock-sensitivity in shell-like structures: with simulations of spherical shell buckling. (English) Zbl 1334.74038

74G60 Bifurcation and buckling
74K25 Shells
74H15 Numerical approximation of solutions of dynamical problems in solid mechanics
74H55 Stability of dynamical problems in solid mechanics
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[1] Ashwell, D. G. [1960] ” On the large deflection of a spherical shell with an inward point load,” Proc. Symp. Theory of Thin Elastic Shells, Delft, 24-28 August 1959.
[2] Barton, D. A. W. & Sieber, J. [2013] ” Systematic experimental exploration of bifurcations with noninvasive control,” Phys. Rev. E87, 052916. genRefLink(16, ’S0218127416300032BIB002’, ’10.1103%252FPhysRevE.87.052916’); genRefLink(128, ’S0218127416300032BIB002’, ’000319658900013’);
[3] Bauer, L., Reiss, E. L. & Keller, H. B. [1970] ” Axisymmetric buckling of hollow spheres and hemispheres,” Commun. Pure Appl. Math.23, 529-568. genRefLink(16, ’S0218127416300032BIB003’, ’10.1002%252Fcpa.3160230402’); genRefLink(128, ’S0218127416300032BIB003’, ’A1970H278100001’); · Zbl 0194.26804
[4] Berke, L. & Carlson, R. L. [1968] ” Experimental studies of the post buckling behaviour of complete spherical shells,” Exp. Mech.8, 548-553. genRefLink(16, ’S0218127416300032BIB004’, ’10.1007%252FBF02327517’);
[5] Boardman, H. C. [1944] ”Vacuum tests on hortonspheres,” Water Tower.
[6] Bushnell, D. [1981] ” Buckling of shells – Pitfall for designers,” AIAA19, 1183-1226. genRefLink(16, ’S0218127416300032BIB006’, ’10.2514%252F3.60058’);
[7] Bushnell, D. [2015] Shell Buckling, website, http://shell-buckling.com/index.php.
[8] Carlson, R. L., Sendelbeck, R. L. & Hoff, N. J. [1967] ” Experimental studies of the buckling of complete spherical shells,” Exp. Mech.7, 281-288. genRefLink(16, ’S0218127416300032BIB008’, ’10.1007%252FBF02327133’); genRefLink(128, ’S0218127416300032BIB008’, ’A19679962500001’);
[9] Elishakoff, I. [2014] Resolution of the Twentieth Century Conundrum in Elastic Stability (World Scientific, London). [Abstract]
[10] Friedrichs, K. O. [1941] ” On the minimum buckling load of spherical shells,” Applied Mechanics. Theodore von Karman Anniversary Volume (Calif. Inst. of Tech., Pasadena), pp. 258-272.
[11] Gabril’iants, A. G. & Feodos’ev, V. I. [1961] ” Axially-symmetric forms of equilibrium of an elastic spherical shell under uniformly distributed pressure,” Appl. Math. Mech.25, 1629. genRefLink(16, ’S0218127416300032BIB011’, ’10.1016%252F0021-8928%252862%252990141-7’);
[12] Godoy, L. A., Jaca, R. C., Sosa, E. M. & Flores, F. G. [2015] ” A penalty approach to obtain lower bound buckling loads for imperfection-sensitive shells,” Thin-Walled Structures95, 183-195. genRefLink(16, ’S0218127416300032BIB012’, ’10.1016%252Fj.tws.2015.07.005’); genRefLink(128, ’S0218127416300032BIB012’, ’000361922500018’);
[13] Graff, M., Scheidl, R., Troger, H. & Weinmuller, E. [1985] ” An investigation of the complete post-buckling behaviour of axisymmetric spherical shells,” J. Appl. Math. Phys.36, 803-821. genRefLink(16, ’S0218127416300032BIB013’, ’10.1007%252FBF00944895’);
[14] Horak, J., Lord, G. J. & Peletier, M. A. [2006] ” Cylinder buckling: The mountain pass as an organizing centre,” SIAM J. Appl. Math.66, 1793-1824. genRefLink(16, ’S0218127416300032BIB014’, ’10.1137%252F050635778’); genRefLink(128, ’S0218127416300032BIB014’, ’000240043400016’); · Zbl 1134.35042
[15] Hunt, G. W., Bolt, H. M. & Thompson, J. M. T. [1989] ” Structural localization phenomena and the dynamical phase-space analogy,” Proc. Roy. Soc. A425, 245-267. genRefLink(16, ’S0218127416300032BIB015’, ’10.1098%252Frspa.1989.0105’); · Zbl 0697.73043
[16] Hunt, G. W., Peletier, M. A., Champneys, A. R., Woods, P. D., Ahmer Wadee, M., Budd, C. J. & Lord, G. J. [2000] ” Cellular buckling in long structures,” Nonlin. Dyn.21, 3-29. genRefLink(16, ’S0218127416300032BIB016’, ’10.1023%252FA%253A1008398006403’); genRefLink(128, ’S0218127416300032BIB016’, ’000085032100002’); · Zbl 0974.74024
[17] Hunt, G. W., Lord, G. J. & Peletier, M. A. [2003] ” Cylindrical shell buckling: A characterization of localization and periodicity,” Discr. Contin. Dyn. Syst. Ser. B3, 505-518. genRefLink(16, ’S0218127416300032BIB017’, ’10.3934%252Fdcdsb.2003.3.505’); genRefLink(128, ’S0218127416300032BIB017’, ’000187071300003’); · Zbl 1046.74017
[18] Hunt, G. W. [2011] ” Reflections and symmetries in space and time,” IMA J. Appl. Math.76, 2-26. genRefLink(16, ’S0218127416300032BIB018’, ’10.1093%252Fimamat%252Fhxq063’); genRefLink(128, ’S0218127416300032BIB018’, ’000286674200002’);
[19] Hutchinson, J. W. [1967] ” Imperfection sensitivity of externally pressurised spherical shells,” J. Appl. Mech.34, 49-55. genRefLink(16, ’S0218127416300032BIB019’, ’10.1115%252F1.3607667’); genRefLink(128, ’S0218127416300032BIB019’, ’A19679105600009’);
[20] Koga, T. & Hoff, N. [1969] ” The axisymmetric buckling of initially imperfect complete spherical shells,” Int. J. Solids Structur.5, 679-697. genRefLink(16, ’S0218127416300032BIB020’, ’10.1016%252F0020-7683%252869%252990088-2’); · Zbl 0174.27203
[21] Koiter, W. T. [1945] ”On the stability of elastic equilibrium,” Dissertation, Delft, Holland; [1967] An English translation is available in Tech. Trans. F 10, 833.
[22] Koiter, W. T. [1969] ” The nonlinear buckling problem of a complete spherical shell under uniform external pressure, Parts I, II, III and lV,” Proc. Kon. Ned. Akad. Wet. Ser. B72, 40-123. · Zbl 0197.22302
[23] Poston, T. & Stewart, I. [1978] Catastrophe Theory and Its Applications (Pitman, London). · Zbl 0382.58006
[24] Sabir, A. B. [1964] ” Large deflection and buckling behaviour of a spherical shell with inward point load and uniform external pressure,” J. Mech. Eng. Sci.6, 394-403. genRefLink(16, ’S0218127416300032BIB024’, ’10.1243%252FJMES_JOUR_1964_006_054_02’); genRefLink(128, ’S0218127416300032BIB024’, ’A19646081300010’);
[25] Schwerin, E. [1922] ” Zur Stabilitat der dunnwandigen Hohlkugel unter gleichmassigem Aussendruck,” Z. Angew. Math. Mech.2, 81. genRefLink(16, ’S0218127416300032BIB025’, ’10.1002%252Fzamm.19220020201’);
[26] Takei, A., Jin, L., Hutchinson, J. W. & Fujita, H. [2014] ” Ridge localizations and networks in thin films compressed by the incremental release of a large equi-biaxial pre-stretch in the substrate,” Adv. Mater.26, 4061-4067. genRefLink(16, ’S0218127416300032BIB026’, ’10.1002%252Fadma.201306162’); genRefLink(128, ’S0218127416300032BIB026’, ’000337970900011’);
[27] Thompson, J. M. T. [1960a] ” Elastic buckling of thin spherical shells,” Symp. Nuclear Reactor Containment Buildings and Pressure Vessels, Glasgow, May 1960, eds. Thomson, A. S. T. et al. (Butterworths, London), pp. 257-285.
[28] Thompson, J. M. T. [1960b] ” Making of thin metal shells for model stress analysis,” J. Mech. Eng. Sci.2, 105-108. genRefLink(16, ’S0218127416300032BIB028’, ’10.1243%252FJMES_JOUR_1960_002_019_02’);
[29] Thompson, J. M. T. [1961] The Elastic Instability of Spherical Shells, PhD dissertation, Cambridge University, September 1961.
[30] Thompson, J. M. T. [1962] ” The elastic instability of a complete spherical shell,” Aero. Quart.13, 189-201.
[31] Thompson, J. M. T. [1964a] ” The post-buckling of a spherical shell by computer analysis,” World Conf. Shell Structures, San Francisco, Oct 1962, eds. Medwadowski, S. J. et al. (National Academy of Sciences, Washington), pp. 181-188.
[32] Thompson, J. M. T. [1964b] ” The rotationally-symmetric branching behaviour of a complete spherical shell,” Proc. R. Neth. Acad. Sci. B67, 295-311. · Zbl 0121.41804
[33] Thompson, J. M. T. & Hunt, G. W. [1973] A General Theory of Elastic Stability (Wiley, London).
[34] Thompson, J. M. T. [1975] ” Experiments in catastrophe,” Nature254, 392-395. genRefLink(16, ’S0218127416300032BIB034’, ’10.1038%252F254392a0’); genRefLink(128, ’S0218127416300032BIB034’, ’A1975W023800021’);
[35] Thompson, J. M. T. & Hunt, G. W. [1975] ” Towards a unified bifurcation theory,” J. Appl. Math. Phys. (ZAMP)26, 581-604. genRefLink(16, ’S0218127416300032BIB035’, ’10.1007%252FBF01594031’); genRefLink(128, ’S0218127416300032BIB035’, ’A1975AY42200007’);
[36] Thompson, J. M. T. & Hunt, G. W. [1984] Elastic Instability Phenomena (Wiley, Chichester). · Zbl 0636.73034
[37] Thompson, J. M. T. & Champneys, A. R. [1996] ” From helix to localized writhing in the torsional post-buckling of elastic rods,” Proc. Roy. Soc. A452, 117-138. genRefLink(16, ’S0218127416300032BIB037’, ’10.1098%252Frspa.1996.0007’); · Zbl 0946.74025
[38] Thompson, J. M. T. [2013] ” Advice to a young researcher: With reminiscences of a life in science,” Phil. Trans. Roy. Soc. A371, 20120425. genRefLink(16, ’S0218127416300032BIB038’, ’10.1098%252Frsta.2012.0425’); · Zbl 1320.01056
[39] Thompson, J. M. T. & van der Heijden, G. H. M. [2014] ” Quantified ’shock-sensitivity’ above the Maxwell load,” Int. J. Bifurcation and Chaos24, 1430009-1-14. [Abstract] · Zbl 1296.74059
[40] Thompson, J. M. T. [2015] ” Advances in shell buckling: Theory and experiments,” Int. J. Bifurcation and Chaos25, 1530001-1-25. [Abstract]
[41] Tokugawa, T. [1936] ” Experiments on elastic stability of thin spherical shells under uniform external pressure and some idea of rough approximation to calculation of its collapsing pressure,” J. Soc. Nav. Arch. Japan1936, 179-194.
[42] Tsien, H. S. [1942] ” Theory for the buckling of thin shells,” J. Aero. Sci.9, 373-384. genRefLink(16, ’S0218127416300032BIB042’, ’10.2514%252F8.10911’);
[43] Tsien, H. S. [1947] ” Lower buckling load in the non-linear buckling theory for thin shells,” Quart. Appl. Math.5, 236-237. genRefLink(128, ’S0218127416300032BIB043’, ’A1947XR59400010’);
[44] van der Heijden, G. H. M. & Thompson, J. M. T. [2000] ” Helical and localized buckling in twisted rods: A unified analysis of the symmetric case,” Nonlin. Dyn.21, 71-99. genRefLink(16, ’S0218127416300032BIB044’, ’10.1023%252FA%253A1008310425967’); genRefLink(128, ’S0218127416300032BIB044’, ’000085032100005’); · Zbl 0959.74022
[45] van der Heijden, G. H. M. [2001] ” The static deformation of a twisted elastic rod constrained to lie on a cylinder,” Proc. Roy. Soc. A457, 695-715. genRefLink(16, ’S0218127416300032BIB045’, ’10.1098%252Frspa.2000.0688’); · Zbl 1014.74043
[46] van der Heijden, G. H. M., Champneys, A. R. & Thompson, J. M. T. [2002] ” Spatially complex localization in twisted elastic rods constrained to a cylinder,” Int. J. Solids Structur.39, 1863-1883. genRefLink(16, ’S0218127416300032BIB046’, ’10.1016%252FS0020-7683%252801%252900234-7’); genRefLink(128, ’S0218127416300032BIB046’, ’000175633700010’); · Zbl 1006.74521
[47] van der Heijden, A. M. A. (ed.) [2012] W. T. Koiter’s Elastic Stability of Solids and Structures (Cambridge University Press, Cambridge, UK).
[48] van der Neut, A. [1932] De Elastische Stabiliteit van den Dunwandigen Bol, Dissertation, Delft.
[49] von Kármán, Th. & Tsien, H. S. [1939] ” The buckling of spherical shells by external pressure,” J. Aero. Sci.7, 43-50. genRefLink(16, ’S0218127416300032BIB049’, ’10.2514%252F8.1019’);
[50] von Kármán, T. & Tsien, H. S. [1941] ” The buckling of thin cylindrical shells under axial compression,” J. Aero. Sci.8, 303-312. genRefLink(16, ’S0218127416300032BIB050’, ’10.2514%252F8.10722’); · Zbl 0060.42403
[51] Zick, L. P. & Carlson, C. E. [1947] ” Vacuum test of sphere to failure,” Water Tower.
[52] Zoelly, R. [1915] Ober ein Knickungsproblem an der Kugelschale, Dissertation, Zurich.
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