A review of papers that investigate the static and dynamic coupled buckling and post-buckling behaviour of thin-walled structures is carried out. The problem of static coupled buckling is sufficiently well-recognized. The analysis of dynamic interactive buckling is limited in practice to columns, single plates and shells. The applications of finite element method (FEM) or/and analytical-numerical method (ANM) to solve interaction buckling problems are on-going. In Poland, the team of scientists from the Department of Strength of Materials, Lodz University of Technology and co-workers developed the analytical-numerical method. This method allows to determine static buckling stresses, natural frequencies, coefficients of the equation describing the post-buckling equilibrium path and dynamic response of the plate structure subjected to compression load and/or bending moment. Using the dynamic buckling criteria, it is possible to determine the dynamic critical load. They presented a lot of interesting results for problems of the static and dynamic coupled buckling of thin-walled plate structures with complex shapes of cross-sections, including an interaction of component plates. The most important advantage of presented analytical-numerical method is that it enables to describe all buckling modes and the post-buckling behaviours of thin-walled columns made of different materials. Thin isotropic, orthotropic or laminate structures were considered.
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1. Ali M.A. Sridharan S. (1988) A versatile model for interactive buckling of columns and beam-columns International Journal of Solids and Structures Vol. 24 481–486.
2. Ari-Gur J. Simonetta S.R. (1997) Dynamic pulse buckling of rectangular composite plates Composites Part B Vol. 28B 301-308.
3. Bangash M.Y.H. (2009) Shock. impact and explosion Structural analysis and design Springer Verlag New York USA.
4. Bao G. Jiang W. Roberts J.C. (1997) Analytic and finite element solutions for bending and buckling of orthotropic rectangular plates Int J Solid Struct Vol. 34 No. 14 1797–1822.
5. Barbero E. Tomblin J. (1993) Euler buckling of thin-walled composite columns Thin-Walled Structures Vol. 17 237–258.
6. Barbero E.J. Madeo A. Zagari G. Zinno R. Zucco G. (2014) Koiter asymptotic analysis of folded laminated composite plates Composites Part B: Engineering Vol.61 267-274.
7. Barsoum R.S. Gallagher R.H. (2009) Finite element analysis of torsional and torsional-flexural stability problems Int. Journal for Numerical Methods in Engineering Vol. 2 335-352.
8. Bazant Z.P. Cedolin L. (2010) Stability of Structures. Elastic. Inelastic. Fracture and Damage Theories Oxford University Press UK.
9. Becque J. Rasmusen K.J.R. (2009) Experimental investigation of local-overall interaction buckling of stainless steel lipped channel columns J. Constructional Steel Research Vol. 65 1677–1684.
10. Benito R. Sridharan S. (1985) Mode interaction in thin-walled structural members Journal of Structural Mechanics Vol. 12 517-542.
11. Benito R. Sridharan S. (1985). Interactive buckling analysis with finite strips International Journal for Numerical Methods in Engineering Vol. 21145-161.
12. Bradford M.A. (1990) Lateral-distortional buckling of tee-section beams Thin-Walled Structures Vol. 10 13-30.
13. Budiansky B. (1966) Dynamic buckling of elastic structures: criteria and estimates. Report SM-7 NASA CR-66072 USA.
14. Budiansky B. (1966) Survey of some buckling problem. AIAA Journal Vol. 4 1505-1510.
15. Byskov E. (1979) Applicability of an asymptotic expansion for elastic buckling problems with mode interaction AIAA Journal Vol. 17 630-633.
16. Byskov E. (1988) Elastic buckling problem with infinitely many local modes Mechanics of Structures and Machines Vol. 15 413-435.
17. Byskov E. Hutchinson JW. (1977) Mode interaction in axially stiffened cylindrical shells AIAA Journal Vol.15 941-48.
18. Casciaro R. Garcea G. Attanasio G. Giordano F. (1998) Pertubative approach to elastic post-buckling analysis International Journal of Computer & Structure Vol. 66 585-595.
19. Chou S.M. Rhodes J. (1997) Review and compilation of experimental results on thin-walled structures. Computers & Structures Vol. 65 No. 1 47–67.
20. Cui S. Cheong H.K. Hao H. (1999) Experimental study of dynamic buckling of plates under fluid-solid slamming. International Journal of Impact Engineering Vol. 22 675-691.
21. Cui S. Hao H. Cheong H.K. (2002) Theoretical study of dynamic elastic buckling of columns subjected to intermediate velocity impact loads International Journal of Mechanical Science Vol. 44 687-702.
22. Debski H. (2013) Experimental investigation post-buckling behaviour of composite column with top-hat cross section Maintenance and Reliability Vol. 2 105–109.
23. Debski H. Kubiak T. Teter A. (2013a) Buckling and postbuckling behaviour of thin-walled composite channel section column” Composite Structures Vol. 100 195-204.
24. Debski H. Kubiak T. Teter A. (2013b) Experimental investigation of channel-section composite profiles’ behaviour with various sequences of plies subjected to static compression Thin-Walled Structures Vol. 71 147–154.
25. Dvorkin E.N. Bathe KJ. (1984) A continuum mechanics based four-node shell element for general nonlinear analysis Engineering Computations Vol. 1 77-88.
26. Fafard M. Beauleu D. Dhatt C. (1987) Buckling of thin-walled members by finite elements Computers and Structures Vol. 25 183-190.
27. Garcea G. Madeo A. Zagari G. and Casciaro R. (2009) Asymptotic post-buckling FEM analysis using correlational formulation International Journal of Solids and Structures Vol. 46 377–397.
28. Garcea G. Salerno G. Casciaro R. (1999) Sanitizing of locking in Koiter perturbation analysis through mixed formulation Computer Methods in Applied Mechanics and Engineering Vol. 180137-167.
29. Gilat R. Aboudi J. (1995) Dynamic buckling of nonlinear resin matrix composite structures Composite Structures Vol. 32 81-88.
30. Goltermann P. Mollman H. (1989) Interactive buckling in thin-walled beams – II. Applications International Journal of Solids and Structures Vol. 25 729-749.
36. Kappos AJ. Dynamic Loading and Design of Structures Spon Press Taylor & Francis Group 2002.
37. Kirsch U. (2004) Design-oriented Analysis of Structures Unified Approach. Kluwer Academic Publishers USA.
38. Kleiber M. Kotula W. Saran M. (1987) Numerical analysis of dynamic quasi-bifurcation Engineering Computations Vol. 4 48-52.
39. Koiter WT. (1976) General theory of mode interaction in stiffened plate and shell structures WTHD Report 590 Delft.
40. Koiter W.T. Pignataro M. (1974) An alternative approach to the interaction between local and overall buckling in stiffened panels Buckling of Structures/Proceedings of IUTAM Symposium. Cambridge 133–148.
41. Kolakowski Z. (1987a) Mode interaction in thin-walled trapezoidal column under uniform compression Thin-Walled Structures Vol. 5 329-342.
42. Kolakowski Z. (1987b) Mode interaction in wide plate with closed section longitudinal stiffeners under compression Engineering Transactions Vol. 35 591-609.
43. Kolakowski Z. (1988) Some aspects of mode interaction in thin-walled stiffened plate under uniform compression Engineering Transactions Vol. 36 167-179.
44. Kolakowski Z. (1989a) Interactive buckling of thin-walled beams with open and closed cross-section Engineering Transactions Vol. 37 375-397.
45. Kolakowski Z. (1989b) Mode interaction in wide plate with angle section longitudinal stiffeners under compression Engineering Transactions Vol. 37 117-135.
46. Kolakowski Z. (1989c) Some thoughts on mode interaction in thin-walled columns under uniform compression. Thin-Walled Structures Vol. 7 23-35.
47. Kolakowski Z. (1993a) Influence of modification of boundary conditions on load carrying capacity in thin-walled columns in the second order approximation International Journal of Solids and Structures Vol. 30 2597-2609.
48. Kolakowski Z. (1993b) Interactive buckling of thin-walled beams with open and closed cross-sections Thin-Walled Structures Vol. 15 159-183.
49. Kolakowski Z. (1996) Semi-analytical method for the analysis of the interactive buckling of thin-walled elastic structures in the second order approximation International Journal of Solids and Structures Vol. 33 3779-3790.
50. Kolakowski Z. (2007) Some aspects of dynamic interactive buckling of composite columns Thin-Walled Structures Vol. 45 866–871.
51. Kolakowski Z. (2009) Static and dynamic interactive buckling of composite columns Journal of Theoretical and Applied Mechanics Vol. 47 177-192.
52. Kolakowski Z. Mania R.J. (2013) Semi-analytical method versus the FEM for analyzing of the local post-buckling of thin-walled composite structures Composite Structures Vol. 97 99–106.
53. Kolakowski Z. Krolak M. (1995) Interactive elastic buckling of thin-walled closed orthotopic beam-columns Engineering Transactions Vol. 43 571-590.
54. Kolakowski Z. Krolak M. (2002) Modal coupled instabilities of thin-walled composite plate and shell structures Composite Structures Vol. 76 303-313.
55. Kolakowski Z. Krolak M. Kowal-Michalska K. (1999) Mode interactive buckling of thin-walled composite beam-columns regarding distortional deformations International Journal of Engineering Sciences Vol. 37 1577-1596.
56. Kolakowski Z. Kubiak T. (2005) Load-carrying capacity of thin-walled composite structures Composite Structures Vol. 67 417–426.
57. Kolakowski Z. Kubiak T. (2007) Interactive dynamic buckling of orthotropic thin-walled channels subjected to in-plane pulse loading Composite Structures Vol. 81 222-232.
58. Kolakowski Z. Teter A. (1995) Influence of local postbuckling behaviour on bending of thin-walled elastic beams with central intermediate stiffeners Engineering Transactions Vol. 43 No. 3 383-396.
59. Kolakowski Z. Teter A. (1995) Interactive buckling of thin-walled closed elastic column-beams with intermediate stiffeners International Journal of Solid and Structures Vol. 32 1501-1516.
60. Kolakowski Z. Teter A. (2000) Interactive buckling of thin–walled beam–columns with intermediate stiffeners or/and variable thickness International Journal of Solid and Structures Vol. 37 3323–3344.
61. Kounadis A.N. Gantes C. Simitses G. (1997) Nonlinear dynamic buckling of multi-dof structural dissipative system under impact loading International Journal Impact Engineering Vol. 19 63-80.
62. Krolak M. Kowal-Michalska K. Mania R.J. Swiniarski J. (2007) Experimental tests of stability and load carrying capacity of compression thin-walled multi-cell columns of triangular cross-section Thin-Walled Structures Vol. 45 883–887.
63. Krolak M. Mlotkowski A. (1996) Experimental analysis of post-buckling and collapse behaviour of thin-walled box-section beam Thin-Walled Structures Vol. 26 287–314.
64. Kubiak T. (2007) Criteria of dynamic buckling estimation of thin-walled structures Thin-Walled Structures Vol. 45 888–892.
65. Kubiak T. (2013) Static and dynamic buckling of thin-walled plate structures Springer Verlag London UK.
66. Kwon Y.B. Kim B.S. Hancock G.J. (2007) Compression tests of high strength cold-formed steel channels with buckling interaction J. Constructional Steel Research Vol. 63 1590–1602.
67. Lee H.P. Harris P.J. (1979) Post-buckling strength of thin-walled members Computers and Structures Vol. 10 689-702.
68. Lee H.P. Harris P.J. Cheng-Tzu T.H. (1984) A nonlinear finite element computer program for thin-walled member Thin-Walled Structures Vol. 2 355-376.
70. Madenci E. Guven I. (2006) The finite element method and applications in engineering using ANSYS. Springer Verlag New York USA.
71. Magnucka-Blandzi E. Magnucki K. (2011) Buckling. and optimal design of cold-formed thin-walled beams: Review of selected problems Thin-Walled Structures Vol. 49 554-561.
72. Magnucka-Blandzi E. Paczos P. Wasilewicz P. (2012) Buckling study of thin-walled channel beams with double box-flanges in pure bendin Strain Vol. 48 No. 4 317-325.
73. Magnucki K. Paczos P. Kasprzak J. (2010) Elastic buckling of cold-formed thin-walled channel beams with drop flanges Journal of Structural Engineering Vol. 136 No. 7 886-96.
74. Manevich AI. (1981) Interaction of buckling modes of stiffened plate under compression Stroitelnaya Mekhanika i Raschet Sooruzhenii Vol.1 24-29.
75. Manevich AI. (1982) Theory of interaction buckling of stiffened thin-walled structures Prikladnaya Matematika i Mekhanika Vol.46 337-345.
76. Manevich AI. (1985) Stability of shells and plates with T-section stiffeners Stroitelnaya Mekhanika i Raschet Sooruzhenii Vol. 2 3 4-38.
77. Manevich AI. (1988) Interactive buckling of stiffened plate under compression Mekhanika Tverdogo Tela Vol. 5 152-159.
78. Mania R. (2005) Buckling analysis of trapezoidal composite sandwich plate subjected to in-plane compression Composite Structures Vol. 69 482–490.
79. Mania R. Kowal-Michalska K. (2007) Behaviour of composite columns of closed cross-section under in-plane compressive pulse loading Thin-Walled Structures Vol. 45 902-905.
80. Moellmann H. and Goltermann P. (1989) Interactive buckling in thin-walled beams; Part I: Theory; Part II: Applications Inter. Journal of Solids and Structures Vol. 25 715–749.
81. Morris A. (2008) Practical guide to reliable finite element modelling. John Wiley&Sons Inc USA.
82. Niezgodzinski T. Kubiak T. (2005) The problem of stability of web sheets in box-girders of overhead cranes Thin-Walled Structures Vol. 43 1913-1925.
83. Parlapalli M.R. Soh K.C. Shu D.W. Ma G. (2007) Experimental investigation of delamination buckling of stitched composite laminates Composites: Part A; Vol. 38 2024–2033.
84. Petry D. and Fahlbusch G. (2000) Dynamic buckling of thin isotropic plates subjected to in-plane impact Thin-Walled Structures Vol. 38 267-283.
85. Pignataro M. Luongo A. (1987) Asymmetric interactive buckling of thin-walled columns with initial imperfection Thin-Walled Structures Vol. 3 365–386.
86. Pignataro M. Luongo A. (1987) Multiple interactive buckling of thin-walled members in compression Proceedings of the International Colloq. on Stability of Plate and Shell Structures. University Ghent 235–240.
87. Pignataro M. Luongo A. Rizzi N. (1985) On the effect of the local overall interaction on the postbuckling of uniformaly compressed channels Thin-Walled Structures Vol. 3 283-321.
88. Powell G. Klinger R. (1970) Elastic lateral buckling of steel beams Journal of Structural Engineering ASCE Vol. 96 No. 9 1919-1932.
89. Put B.M. Pi Y.L. Trahair N.S. (1999) Lateral buckling test on cold-formed channel beams Journal of Structural Engineering ASCE Vol. 125 No. 5 532–539.
90. Rajasekaran S. Murray D.W. (1973) Coupled local buckling in wide flange beam columns Journal of Structural Engineering ASCE 1973;99(6):1003-23.
91. Schokker A. Sridharan S. Kasagi A. (1996) Dynamic buckling of composite shells. Computers and Structures Vol. 59 43-55.
92. Simitses G.J. (1990) Dynamic stability of suddenly loaded structures Springer Verlag New York USA.
93. Simitses G.J. Hodges D.H. (2006) Fundamentals of structural stability Butterworth-Heinemann USA.
94. Singer J. Arbocz J. Weller T. (1998) Buckling experiments. experimental methods in buckling of thin-walled structure. Basic concepts. columns. beams and plates Vol. 1 John Wiley & Sons Inc. New York USA.
95. Singer J. Arbocz J. Weller T. (2002) Buckling experiments. experimental methods in buckling of thin-walled structure. shells built-up structures. Composites and additional topics Vol. 2 John Wiley & Sons Inc. New York USA.
96. Sridharan S. (1983) Doubly symmetric interactive buckling of plate structures International Journal of Solids and Structures Vol. 19 625-641.
97. Sridharan S. Ali M.A. (1985) Interactive buckling in thin-walled beam-columns Journal of Engineering Mechanics ASCE Vol. 111 1470–1486.
98. Sridharan S. Ali M.A. (1986) An improved interactive buckling analysis of thin-walled columns having doubly symmetric sections International Journal of Solids and Structures Vol. 22 429–443.
99. Sridharan S. Benito R. (1984) Columns static and dynamic interactive buckling Journal of Engineering Mechanics ASCE Vol. 110 49–65.
100. Stronge W.J. (2000) Impact mechanics Cambridge University Press Cambridge New York USA.
101. Tamura Y.S. Babcock C.D. (1975) Dynamic stability of cylindrical shell under step loading Journal of Applied Mechanics Vol. 42 190-194.
102. Teter A. (2007) Static and dynamic interactive buckling of isotropic thin–walled closed columns with variable thickness Thin–Walled Structures Vol. 45 936–940.
103. Teter A. (2010) Dynamic. multimode buckling of the thin-walled columns with subjected to in-plane pulse loading Inter. J. Non-Linear Mechanics Vol. 45 207-218.
104. Teter A. (2011) Dynamic critical load based on different stability criteria for coupled buckling of columns with stiffened open cross-sections Thin-Walled Structures Vol. 49 589-595.
105. Teter A. Kolakowski Z. (2003) Natural frequencies of thin-walled structures with central intermediate stiffeners or/and variable thickness Thin–Walled Structures Vol. 41 291–316.
106. Teter A. Kolakowski Z. (2004) Interactive buckling and load carrying capacity of thin–walled beam–columns with intermediate stiffeners Thin–Walled Structures Vol. 42 211–254.
107. Teter A. Kolakowski Z. (2005) Buckling of thin-walled composite structures with intermediate stiffeners Composite Structures Vol. 69 421-428.
108. Teter A. Kolakowski Z. (2013) Coupled dynamic buckling of thin-walled composite columns with open cross-sections Composite Structures Vol.95 28–34.
109. Thompson J.M.T. Hunt G.W. (1973) General Theory of Elastic Stability Wiley New York USA.
110. Toneff J.D. Stiemer S.F. and Osterrieder P. (1987) Local and overall buckling in thin-walled beams and columns. Journal of Structural Engineering ASCE Vol. 113 No. 4 769-786.
111. Turvey G.J. Zhang Y. (2006) A computational and experimental analysis of the buckling. postbuckling and initial failure of pultruded GRP columns Computers & Structures Vol. 84 1527–1537.
112. Tvergaard V. (1973) Imperfections sensitivity of a wide integrally stiffened panel under compression International Journal of Solids and Structures Vol. 9177-192.
113. Tvergaard V. (1973) Influence of post-buckling behaviour on optimum design of stiffened panels International Journal of Solids and Structures Vol. 9 1519–34.
114. van der Heijden A.M.A. (ed.) (2009) WT. Koiter’s elastic stability of solids and structures Cambridge University Press UK.
115. Virgin L.N. (2007) Vibration of axially loaded structures Cambridge University Press UK.
116. Volmir S.A. (1972) Nonlinear dynamics of plates and shells Science Moscow Russia.
117. Warminski J. Teter A. (2012) Non-linear parametric vibrations of a composite column un-der uniform compression Proceedings of the Institution of Mechanical Engineers. Part C: Journal of Mechanical Engineering Science Vol. 226 1921-1938.
118. Weller T. Abramovich H. Yaffe R. (1989) Dynamic buckling of beams and plates subjected to axial impact Composite Structures Vol. 37 835-851.
119. White D.W. Abel J.F. (1990) Accurate and efficient nonlinear formulation of a nine-node shell element with spurious mode control Computers and Structures Vol. 35 621-641.
120. Wong P.M.H. Wang Y.C. (2007) An experimental study of pultruded glass fibre reinforced plastics channel columns at elevated temperatures Computers & Structures Vol. 81 84–95.
121. Zhang T. Liu T. Zhao Y. (2004) Nonlinear dynamic buckling of stiffened plates under in-plane impact load Journal of Zheijang University Science Vol. 5 609-617.