Some aspects of the axial extension mode in an elastic thin-walled beam-column

Kołakowski, Z.

Artykuł - szczegóły

Tytuł artykułu

Some aspects of the axial extension mode in an elastic thin-walled beam-column

Autorzy

Kołakowski Z.

Treść / Zawartość

Pełne teksty:

httpwww_ptmts_org_pl2012-1-kolakowski.pdf

Pobierz

Identyfikatory

Warianty tytułu

Pewne aspekty osiowej postaci wzdłużnej w sprężystej cienkościennej belce-słupie

Języki publikacji

Abstrakty

The present paper deals with the influence of the axial extension mode on static and dynamic interactive buckling of a thin-walled beam-column with imperfections subjected to uniform compression when the shear lag phenomenon and distortional deformations are taken into account. A plate model (2D) is adopted for the beam-column. One- and two-dimensional models of the elements are compared, too. The structure is assumed to be simply supported at the ends. Equations of motion of the component plates are obtained from Hamilton’s Principle, taking into account all components of inertia forces. Within the frame of the first order nonlinear approximation, the dynamic problem of modal interactive buckling is solved by the transition matrix using the perturbation method and Godunov’s orthogonalization.

W prezentowanej pracy omówiono wpływ osiowej wzdłużnej postaci na statyczne i dynamiczne interakcyjne wyboczenie cienkościennej belki-słupa z niedokładnościami poddanej równomiernemu ściskaniu przy uwzględnieniu zjawiska shear-lag oraz dystorsyjnej deformacji. Przyjęto płytowy model (2D) belki-słupa. Porównano jedno- i dwuwymiarowe modele elementów. Konstrukcja jest przegubowo podparta na obu końcach. Równania ruchu płyt składowych otrzymano z zasady Hamiltona, biorąc pod uwagę wszystkie składowe sił bezwładności. Dynamiczne zagadnienie modalnego interakcyjnego wyboczenia w ramach pierwszego rzędu nieliniowej aproksymacji rozwiązano metodą macierzy przeniesienia, wykorzystując metodę perturbacyjną i ortogonalizację Godunova.

Słowa kluczowe

axial extension mode eigenvalue problem dynamic interactive buckling thin-walled structure

Wydawca

Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej

Czasopismo

Journal of Theoretical and Applied Mechanics

Rocznik

2012

Tom

Vol. 50 nr 1

Strony

147--168

Opis fizyczny

Bibliogr. 52 Poz., rys., tab.

Twórcy

autor

Kołakowski Z.

Technical University of Lodz, Department of Strength of Materials and Structures, Łódź, Poland, zbigniew.kolakowski@p.lodz.pl

Bibliografia

1. Adany S., Schafer B.W., 2006a, Buckling mode decomposition of single-branched open cross-section members via finite strip method: Derivation, Thin-Walled Structures, 44, 563-584
2. Adany S., Schafer B.W., 2006b, Buckling mode decomposition of single-branched open cross-section members via finite strip method: Application and examples, Thin-Walled Structures, 44, 585-600
3. Adany S., Schafer B.W., 2008, A full modal decomposition of thin-walled, single-branched open cross-section members via the constrained finite strip method, Journal of Constructional Steel Research, 64, 12-29
4. Adany S., Silvestre N., Schafer B.W., Camotim D., 2006, Buckling analysis of unbranched thin-walled members using cFSM and GBT: A comparative study, Proceedings of International Colloquium on Stability and Ductility of Steel Structures SDSS 2006, Camotim D., Silvestre N., Dinis P.B. (Eds.), Instituto Superior Tecnico, Lisbon, 205-212
5. Adany S., Silvestre N., Schafer B.W., Camotim D., 2007, On the identification and characterization of local, distortional and global modes in thinwalled members using the cFSM and GBT approaches, Proceedings of the Sixth International Conference on Steel and Aluminum Structures ICSAS’2007, Beale R.G. (Ed.), Oxford Brookes University, 760-767
6. Adany S., Silvestre N., Schafer B.W., Camotim D., 2008, Buckling mode identification of thin-walled members: A comparison between cFSM and CBT approaches, Proceedings of the Fifth International Conference on Coupled Instabilities in Metal Structures CIMS2008, Rasmussen K. and Wilkinson T. (Eds.), University Publishing Service, The University of Sydney, 249-256
7. Ali M. A., Sridharan S., 1988, A versatile model for interactive buckling of columns and beam-columns, Int. J. Solids Structures, 24, 5, 481-486
8. Ari-Gur J., Simonetta S.R., 1997, Dynamic pulse buckling of rectangular composite plates, Composites Part B, 28B, 301-308
9. Basaglia C., Camotim D., Silvestre N., 2008, GBT-based post-buckling analysis of thin-walled lipped I-section steel columns, Proceedings of the Fifth International Conference on Coupled Instabilities in Metal Structures CIMS2008, Rasmussen K. and Wilkinson T. (Eds.), University Publishing Service, The University of Sydney, 241-248
10. Benito R., Sridharan S., 1984-85,Mode interaction in thin-walled structural members, J. Struct. Mech., 12, 4, 517-542
11. Budiansky B., Hutchinson J.W., 1966, Dynamic buckling of imperfection-sensitive structures, Proc. of the Eleventh International Congress of Applied Mechanics, Goetler H. (Ed.), Munich, 636-651
12. Byskov E., 1987-88, Elastic buckling problem with infinitely many local modes, Mechanics of Structures and Machines, 15, 4, 413-435
13. Byskov E., Hutchinson J.W., 1977, Mode interaction in axially stiffened cylindrical shells, AIAA J., 15, 7, 941-948
14. Camotim D., Basaglia C., Silvestre N., 2008, GBT buckling analysis on thin-walled steel frames, Proceedings of the Fifth International Conference on Coupled Instabilities in Metal Structures CIMS2008, Rasmussen K. and Wilkinson T. (Eds.), University Publishing Service, The University of Sydney, 1-18
15. Camotin D., Dinis P.B., 2009, Coupled instabilities with distorsional buckling in cold-formed steel lipped channel columns, XII-th Symposium on Stability of Structures, Zakopane, Poland, 13-32
16. Camotim D., Prola I. C., 1996, On the stability of thin-walled columns with Z, S and sigma sections, Proc. of Second Int. Conf. on Coupled Instability In Metal Structures, Imperial Press College, 149-156
17. Davies J.M., 2000, Recent research advances in cold-formed steel structures, Journal of Constructional Steel Research, 55, 267-288
18. Dinis P.B., Camotim D., Silvestre N., 2007, FEM-based analysis of the local-plate/distortional mode interaction in cold-formed steel lipped channel columns, Computers and Structures, 85, 1461-1474
19. Gantes C.J., Kounadis A.N., Raftoyiannis J., Bolotin V.V., 2001, A dynamic buckling geometric approach of 2-DOF autonomous potential lumpedmass system under impact loading, Int. J. Solids Structures, 38, 4071-4089
20. Hutchinson J.W., Budiansky B., 1966, Dynamic buckling estimates, AIAA Journal, 4-3, 525-530
21. Huyan X., Simitses G.J., 1997, Dynamic buckling of imperfect cylindrical shells under axial compression and bending moment, AIAA Journal, 35, 8, 1404-1412
22. Kleiber M., Kotula W., Saran M., 1987, Numerical analysis of dynamic quasi-bifurcation, Eng. Comput., 4, 48-52
23. Koiter W.T., 1976, General theory of mode interaction in stiffened plate and shell structures, WTHD, Report 590, Delft
24. Koiter W.T., Pignataro M., 1976, An alternative approach to the interaction between local and overall buckling in stiffened panels, [In:] Buckling of Structures – Proc. of IUTAM Symposium, Cambridge, 1974, 133-148
25. Koiter W.T., van der Neut A., 1980, Interaction between local and overall buckling of stiffened compression panels, [In:] Thin-Walled Structures, J. Rhodes and A.G. Walker (Eds.), Granada, St. Albans, part I, 51-56, part II, 66-86
26. Kolakowski Z., 1993, Interactive buckling of thin-walled beams with open and closed cross-sections, Thin-Walled Structures, 15, 159-183
27. Kołakowski Z., 2010, Static and dynamic interactive buckling regarding Arial extension mode of thin-walled channel, JTAM, 48, 3, 703-714
28. Kolakowski Z., Kowal-Michalska K., Eds., 1999, Selected Problems of Instabilities in Composite Structures, A Series of Monographs, Technical University of Lodz, Poland, p. 222
29. Kołakowski Z., Kowal-Michalska K., 2010, Influence of the axial mode on interactive buckling of thin-walled channels in the first nonlinear approximation, [In:] Shell Structures: Theory and Applications, 2, Pietraszkiewicz & Kreja (Eds.), Taylor & Francis Group, London, 125-128
30. Kolakowski Z., Kowal-Michalska K., 2011, Interactive buckling regarding the axial extension mode of a thin-walled channel under uniform compression in the first nonlinear approximation, Int. J. Solids Structures, 48, 1, 119-125
31. Kolakowski Z., Krolak M., 2006, Modal coupled instabilities of thin-walled composite plate and shell structures, Composite Structures, 76, 303-313
32. Kolakowski Z., Krolak M., Kowal-Michalska K., 1999, Modal interactive buckling of thin-walled composite beam-columns regarding distortional deformations, Int. J. Eng. Sci., 37, 1577-1596
33. Kolakowski Z., Teter A., 2000, Interactive buckling of thin-walled beam-columns with intermediate stiffeners or/and variable thickness, Int. J. Solids Structures, 37, 3323-3344
34. Kowal-Michalska K., Ed., 2007, Dynamic Stability of Composite Plated Structures, WNT, Warsaw, p. 172 [in Polish]
35. Manevich A.I., 1985, Stability of shells and plates with T-section stiffeners, Stroitel’naya Mekhanika i Raschet Sooruzhenii, 2, 34-38 [in Russian]
36. Manevich A.I., 1988, Interactive buckling of stiffened plate under compression, Mekhanika Tverdogo Tela, 5, 152-159 [in Russian]
37. Moellmann H., Goltermann P., 1989, Interactive buckling in thin-walled beams; Part I: Theory; Part II: Applications, Int. J. Solids Structures, 25, 7, 715-728, 729-749
38. Opoka S., Pietraszkiewicz W., 2004, Intrinsic equations for non-linear deformation and stability of thin elastic shells, International Journal of Solids and Structures, 41, 3275-3292
39. Papazoglou V.J., Tsouvalis N.G., 1995, Large deflection dynamic response of composite laminated plates under in-plane loads, Composite Structures, 33, 237-252
40. Petry D., Fahlbusch G., 2000, Dynamic buckling of thin isotropic plater subjected to in-plane impact, Thin-Walled Structures, 38, 267-283
41. Pietraszkiewicz W., 1989, Geometrically nonlinear theories of thin elastic shells, Advances in Mechanics, 12, 1, 51-130
42. Pignataro M., Luongo A., 1987, Asymmetric interactive buckling of thinwalled columns with initial imperfection, Thin-Walled Structures, 3, 365-386
43. Pignataro M., Luongo A., Rizzi N., 1985, On the effect of the local overall interaction on the postbuckling of uniformly compressed channels, Thin-Walled Structures, 3, 283-321
44. Schafer B.W., 2006, Review: The direct strength method of cold-formed member design, Proceedings of International Colloquium on Stability and Ductility of Steel Structures SDSS 2006, Camotim D., Silvestre N., Dinis P.B. (Eds.), Instituto Superior Tecnico, Lisbon, 49-65
45. Schokker A., Sridharan S., Kasagi A., 1996, Dynamic buckling of composite shells, Computers and Structures, 59, 1, 43-55
46. Silva N.M.F., Camotim D., Silvestre N., 2008, GBT cross-section analysis of thin-walled members with arbitrary cross-sections: A novel approach, Proceedings of the Fifth International Conference on Thin-Walled Structures 2008, Mahendran M. (Ed.), Queensland University of Technology, Brisbane, Australia, 1161-1171
47. Sridharan S., Ali M.A., 1986, An improved interactive buckling analysis of thin-walled columns having doubly symmetric sections, Int. J. Solids Structures, 22, 4, 429-443
48. Sridharan S., Benito R., 1984, Columns: static and dynamic interactive buckling, J. of Engineering Mechanics, ASCE, 110-1, 49-65
49. Sridharan S., Peng M.H., 1989, Performance of axially compressed stiffened panels, Int. J. Solids and Structures, 25, 8, 879-899
50. Teter A., Kolakowski Z., 2003, Natural frequencies of thin-walled structures with central intermediate stiffeners or/and variable thickness, Thin-Walled Structures, 41, 291-316
51. Teter A., Kolakowski Z., 2004, Interactive buckling and load carrying capacity of thin-walled beam-columns with intermediate stiffeners, Thin-Walled Structures, 42, 211-254
52. Volmir S.A., 1972, Nonlinear Dynamics of Plates and Shells, Science,Moscow, p. 432 [in Russian]

Typ dokumentu

Bibliografia

Identyfikator YADDA

bwmeta1.element.baztech-article-BWM6-0010-0043