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Towards imperfection insensitive buckling response of shell structures-shells with plate-like post-buckled responses

Published online by Cambridge University Press:  29 February 2016

S. C. White  and
P. M. Weaver
S. C. White*
Affiliation:
Advanced Composite Centre for Innovation and Science, University of BristolBristol
P. M. Weaver*
Affiliation:
Advanced Composite Centre for Innovation and Science, University of BristolBristol
*
[email protected]
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Abstract

The imperfection sensitivity of cylindrical panels under compression loading is shown to be not only reduced but effectively eliminated using stiffness tailoring techniques. Shells are designed with variable angle-tow (VAT) laminae, giving their laminates variable-stiffness properties over the surface co-ordinates. By employing an asymptotic model of the non-linear shell behaviour and a genetic algorithm, the post-buckling stability was maximised with respect to the VAT design variables. Results for optimised straight-fibre and VAT shells are presented in comparison with quasi-isotropic designs. In the straight-fibre case, small improvements in the post-buckling stability are shown to be possible but at the expense of the buckling load. In the VAT case, on the other hand, considerable improvements in the post-buckling stability are obtained and drops in axial stiffness and load associated with buckling are reduced to negligible levels. The improvements are shown to be a result of a benign membrane stress distribution prior to buckling and a localisation of the buckling mode. The asymptotic results are compared with non-linear finite-element analyses and are found to be in good agreement. Potential future multi-objective optimisation studies are discussed.

Keywords

Bucklingpost-bucklingcompositeshellsimperfection-sensitivityvariable stiffnessComposite materials
Type
Research Article
Information
The Aeronautical Journal , Volume 120 , Issue 1224 , February 2016 , pp. 233 - 253
Copyright
Copyright © Royal Aeronautical Society 2016 

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References

1.Koiter, W.T. The stability of elastic equilibrium, PhD dissertation, Polytechnic Institute of Delft, Delft, The Netherlands, 1945.Google Scholar
2.vonKármán, T. and Tsien, H.S.The buckling of thin cylindrical shells under axial compression, J Spacecr Rockets, 1941, 40, (6), pp 303–312.Google Scholar
3.Peterson, J.P., Seide, P. and Weingarten, V.I. Buckling of thin-walled circular cylinders, NASA Langley Research Center, Hampton, VA, USA, Rep. NASA-SP-8007, 1968.Google Scholar
4.Koiter, W.T. Buckling and post-buckling behaviour of a cylindrical panel under axial compression, Nationaal Luchtvaartlaboratorium, Rep. S. 476, 1955.Google Scholar
5.Khot, N.S. and Venkayya, V.B. Effect of fiber orientation on initial postbuckling behavior and imperfection sensitivity of composite cylindrical shells, Air force flight dynamics laboratory, Wright-Patterson Air Force Base, Rep. AFFDL-TR-70-125, December 1970.CrossRefGoogle Scholar
6.Pope, C.G.The buckling behaviour in axial compression of slightly-curved panels, including the effect of shear deformability, Int J Solids Struct, 1969, 4, (3), pp 323–340.CrossRefGoogle Scholar
7.Bisagni, C. and Cordisco, P.Testing of stiffened composite cylindrical shells in the postbuckling range until failure, AIAA J, 2004, 42, (9), pp 1806–1817.CrossRefGoogle Scholar
8.Mang, H.A., Schranz, C. and Mackenzie-Helnwein, P.Conversion from imperfection-sensitive into imperfection-insensitive elastic structures I: Theory, Comput Methods Appl Mech Eng, 2006, 195, (13), pp 1422–1457.CrossRefGoogle Scholar
9.Schranz, C., Krenn, B. and Mang, H.A.Conversion from imperfection-sensitive into imperfection-insensitive elastic structures. II: Numerical investigation, Comput Methods Appl Mech Eng, 2006, 195, (13), pp 1458–1479.CrossRefGoogle Scholar
10.Hilburger, M.W. Developing the next generation shell buckling design factors and technologies, Proceedings of the 53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, Honolulu, HI, US, 23-26 April 2012.CrossRefGoogle Scholar
11.Wu, K.C., Stanford, B.K., Hrinda, G.A., Wang, Z., Martin, R.A. and Kim, H.A. Structural assessment of advanced composite tow-steered shells, Proceedings of the 54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, Boston, MA, US, 8-11 April 2013.CrossRefGoogle Scholar
12.Burgueño, R., Hu, N., Heeringa, A. and Lajnef, N.Tailoring the elastic postbuckling response of thin-walled cylindrical composite shells under axial compression, Thin-Walled Structures, 2014, 84, pp 14–25.CrossRefGoogle Scholar
13.Ning, X. and Pellegrino, S. Imperfection-insensitive axially loaded cylindrical shells, Proceedings of the 54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, Boston, MA, US, 8-11 April 2013.CrossRefGoogle Scholar
14.Jullien, J.F. and Araar, M.Towards an optimal cylindrical shell structures under external pressure, Buckling of Shell Structures, on Land, in the Sea, and in the Air, Elsevier Applied Science, London, 1991, pp 21–32.CrossRefGoogle Scholar
15.Lanzo, A.D., Garcea, G. and Casciaro, R.Asymptotic post-buckling analysis of rectangular plates by HC finite elements, Int J Numer Meth Eng, 1995, 38, (14), pp 2325–2345.CrossRefGoogle Scholar
16.Lanzo, A.D. and Garcea, G.Koiter’s analysis of thin-walled structures by a finite element approach, Int J Numer Meth Eng, 1996, 39, (17), pp 3007–3031.3.0.CO;2-S>CrossRefGoogle Scholar
17.Casciaro, R., Garcea, G., Attanasio, G. and Giordano, F.Perturbation approach to elastic post-buckling analysis, Comput. Struct, 1998, 66, (5), pp 585–595.CrossRefGoogle Scholar
18.van der Heijden, A.M.W.T. Koiter’s Elastic Stability of Solids and Structures, 2012, Cambridge University Press, Cambridge, UK.Google Scholar
19.White, S.C., Raju, G. and Weaver, P.M.Initial post-buckling of variable-stiffness curved panels, J Mech Phys Solids, 71, pp 132–155.CrossRefGoogle Scholar
20.Salerno, G. and Casciaro, R.Mode jumping and attractive paths in multimode elastic buckling, Int J Numer Methods Eng, 1997, 40, (5), pp 833–861.3.0.CO;2-6>CrossRefGoogle Scholar
21.Gen, M. and Cheng, R.Genetic Algorithms and Engineering Optimization, 2000, John Wiley & Sons, Chichester.Google Scholar
22.MATLAB and Global Optimisation Toolbox 2012b, The MathWorks, Inc., Natick, Massachusetts, US.Google Scholar
23.Abaqus, ver. 6.12, Dassault Systemes, Vélizy-Villacoublay, Fance.Google Scholar
24.Pandey, M.D. and Sherbourne, A.N.Postbuckling behaviour of optimized rectangular composite laminates, Compos Struct, 1993, 23, (1), pp 27–38.CrossRefGoogle Scholar
25.Hilburger, M.W., Nemeth, M.P. and Starnes, J.H. Jr Nonlinear and buckling behavior of curved panels subjected to combined loads, Proceedings of the 42nd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, Seattle, WA, 2001.CrossRefGoogle Scholar
26.Donnell, L.H. A new theory for the buckling of thin cylinders under axial compression, N.A.C.A., Rep. AER-56-12, 1934.CrossRefGoogle Scholar
27.Sanders, J.L. Nonlinear theories for thin shells, Division of Engineering and Applied Physics, Harvard, February 1961.CrossRefGoogle Scholar
28.Shu, C.Differential Quadrature and Its Application in Engineering, 2000, Springer-Verlag, London.CrossRefGoogle Scholar
29.Byskov, E. and Hutchinson, J.W.Mode interaction in axially stiffened cylindrical shells, AIAA J, 1971, 15, (7), pp 941–948.CrossRefGoogle Scholar