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Buckling interaction in regular arrays of distorted hexagonal plates

Published online by Cambridge University Press:  04 July 2016

C. B. York*
Affiliation:
Department of Aerospace Engineering, University of Glasgow

Abstract

Linear elastic buckling strength assessments are presented for a range of thin plate arrays with optimal strength to weight ratio configurations subject to a range of arbitrary in-plane stress states. The outcomes of the assessment are presented as design curves demonstrating relative buckling strength increases with respect to the classical square plate datum of equal mass.

A stiffness matrix method is adopted for the initial buckling strength predictions. The method is based on exact flat plate theory and assumes that the plate is continuous over supports, whereby deformations in one cell of the plate array influence the deformations in adjacent cells. The supporting webs of each cell are approximated in this study by simple rigid supports that enforce nodal lines or lines of zero out-of-plane displacement in the buckled panel, i.e. the bending and torsional stiffness provided by the supporting webs of the real structure are ignored. Selected results are validated by FEM prediction.

Type
Research Article
Copyright
Copyright © Royal Aeronautical Society 2003 

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References

1. Thompson, D.W. On Growth and Form, 1917, Cambridge University Press, Edinburgh.Google Scholar
2. York, C.B. Elastic buckling design curves for isotropic rectangular plates with continuity or elastic edge restraint against rotation, Aeronaut J, 2000, 104, (1034), pp 175182.Google Scholar
3. Huyton, P. and York, C.B. Buckling design curves for compression loaded skew plate structures, J Aero Eng, ASCE, 2001, 14, (3), pp 92101.Google Scholar
4. Morley, L.S.D. Skew Plates and Structures, 1963, Pergamon Press, Oxford.Google Scholar
5. Guest, J. The buckling of uniformly compressed parallelogram plates having all edges clamped, 1951, ARL-SM-172.Google Scholar
6. Guest, J. The compressive buckling of a parallelogram plate simply supported along all four edges, 1952, ARL-SM-199.Google Scholar
7. Wittrick, W.H. Buckling of oblique plates with clamped edges under uniform compression. Aeronaut Q, 1953, 4, pp 151163.Google Scholar
8. Durvasula, S. Buckling of simply supported skew plates, ASCE (EM), 1971, 97, (3), pp 967979.Google Scholar
9. Kennedy, J.B. and Prabhakara, M.K. Buckling of simply supported orthotropic skew plates, Aeronaut Q, 1978, 29, pp 161172.Google Scholar
10. Fried, I. and Schmitt, K. Numerical results from the application of gradient iterative techniques to the finite element vibration and stability analysis of skew plates, Aeronaut J, 1972, 76, pp 166169.Google Scholar
11. Jaunky, N., Knight, N.F. and Ambur, D.R. Buckling of arbitrary quadrilateral anisotropic plates, AIAA J, 1995, 33, (5), pp 938944.Google Scholar
12. Mizusawa, T. and Leonard, J.W. Vibration and buckling of plates with mixed boundary conditions, Eng Struct, 1990, 12, pp 285290.Google Scholar
13. Wittrick, W.H. Buckling of oblique plates with clamped edges under uniform shear, Aeronaut Q, 1954, 5, pp 3951.Google Scholar
14. Yoshimura, Y. and Iwata, K. Buckling of simply supported oblique plates, J Appl Mech, 1963, 30, (2), pp 363366.Google Scholar
15. Ashton, J.E. Stability of clamped skew plates under combined loads, J Appl Mech, 1969, 36,(1),pp 139140.Google Scholar
16. Durvasula, S. Buckling of clamped skew plates, AIAA J, 1970, 8,(1). pp 178181.Google Scholar
17. Mizusawa, T., Kajita, T. and Naruoka, M. Analysis of skew plate problems with various constraints, J Sound Vih, 1980,73, (4), pp 575584.Google Scholar
18. Xiano, Y., Wang, CM. and Kitipornchai, S. Shear buckling of simply supported skew Mindlin plates, AIAA J, 1994,33, (2), pp 377378.Google Scholar
19. Huyton, P. and York, C.B. Buckling of skew plates with plan-form taper, 2002, 43rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, Paper No AIAA-2002-1572. Denver, CO, 2002.Google Scholar
20. Liew, K.M. and Wang, CM. Elastic buckling of regular polygonal plates, Thin-Walled Struct, 1995, 21, (2), pp 163173.Google Scholar
21. WANG, CM., Xiang, Y., Kitipornchai, S. and Liew, K.M. Buckling solutions for Mindlin plates of various shapes, Eng Struct, 1994, 16. (2),pp 119127.Google Scholar
22. Wang, CM. Buckling of polygonal and circular sandwich plates. AIAA J, 1995, 33,(5), pp 962964.Google Scholar
23. York, C.B. Application of skew-transversely-repetitive analysis for buckling of plate arrays with curved or straight internal supports, 1996. 20th International Council of the Aeronautical Sciences, Sorrento, Italy.Google Scholar
24. York, C.B. Elastic buckling interaction in regular arrays of thin polygonal plates, 2001, 42nd AIAA/ASME/ASCE/AHS/ASC Structures. Structural Dynamics and Materials Conference, Paper No 2001-1331. Seattle, WA, 2001.Google Scholar
25. Budiansky, B., , Connor, R.W. and Stein, M. Buckling in shear of continuous flat plates, 1948, National Committee for Aeronautics (NACA)TN 1565.Google Scholar
26. Anderson, R.A., Charts giving critical compressive stress of continuous flat sheet divided into parallelogram-shaped panels, 1951, NACA TN 2392.Google Scholar
27. York, C.B., and Williams, F.W. Theory and buckling results for infinitely wide stiffened skew plate assemblies, Compos Struct, 1994, 28. pp 189200.Google Scholar
28. York, C.B., Influence of continuity and aspect-ratio on the buckling of skew plates and plate assemblies, Int J Solids Struct, 1996, 33, (15), pp 21332159.Google Scholar
29. Wittrick, W.H. and Williams, F.W. Buckling and vibration of anisotropic or isotropic plate assemblies under combined loadings, Int J Mech Sci, 1974,16, pp 209239.Google Scholar
30. ABAQUS/Standard, Version 5.8, 1998, Hibbit, Karlsson and Sorensen.Google Scholar
31. York, C.B. and Williams, F.W. Aircraft wing panel buckling analysis: efficiency by approximations, Comput Struct, 1998, 68, (6), pp 665 676. See also Comput Struct, 1998, 69, (1), p 785.Google Scholar
32. Anderson, M.S., Williams, F.W. and Wright, C.J. Buckling and vibration of any prismatic assembly of shear and compression loaded anisotropic plates with an arbitrary supporting structure, Int J Mech Sci. 1983,25, pp 585596.Google Scholar
33. Williams, F.W. and Anderson, M.S. Buckling and vibration analysis of shear-loaded prismatic plate assemblies with supporting structures utilizing symmetric or repetitive cross-sections. Aspects of the Analysis of Plate Structures — a Volume in Honour of W.H. Wittrick, 1985. Dawe, D.J., Horsington, R.W., Kamtekar, A.G. and Little, G.H. (Eds), pp 5177, Oxford University Press, Oxford.Google Scholar