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Application of the Discrete Element Method to the Buckling Analysis of Rectangular Plates under Arbitrary Membrane Loading

Published online by Cambridge University Press:  07 June 2016

D. J. Dawe
D. J. Dawe*
Affiliation:
Royal Aircraft Establishment, Farnborough
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Summary

The discrete element displacement method is used to analyse the instability of flat rectangular plates subjected to arbitrary systems of in-plane loading. Critical load intensities calculated in a range of applications, some of which include discrete reinforcing members, are compared with the predictions of past investigators and demonstrate the accuracy of the procedure.

Type
Research Article
Information
Aeronautical Quarterly , Volume 20 , Issue 2 , May 1969 , pp. 114 - 128
Copyright
Copyright © Royal Aeronautical Society. 1969

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References

1. Timoshenko, S. P. and Gere, J. M. Theory of elastic stability. Chapter 9. Second edition, McGraw-Hill, New York, 1961.Google Scholar
2. Gerard, G. and Becker, H. Handbook of structural stability. Part I—Buckling of flat plates. NACA TN 3781, 1957.Google Scholar
3. Martin, H. C. On the derivation of stiffness matrices for the analysis of large deflection and stability problems. Proceedings of the Conference on Matrix Methods in Structural Mechanics. Wright-Patterson Air Force Base, Ohio, 1965.Google Scholar
4. Turner, M. J., Dill, E. H., Martin, H. C. and Melosh, R. J. Large deflections of structures subjected to heating and external loads. Journal of the Aerospace Sciences, Vol. 27, p. 97,1960.Google Scholar
5. Greene, E. C. Buckling loads for columns of variable section. The Boeing Company, Structural Analysis Research Memo 12, 1960.Google Scholar
6. Gallagher, R. H. and Padlog, J. Discrete element approach to structural instability analysis. AIAA Journal, Vol. 1, p. 1437, 1963.Google Scholar
7. Oden, J. T. Calculation of geometric stiffness matrices for complex structures. AIAA Journal, Vol. 4, p. 1480, 1966.Google Scholar
8. Greene, B. C. Stiffness matrix for bending of a rectangular plate element with initial membrane stresses. The Boeing Company, Structural Analysis Research Memo 45, 1962.Google Scholar
9 Kapur, K. K. and Hartz, B. J. Stability of plates using the finite element method. Journal of the Engineering Mechanics Division, American Society of Civil Engineers, Vol. 92, p. 177, 1966.Google Scholar
10. Argyris, J. H. Matrix displacement analysis of plates and shells. Ingenieur-Archiv, Vol. XXXV, p. 102, 1966.Google Scholar
11. Gallagher, R. H., Gellatly, R. A., Padlog, J. and Mallett, R. H. A discrete element procedure for thin shell instability analysis. AIAA Journal, Vol. 5, p. 138, 1967.CrossRefGoogle Scholar
12. Schmit, L. A., Bogner, F. K. and Fox, R. L. Finite deflection structural analysis using plate and shell discrete elements. AIAA Journal, Vol. 6, p. 781, 1968.Google Scholar
13. Dawe, D. J. On assumed displacements for the rectangular plate bending element. Journal of the Royal Aeronautical Society, Vol. 71, p. 722, 1967.Google Scholar
14. Argyris, J. H. and Kelsey, S. Energy theorems and structural analysis. Butterworth, London, 1960.Google Scholar
15. Bazeley, G. P., Cheung, Y. K., Irons, B. M. R. and Zienkiewicz, O. C. Triangular plate elements in bending: conforming and non-conforming solutions. Proceedings of the Conference on Matrix Methods in Structural Mechanics, Wright-Patterson Air Force Base, Ohio, 1965.Google Scholar
16. Bogner, F. K., Fox, R. L. and Schmit, L. A. The generation of inter-element compatible stiffness and mass matrices by the use of interpolation formulas. Proceedings of the Conference on Matrix Methods in Structural Mechanics, Wright-Patterson Air Force Base, Ohio, 1965.Google Scholar
17. Libove, C. and Stein, M. Charts for critical combinations of longitudinal and transverse direct stress for flat rectangular plates. NACA ARR L6A05, 1946.Google Scholar
18. Walker, A. C. Local instability in plates and channel struts. Journal of the Structures Division, American Society of Civil Engineers, Vol. 92, p. 39, 1966.Google Scholar
19. White, R. N. and Cottingham, W. S. Stability of plates under partial edge loadings. Journal of the Engineering Mechanics Division, American Society of Civil Engineers, Vol. 88, p. 67, 1962.Google Scholar
20. Leggett, D. M. A. The effect of two isolated forces on the elastic stability of a flat rectangular plate. Proceedings, Cambridge Philosophical Society, Vol. 33, p. 325, 1937.Google Scholar
21. Sommerfeld, A. Uber die Knicksicherheit der Stege von Walzwerkprofilen. Zeitschrift für Mathematik und Physik, Vol. 54, p. 113 and p. 318, 1906.Google Scholar
22. Dawe, D. J. Discrete element analysis of the lateral vibration of rectangular plates in the presence of membrane stresses. Unpublished Ministry of Technology report.Google Scholar