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Discrete-Element Methods for Stability Analysis of Complex Structures

Published online by Cambridge University Press:  04 July 2016

J. S. Przemieniecki
J. S. Przemieniecki*
Affiliation:
Air Force Institute of Technology, Wright-Patterson Air Force Base, Dayton, Ohio
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Extract

The matrix methods of structural analysis developed specifically for use on modern digital computers have now become universally accepted in structural design. These methods provide a means for rapid and accurate stress and deflection analysis of complex structures under static and dynamic loading conditions and they can also be used very effectively for the stability analysis. In the conventional stability analysis two possible approaches are normally used; either the differential equations describing the structural deflections are formulated and the lowest eigenvalue representing the buckling load condition is found for a given set of boundary conditions, or alternatively, if the differential equations are too difficult to prescribe, approximate deflection shapes are used in the strain energy expression for large deflections which is subsequently minimised, leading to the stability determinant whose lowest root represents the instability condition. When designing complex structures the conventional methods of finding buckling load conditions are extremely difficult to apply, and therefore in such cases we have to rely on the matrix methods of stability analysis.

Type
Supplementary Papers
Information
The Aeronautical Journal , Volume 72 , Issue 696 , December 1968 , pp. 1077 - 1086
Copyright
Copyright © Royal Aeronautical Society 1968 

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References

1. Turner, M. J., Dill, E. H., Martin, H. C. and Melosh, R. J. Large deflections of structures subjected to heating and external loads, J Aerospace Sciences, Vol 27, pp 97–102, 1960.Google Scholar
2. Rodden, W. P., Jones, J. P. and Bhuta, P. G. A matrix formulation of the transverse structural influence coefficients of an axially loaded Timoshenko beam, J Am Inst Aero Astro, Vol 1, pp 225–227, 1963.Google Scholar
3. Gallagher, R. H. and Padlog, J. Discrete element approach to structural instability analysis, J Am Inst Aero Astro, Vol 1, pp 1437–1439, 1963.Google Scholar
4. Archer, J. S. Consistent matrix formulations for structural analysis using finite-element techniques, J Am Inst Aero Astro, Vol 3, pp 1910–1918, 1965.Google Scholar
5. Martin, H. C. Large deflection and stability analysis by the direct stiffness method, NASA Technical Report No. 32-931, Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California, 1966.Google Scholar
6. McMinn, S. J. The effect of axial loads on the stiffness of rigid-jointed plane frames, Proc. Conf. on Matrix Methods in Structural Mechanics, 26th-28th October 1965, Wright-Patterson Air Force Base, Ohio, AFFDL TR 66-80, 1966.Google Scholar
7. Oden, J. T. Calculation of geometric stiffness matrices for complex structures, J Am Inst Aero Astro, Vol 4, pp 1480–1482, 1966.Google Scholar
8. Przemieniecki, J. S. Theory of Matrix Structural Analysis, McGraw-Hill Book Company, Inc, 1968.Google Scholar
9. Turner, M. J., Martin, H. C. and Weikel, R. C. Further development and application of the stiffness method, AGARDograph 72, Matrix Methods of Structural Analysis, pp 203–266, The Macmillan Company, New York, 1964.Google Scholar
10. Martin, H. C. On the derivation of stiffness matrices for the analysis of large deflection and stability problems, Proc. Conf. on Matrix Methods in Structural Mechanics, 26th-28th October 1965, Wright-Patterson Air Force Base, Ohio, AFFDL TR 66-80, 1966.Google Scholar
11. Kapur, K. K. and Hartz, B. J. Stability of plates using the finite element method, J Eng Mech Div Am Soc Civil Engineers, Vol 92, pp 177–195, 1966 Google Scholar
12. Gallagher, R. H., Gellatly, R. A., Padlog, J. and Mallet, R. H. A discrete element procedure for thin-shell instability analysis, J Am Inst Aero Astro, Vol 5, 138–145, 1967.Google Scholar
13. Wallace, C. D. Matrix Analysis of Axisymmetric Shells Under General Loading, MS Thesis, Air Force Institute of Technology, Wright-Patterson Air Force Base, Ohio, 1966.Google Scholar
14. Eastep, F. E.Vibrational Analysis of a Free-free Beam Subjected to an Axial Load, MS Thesis, Air Force Institute of Technology, Wright-Patterson Air Force Base, Ohio, 1963.Google Scholar
15. Przemieniecki, J. S. Matrix analysis of aerospace structures, Proc. 5th International Symposium on Space Technology and Science, 2nd-7th September 1963, Tokyo, Japan, 477-500, 1963.Google Scholar
16. Argyris, J. H. Recent Advances in Matrix Methods of Structural Analysis, Progress in Aeronautical Sciences, Vol 4, The Macmillan Company, New York, 1964, also in Matrix Methods of Structural Analysis, edited by B., Fraeus De Veubeke, AGARDograph 72, 1-164, The Macmillan Company, New York, 1964.Google Scholar
17. Argyris, J. H. Matrix analysis of three-dimensional elastic media, small and large deflections, J Am Inst Aero Astro, Vol 3, pp 45–51, 1965.Google Scholar
18. Argyris, J. H. Continua and discontinua, Proc. Conf. on Matrix Methods in Structural Mechanics, 26th-28th October 1965, Wright-Patterson Air Force Base, Ohio, AFFDL TR 66-80, 1966.Google Scholar
19. Warren, D. S. A Matrix Method for the Analysis of the Buckling of Structural Panels Subjected to Creep Environment, Flight Dynamics Laboratory, Report ASD TDR 62-740, Wright-Patterson Air Force Base, Ohio, 1962.Google Scholar
20. Lansing, W., Jones, I. W. and Ratner, P. Nonlinear analysis of heated, cambered wings by the matrix force method, J Am Inst Aero Astro, Vol 1, pp 1619–1626, 1963.Google Scholar
21. Przemieniecki, J. S. Equivalent mass matrices for rectangular plates in bending, J Am Inst Aero Astro, Vol 4, pp 949–950, 1966.Google Scholar
22. Dawe, D. J. On assumed displacements for the rectangular plate bending elements, J Royal Aero Soc, Vol 71, pp 722–724, 1967.Google Scholar