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Some General Considerations on the Natural Mode Technique

Part II. Large Displacements*

Published online by Cambridge University Press:  04 July 2016

J. H. Argyris  and
D. W. Scharpf
J. H. Argyris
Affiliation:
Imperial College of Science and Technology, University of London
D. W. Scharpf
Affiliation:
Institut für Statik und Dynamik der Luft-und Raumfahrtkonstruktionen, Universität Stuttgart
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Extract

We continue our fundamental discourse on the natural modes in an element and extend our considerations to large displacements. First, we present a general procedure for establishing the so-called geometrical stiffness kG, when the natural modes of the complete element are given. The theory is a substantial generalisation and clarification of the method initially given in refs. 2 and 3 and shows that in establishing the modification to the transformation matrix aN it is necessary to ignore the contribution of the natural modes, which cause rotation at the nodal points but no displacement there. The point is subtle and was not made in ref. 2, although the applications given there are correct. As an example, the geometrical stiffness of a straight beam in space with all degrees of freedom is established. There follows the extension of the geometrical stiffness concept to a sub-element. This is of great practical significance for two reasons. First, it allows to derive the geometrical stiffness of elements of complex shape and behaviour, e.g. curved beams in space subjected to normal forces, bending moments and torque.

Type
Supplementary Papers
Information
The Aeronautical Journal , Volume 73 , Issue 700 , April 1969 , pp. 361 - 368
Copyright
Copyright © Royal Aeronautical Society 1969 

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Footnotes

*

Part I was published in the March JOURNAL pp 218 as Technical Note 19.

References

1. Argyris, J. H. and Scharpf, D. W. Some General Con siderations on the Natural Mode Technique. Part I. Small Displacements. AJRAeS, Vol 73, No 699, pp 218–226, March 1969.Google Scholar
2. Argyris, J. H. Oontinua and Discontinua. Opening Paper to the Air Force Conference on Matrix Methods in Structural Mechanics at WPAFB, Dayton, Ohio, 26th-28th October 1965. Proceedings, Dec. 1966.Google Scholar
3. Argyris, J. H. Recent Advances in Matrix Methods of Structural Analysis. Pergamon Press, 1963.Google Scholar
4. Argyris, J. H. and Scharpf, D. W. A Sequel to TN 13: The Curved Tetrahedronal and Triangular Elements TEC and TRic for the Matrix Displacement Method. Part II. Large Displacements. AJRAeS, Vol 73, No 697, pp 55–65, January 1969.Google Scholar