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Membrane Parallelogram Element with Linearly Varying Edge Strain for Matrix Displacement Method

Published online by Cambridge University Press:  04 July 2016

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

Extract

A further element for the Matrix Displacement method discussed in the author’s Main Lecture was a parallelogram or arbitrary anisotropy under plane stress. As for the other elements analysed in the preceding technical notes of this series, we assign to the parallelogram a linear variation of the strain along the edges. This is a more general specification of the strain pattern than for the parallelogram in ref. 2. Consequently, it is necessary to introduce additional nodal points in order to account for the increased number of kinematic freedoms. In the present case eight nodal points are provided as against four in the original model. The procedure is best understood in

Type
Technical Notes
Copyright
Copyright © Royal Aeronautical Society 1966

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References

1. Argyris, J. H. The Computer Shapes the Theory, Lecture to the Royal Aeronautical Society, 18th May 1965, to be published in the Journal of the Royal Aeronautical Society. Google Scholar
2. Argyris, J. H. Recent Advances in Matrix Methods of Structural Analysis, Progress in Aeronautical Sciences, Vol. 4, Pergamon Press, Oxford, 1963.Google Scholar
3. Argyris, J. H. Some Results on the Free-Free Oscillations of Aircraft Type Structures, Research Report to The Boeing Company, Airplane Division, November 1964; also read at the International Symposium of the IUTAM on the Mechanics of Linear Vibrations, Société Francaise des Mecaniciens, and British National Committee for Theoretical and Applied Mechanics, Paris, April 1965, to be published by the Societe Frangaise des Mecaniciens, 1965.Google Scholar
4. Argyris, J. H. Matrix Analysis of Three-Dimensional Elastic Media, Small and Large Displacements. Journal of the AIAA, Vol. 3, No. 1, pp 4551, January 1965.Google Scholar
5. Argyris, J. H. Three-Dimensional Anisotropic and In-homogeneous Elastic Media; Matrix Analysis for Small and Large Displacements. Ingenieur Archiv, Vol. 34, No. 1, pp 3355, January 1965.Google Scholar
6. Argyris, J. H. Triangular Elements with Linearly Varying Strain for the Matrix Displacement Method. Journal of the Royal Aeronautical Society, Vol. 69, October 1965.CrossRefGoogle Scholar
7. Argyris, J. H. Reinforced Fields of Triangular Elements with Linearly Varying Strain, Effect of Initial Strains, Journal of the Royal Aeronautical Society, Vol. 69, November 1965.Google Scholar
8. Argyris, J. H. Matrix Displacement Analysis of Anisotropic Shells by Triangular Elements. Journal of the Royal Aeronautical Society, Vol. 69, November 1965.Google Scholar
9. Argyris, J. H. Tetrahedron Elements with Linearly Varying Strain for the Matrix Displacement Method. Journal of the Royal Aeronautical Society, Vol. 69, December 1965.Google Scholar
10. Morley, L. S. D. Skew Plates and Structures, Pergamon Press, Oxford, 1963.Google Scholar
11. Archer, J. S. Consistent Mass Matrix for Distributed Mass Systems. Proc ASCE, Journal of the Structural Division, 89, pp 161178, August 1963.Google Scholar
12. Argyris, J. H. Continua and Discontinua, An Apercu of Recent Developments of the Matrix Displacement Method, Opening Paper to the Air Force Conference on Matrix Methods, in Structural Mechanics at Wright-Patterson Air Force Base, Dayton, Ohio, 26th-28th October 1965. To be published. Google Scholar
13. Argyris, J. H. Membrane Parallelogram Element with Linearly Varying Edge Strain for Matrix Displacement Method. Research Report to the Boeing Co., Airplane Division, December 1964.Google Scholar
14. Argyris, J. H., Kamel, H., Sφrensen, M., Schmid, G. and Pretsch, H. Automatic System for Kinematic Analysis (ASKA) Research Report to the Boeing Co., Airplane Division, February 1965. To be published externally. Google Scholar