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A Sequel to Technical Note 13: The Curved Tetrahedronal and Triangular Elements TEC and TRIC for the Matrix Displacement Method

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

It is by now well established that the computational analysis of significant problems in structural and continuum mechanics by the matrix displacement method often requires elements of higher sophistication than used in the past. This refers, in particular, to regions of steep stress gradients, which are frequently associated with marked changes in geometry, involving rapid variations of the radius of curvature. The philosophy underlying the idealisation of such configurations into finite elements was discussed in broad terms in ref. 1. It was emphasised that the so successful, constant strain, two-dimensional TRIM 3 and three-dimensional TET 4 elements do not, in general, prove the best choice. For this reason elements with a linear variation of strain like TRIM 6 and TET 10 were originally evolved and followed up with the quadratic strain elements TRIM 15, TRIA 4 (two-dimensional) and TET 20, TEA 8 (three-dimensional) of ref. 2. However, all these elements are characterised by straight edges and necessitate a polygonisation or polyhedrisation in the idealisation process. This may not be critical in many problems, but is sometimes of doubtful validity in the immediate neighbourhood of a curved boundary, where stress concentrations are most pronounced. To overcome this difficulty with a significant (local) increase of elements does not always yield the most economical and technically satisfactory solution. Moreover, there arises another inevitable shortcoming when dealing with TRIM and TET elements with a linear or quadratic variation of strain. Indeed, while TRIM 3 and TET 4 elements permit a very elegant extension into the realm of large displacements, this is not possible for the higher order TRIM and TET elements. This is simply due to the fact that TRIM 3 and TET 4 elements, by virtue of their specification, always remain straight under any magnitude of strain, but this is not so for the triangular and tetrahedron elements of higher sophistication.

Type
Technical Notes
Information
The Aeronautical Journal , Volume 73 , Issue 697 , January 1969 , pp. 55 - 65
Copyright
Copyright © Royal Aeronautical Society 1969 

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References

1. Argyris, J. H. and Scharpf, D. W. A Sequel to Technical Note 13: The Curved Tetrahedronal and Triangular Elements TEC and TRIC for the Matrix Displacement Method, Part I. Small Displacements. The Aeronautical Journal of the Royal Aeronautical Society, Vol 73 No 697, pp. 55–61, January 1969.Google Scholar
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4. Argyris, J. H. Continua and Discontinua, Opening Paper to the First Air Force Conference on Matrix Methods in Structural Mechanics at Wright-Patterson Air Force Base, Dayton, Ohio, 26th-28th October 1965. Proceedings, 1966.Google Scholar
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