Volume 15 article 457 pages: 383 - 388

Published: Sep 20, 2017

DOI: 10.5937/jaes15-14766

A DISCUSSION ON THE STIFFNESS MATRICES USED IN TENSEGRITY STRUCTURES

Luisa Maria Gil-Martin
Luisa Maria Gil-Martin
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∙ Manuel Alejandro Fernandez-Ruiz
Manuel Alejandro Fernandez-Ruiz
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∙ Enrique Hernandez-Montes
Enrique Hernandez-Montes
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Abstract

The expression stiffness matrices used in the study of tensegrity structures has inherited a formulation initially conceived for the shape finding problems of tension structures. Nevertheless stiffness and geometrical stiffness matrices are well known concepts of structural analysis and all the formulations which are used need to be congruent. In this paper, we present a formal discussion about the formulations used in several publications showing that they are not equivalent. A classic example is presented, which has been solved using several expressions available in the relevant literature, the results have been compared with a classical finite element software, showing the discrepancies.

References

O. C. Zienkiewicz, The finite element method. 3rdEd. McGraw-Hill (London). (1977)

G.G. Estrada, H.J. Bungartz, C. Mohrdieck, Numerical form-finding of tensegrity structures. International Journal of Solid and structures 43 (2006) 6855-6868

H.C. Tran, J. Lee, Advanced form-finding of tensegrity structures. Computers and Structures 88 (2010) 237-246.

D. Veenendaal, P. Block, An overview and comparison of structural form finding methods for general networks. International Journal of Solids and structures 49 (2012) 3741- 3753.

H. J. Schek, The force density method for form-finding and computation of general networks. Computer Methods in Applied Mechanics and Engineering, vol. 3, (1974) 115–134.

I. Němec, M. Trcala, I. Ševčík, H. Štekbauer, New Formula for Geometric Stiffness Matrix Calculation. Journal of Applied Mathematics and Physics, 4, (2016) 733-748.

A. G. Tibert, S. Pellegrino, Review of Form- Finding Methods for Tensegrity Structures. International Journal of Space Structures, vol. 18, no. 4, (2009) 209–223.

R. W. Clough, J. Penzien, Dynamics of structures. 2nd ed. New York: McGraw-Hill, Inc. (1993).

L.M.Gil-Martín, E. Hernández-Montes, M. Aschheim, Optimal design of planar frames based on stability criterion using first-order analysis, Engineering Structures 28, (2006) 1780–1786.