New Formula for Geometric Stiffness Matrix Calculation
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Date
2016-04-27
ORCID
Advisor
Referee
Mark
Journal Title
Journal ISSN
Volume Title
Publisher
Scientific Research Publishing
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Abstract
The standard formula for geometric stiffness matrix calculation, which is convenient for most engineering
applications, is seen to be unsatisfactory for large strains because of poor accuracy, low
convergence rate, and stability. For very large compressions, the tangent stiffness in the direction
of the compression can even become negative, which can be regarded as physical nonsense. So in
many cases rubber materials exposed to great compression cannot be analyzed, or the analysis
could lead to very poor convergence. Problems with the standard geometric stiffness matrix can
even occur with a small strain in the case of plastic yielding, which eventuates even greater practical
problems. The authors demonstrate that amore precisional approach would not lead to such
strange and theoretically unjustified results. An improved formula that would eliminate the disadvantages
mentioned above and leads to higher convergence rate and more robust computations
is suggested in this paper. The new formula can be derived from the principle of virtual work using
a modified Green-Lagrange strain tensor, or from equilibrium conditions where in the choice
of a specific strain measure is not needed for the geometric stiffness derivation (which can also be
used for derivation of geometric stiffness of a rigid truss member). The new formula has been verified
in practice with many calculations and implemented in the RFEM and SCIA Engineer programs.
The advantages of the new formula in comparison with the standard formula are shown
using several examples.
Description
Citation
Journal of Applied Mathematics and Physics. 2016, vol. 2016, issue 4, p. 733-748.
http://file.scirp.org/Html/7-1720559_65967.htm
http://file.scirp.org/Html/7-1720559_65967.htm
Document type
Peer-reviewed
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Language of document
en