New Formula for Geometric Stiffness Matrix Calculation

 dc.contributor.author Němec, Ivan cs dc.contributor.author Trcala, Miroslav cs dc.contributor.author Ševčík, Ivan cs dc.contributor.author Štekbauer, Hynek cs dc.date.accessioned 2017-11-07T07:53:11Z dc.date.available 2017-11-07T07:53:11Z dc.date.issued 2016-04-27 cs dc.identifier.citation Journal of Applied Mathematics and Physics. 2016, vol. 2016, issue 4, p. 733-748. en dc.identifier.issn 2327-4379 cs dc.identifier.other 133151 cs dc.identifier.uri http://hdl.handle.net/11012/70141 dc.description.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. en dc.format text cs dc.format.extent 733-748 cs dc.format.mimetype application/pdf cs dc.language.iso en cs dc.publisher Scientific Research Publishing cs dc.relation.ispartof Journal of Applied Mathematics and Physics cs dc.relation.uri http://file.scirp.org/Html/7-1720559_65967.htm cs dc.rights Creative Commons Attribution 4.0 International cs dc.rights.uri http://creativecommons.org/licenses/by/4.0/ cs dc.subject Geometric Stiffness en dc.subject Stress Stiffness en dc.subject Initial Stress Stiffness en dc.subject Tangent Stiffness Matrix en dc.subject Finite Element Method en dc.subject Principle of Virtual Work en dc.subject Strain Measure en dc.title New Formula for Geometric Stiffness Matrix Calculation en dc.title.alternative New Formula for Geometric Stiffness Matrix Calculation cs thesis.grantor Vysoké učení technické v Brně. Fakulta stavební. Ústav stavební mechaniky cs sync.item.dbid VAV-133151 en sync.item.dbtype VAV en sync.item.insts 2019.06.17 10:23:40 en sync.item.modts 2019.05.18 00:41:05 en dc.coverage.issue 4 cs dc.coverage.volume 2016 cs dc.identifier.doi 10.4236//jamp.2016.44084 cs dc.rights.access openAccess cs dc.rights.sherpa http://www.sherpa.ac.uk/romeo/issn/2327-4379/ cs dc.type.driver article en dc.type.status Peer-reviewed en dc.type.version publishedVersion en
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