New Formula for Geometric Stiffness Matrix Calculation

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dc.contributor.authorNěmec, Ivancs
dc.contributor.authorTrcala, Miroslavcs
dc.contributor.authorŠevčík, Ivancs
dc.contributor.authorŠtekbauer, Hynekcs
dc.coverage.issue4cs
dc.coverage.volume2016cs
dc.date.accessioned2017-11-07T07:53:11Z
dc.date.available2017-11-07T07:53:11Z
dc.date.issued2016-04-27cs
dc.description.abstractThe 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.formattextcs
dc.format.extent733-748cs
dc.format.mimetypeapplication/pdfcs
dc.identifier.citationJournal of Applied Mathematics and Physics. 2016, vol. 2016, issue 4, p. 733-748.en
dc.identifier.doi10.4236//jamp.2016.44084cs
dc.identifier.issn2327-4379cs
dc.identifier.other133151cs
dc.identifier.urihttp://hdl.handle.net/11012/70141
dc.language.isoencs
dc.publisherScientific Research Publishingcs
dc.relation.ispartofJournal of Applied Mathematics and Physicscs
dc.relation.urihttp://file.scirp.org/Html/7-1720559_65967.htmcs
dc.rightsCreative Commons Attribution 4.0 Internationalcs
dc.rights.accessopenAccesscs
dc.rights.sherpahttp://www.sherpa.ac.uk/romeo/issn/2327-4379/cs
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/cs
dc.subjectGeometric Stiffnessen
dc.subjectStress Stiffnessen
dc.subjectInitial Stress Stiffnessen
dc.subjectTangent Stiffness Matrixen
dc.subjectFinite Element Methoden
dc.subjectPrinciple of Virtual Worken
dc.subjectStrain Measureen
dc.titleNew Formula for Geometric Stiffness Matrix Calculationen
dc.title.alternativeNew Formula for Geometric Stiffness Matrix Calculationcs
dc.type.driverarticleen
dc.type.statusPeer-revieweden
dc.type.versionpublishedVersionen
sync.item.dbidVAV-133151en
sync.item.dbtypeVAVen
sync.item.insts2020.03.31 00:58:42en
sync.item.modts2020.03.30 22:57:30en
thesis.grantorVysoké učení technické v Brně. Fakulta stavební. Ústav stavební mechanikycs
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