New Formula for Geometric Stiffness Matrix Calculation

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26110%2F16%3APU122650" target="_blank" >RIV/00216305:26110/16:PU122650 - isvavai.cz</a>

Result on the web

<a href="http://file.scirp.org/Html/7-1720559_65967.htm" target="_blank" >http://file.scirp.org/Html/7-1720559_65967.htm</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.4236//jamp.2016.44084" target="_blank" >10.4236//jamp.2016.44084</a>

Result language

angličtina

Original language name

New Formula for Geometric Stiffness Matrix Calculation

Original language description

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.

Czech name

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Czech description

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Type

J_ost - Miscellaneous article in a specialist periodical

CEP classification

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OECD FORD branch

20102 - Construction engineering, Municipal and structural engineering

Project

<a href="/en/project/GA14-25320S" target="_blank" >GA14-25320S: Aspects of the use of complex nonlinear material models</a><br>

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year

2016

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Journal of Applied Mathematics and Physics

ISSN

2327-4379

e-ISSN

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Volume of the periodical

2016

Issue of the periodical within the volume

4

Country of publishing house

US - UNITED STATES

Number of pages

16

Pages from-to

733-748

UT code for WoS article

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EID of the result in the Scopus database

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