New Formula for Geometric Stiffness Matrix Calculation

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

New Formula for Geometric Stiffness Matrix Calculation

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

New Formula for Geometric Stiffness Matrix Calculation

Popis výsledku anglicky

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.

Druh

J_ost - Ostatní články v recenzovaných periodicích

CEP obor

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OECD FORD obor

20102 - Construction engineering, Municipal and structural engineering

Projekt

<a href="/cs/project/GA14-25320S" target="_blank" >GA14-25320S: Aspekty použití komplexních nelineárních materiálových modelů</a><br>

Návaznosti

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

Rok uplatnění

2016

Kód důvěrnosti údajů

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

Název periodika

Journal of Applied Mathematics and Physics

ISSN

2327-4379

e-ISSN

—

Svazek periodika

2016

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

16

Strana od-do

733-748

Kód UT WoS článku

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EID výsledku v databázi Scopus

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