000009292 001__ 9292
000009292 005__ 20141204092426.0
000009292 04107 $$aeng
000009292 046__ $$k12/05/2014
000009292 100__ $$aPlešek, J.
000009292 24500 $$aEstimation of the critical time step for explicit integration

000009292 24630 $$n18.$$pEngineering Mechanics 2012
000009292 260__ $$bInstitute of Theoretical and Applied Mechanics, AS CR, Prague
000009292 506__ $$arestricted
000009292 520__ $$2eng$$aExplicit integration plays a key role in many problems of linear and non-linear dynamics. For example, the finite element method applied to spatial discretization of continua leaves a system of ordinary differential equations to be solved, which is often done by the central difference method. This and similar explicit schemes suffer from magnification of the round-off errors if the time step exceeds certain fixed length known as the critical time step. The corresponding critical Courant number (Cr, dimensionless time step) is inversely proportional to the maximum natural frequency of the system. The well known recommendation Cr = 1 is deemed as the best. In fact, for some configurations this choice may dangerously overestimate the true value. It was shown in an earlier paper by the same authors that by increasing the number of elements in the finite element mesh one will paradoxically improve the mesh’s stability towards its theoretical limit. The present paper refines some details, presenting small scale numerical tests. The first test involves a long truss/bar consisting of one row of elements whose critical Courant number changes as elements are added one after another. Since this increases the critical number one may pick up a time step such that it is supercritical to a certain mesh but becomes subcritical by merely adding one element. In a similar fashion, a square area is tested in the second example, using different arrangements of edge supports. It is concluded that the usual setting, Cr = 1, is not entirely safe.

000009292 540__ $$aText je chráněný podle autorského zákona č. 121/2000 Sb.
000009292 653__ $$aexplicit integration, Courant number, critical time step, wave propagation, dispersion

000009292 7112_ $$aEngineering Mechanics 2012$$cSvratka (CZ)$$d12/05/2014 - 15/05/2014$$gEM2012
000009292 720__ $$aPlešek, J.$$iKolman, R.$$iGabriel, D.
000009292 8560_ $$ffischerc@itam.cas.cz
000009292 8564_ $$s1381627$$uhttps://invenio.itam.cas.cz/record/9292/files/292_Plesek_J-FT.pdf$$yOriginal version of the author's contribution as presented on CD, paper (No. 292).
000009292 962__ $$r8924
000009292 980__ $$aPAPER