Non‐linear dynamics of three‐dimensional rods: Exact energy and momentum conserving algorithms
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Publication:4835815
DOI10.1002/nme.1620380903zbMath0860.73025OpenAlexW2058714499MaRDI QIDQ4835815
N. Tarnow, Manuel Doblaré, Juan C. Simo
Publication date: 23 April 1997
Published in: International Journal for Numerical Methods in Engineering (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1002/nme.1620380903
total angular momentumtotal linear momentumfinite bendingdissipative algorithmsfinite extension sheartime stepping algorithms
Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Finite element methods applied to problems in solid mechanics (74S05)
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Cites Work