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Suppression of spurious intermediate frequency modes in under‐integrated elements by combined stiffness/viscous stabilization
Author(s) -
Daniel William John Trevor,
Belytschko Ted
Publication year - 2005
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1369
Subject(s) - spurious relationship , hourglass , quadrilateral , physics , stiffness , perturbation (astronomy) , finite element method , mathematical analysis , control theory (sociology) , acoustics , mathematics , computer science , statistics , control (management) , quantum mechanics , astronomy , artificial intelligence , thermodynamics
Abstract Solutions employing perturbation stiffness or viscous hourglass control with one‐point quadrature finite elements often exhibit spurious modes in the intermediate frequency range. These spurious frequencies are demonstrated in several examples and their origin is explained. Then it is shown that by critically damping the hourglass modes, these spurious mid‐range frequency modes can be suppressed. Estimates of the hourglass frequency and damping coefficients are provided for the plane 4‐node quadrilateral and a 4‐node shell element. Results are presented that show almost complete annihilation of spurious intermediate frequency modes for both linear and non‐linear problems. Copyright © 2005 John Wiley & Sons, Ltd.