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The effects of element shape on the critical time step in explicit time integrators for elasto‐dynamics
Author(s) -
Askes Harm,
RodríguezFerran Antonio,
Hetherington Jack
Publication year - 2014
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.4819
Subject(s) - element (criminal law) , distortion (music) , bilinear interpolation , finite element method , quadrilateral , mathematics , rule of thumb , integrator , mathematical analysis , geometry , set (abstract data type) , control theory (sociology) , algorithm , computer science , structural engineering , engineering , law , statistics , amplifier , computer network , control (management) , bandwidth (computing) , artificial intelligence , political science , programming language
Summary In this paper, the effects of element shape on the critical time step are investigated. The common rule‐of‐thumb, used in practice, is that the critical time step is set by the shortest distance within an element divided by the dilatational (compressive) wave speed, with a modest safety factor. For regularly shaped elements, many analytical solutions for the critical time step are available, but this paper focusses on distorted element shapes. The main purpose is to verify whether element distortion adversely affects the critical time step or not. Two types of element distortion will be considered, namely aspect ratio distortion and angular distortion, and two particular elements will be studied: four‐noded bilinear quadrilaterals and three‐noded linear triangles. The maximum eigenfrequencies of the distorted elements are determined and compared to those of the corresponding undistorted elements. The critical time steps obtained from single element calculations are also compared to those from calculations based on finite element patches with multiple elements. Copyright © 2014 John Wiley & Sons, Ltd.