The effects of element shape on the critical time step in explicit time integrators for elasto-dynamics
Author (s): Askes, H.; Rodríguez-Ferran, A.; Hetherington, J.
Journal: International Journal for Numerical Methods in Engineering
Volume: 101, Issue 11
Pages: 809 – 824
Date: 2015
Abstract:
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 hortest 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.
Bibtex:
@article {2015-nme4819,
author = {Askes, H., Rodr\’{\i}guez-Ferran, A. and Hetherington, J.}
title = {The effects of element shape on the critical time step in explicit time integrators for elasto-dynamics},
journal = {International Journal for Numerical Methods in Engineering},
volume = {101},
number = {11},
issn = {1097-0207},
url = {http://dx.doi.org/10.1002/nme.4819},
doi = {10.1002/nme.4819},
pages = {809–824},
year = {2015},
}