Title
On A Fourth Order Fea Multistep Time Integration Method For Lightly Damped Media
Abstract
For time integration in finite element analysis, a higher order counterpart of the widely used Newmark method is formulated by applying the three step fourth order Adams-Moulton (AM) method to lightly damped systems with accelerations. A linear system arises for which the solution effort is exactly the same as in Newmark. Using Fade approximations, step-wise and cumulative errors in both methods are assessed for both free and forced response. For comparable accuracy Newmark requires much smaller time steps than AM, even in low frequency modes. Numerical damping at fourth order is introduced into AM. Newmark is numerically stable for all time steps. However, owing to extraneous eigenvalues AM exhibits a critical ratio of time step to period, above which numerical instability occurs. This is problematic in high frequency modes with small time periods. It is shown that this stability limit is not obviated by damping, whether viscous or 'numerical'. Instead, a discussion is given of removal of higher order modes using filters based on the Wavelet Transform.
Publication Date
5-1-2006
Publication Title
Acta Mechanica
Volume
183
Issue
1-2
Number of Pages
23-40
Document Type
Article
Personal Identifier
scopus
DOI Link
https://doi.org/10.1007/s00707-005-0289-0
Copyright Status
Unknown
Socpus ID
33744510838 (Scopus)
Source API URL
https://api.elsevier.com/content/abstract/scopus_id/33744510838
STARS Citation
Nicholson, D. W. and Lin, B., "On A Fourth Order Fea Multistep Time Integration Method For Lightly Damped Media" (2006). Scopus Export 2000s. 8397.
https://stars.library.ucf.edu/scopus2000/8397