Numerical stability of dynamic relaxation analysis of non‐linear structures
- 1 January 1976
- journal article
- research article
- Published by Wiley in International Journal for Numerical Methods in Engineering
- Vol. 10 (6) , 1407-1410
- https://doi.org/10.1002/nme.1620100620
Abstract
The estimation of the parameters (‘fictitious densities’) which control the convergence and numerical stability of a non‐linear Dynamic Relaxation solution is described. The optimal values of these parameters vary during the iterative solution and they are predicted from the Gerschgörin bounds, that is rowsums of the stiffness matrix, which are divided into constant and variable parts for computational convenience. The procedure is illustrated by reference to the analysis of an axially loaded beam on a non‐uniform elastic foundation.Keywords
This publication has 8 references indexed in Scilit:
- Large deflection of plates and beams obeying non-linear stress—strain lawsJournal of Strain Analysis, 1974
- The finite deflection of plane framesInternational Journal of Mechanical Sciences, 1973
- Non‐linear structural analysis by dynamic relaxationInternational Journal for Numerical Methods in Engineering, 1971
- PREDICTION OF COLLAPSE LOADING FOR COMPOSITE HIGHWAY BRIDGES.Proceedings of the Institution of Civil Engineers, 1971
- SHELLS OF REVOLUTION UNDER ARBITRARY LOADING AND THE USE OF FICTITIOUS DENSITIES IN DYNAMIC RELAXATION.Proceedings of the Institution of Civil Engineers, 1970
- Postbuckling of tapered platesInternational Journal of Mechanical Sciences, 1969
- Dynamic-relaxation solution for the large deflection of plates with specified boundary stressesJournal of Strain Analysis, 1969
- Large deflexion of variable-thickness platesInternational Journal of Mechanical Sciences, 1968