Traditionally, the finite element technique has been applied to static and steady-state problems using implicit methods. When nonlinearities exist, equilibrium iterations must be performed using Newton-Raphson or quasi-Newton techniques at each load level. In the presence of complex geometry, nonlinear material behavior, and large relative sliding of material interfaces, solutions using implicit methods often become intractable. A dynamic relaxation algorithm is developed for inclusion in finite element codes. The explicit nature of the method avoids large computer memory requirements and makes possible the solution of large-scale problems. The method described approaches the steady-state solution with no overshoot, a problem which has plagued researchers in the past. The method is included in a general nonlinear finite element code. A description of the method along with a number of new applications involving geometric and material nonlinearities are presented.

1.
Bathe, K. J., Ozdemir, H., and Wilson, E. L., 1974, “Static and Dynamic Geometric and Material Non-Linear Analysis,” SESM Report No. 74-4, Department of Civil Engineering, University of California, Berkeley, CA.
2.
Belytschko, T., 1983, “An Overview of Semidiscretization and Time Integration Procedures,” Computational Methods for Transient Analysis, eds., T. Belytschko and T. J. R. Hughes, North Holland, pp. 1–66.
3.
Brew
J. S.
, and
Brotton
D. M.
,
1971
, “
Non-Linear Structural Analysis by Dynamic Relaxation
,”
International Journal Numerical of Methods in Engineering
, Vol.
3
, pp.
436
483
.
4.
Day
A. S.
,
1965
, “
An Introduction to Dynamic Relaxation
,”
The Engineer
, Vol.
219
, pp.
218
221
.
5.
Kant
T.
, and
Patel
S.
,
1990
, “
Transient/Pseudo-Transient Finite Element Small/Large Deformation Analysis of Two-Dimensional Problems
,”
Computers and Structures
, Vol.
36
, No.
3
, pp.
421
427
.
6.
Otters
J. R. H.
,
1966
, “
Dynamic Relaxation
,”
Proceedings Institute of Civil Engineers
, Vol.
35
, pp.
633
656
.
7.
Pica
A.
, and
Hinton
E.
,
1980
, “
Transient and Pseudo-Transient Analysis of Mindlin Plates
,”
International Journal of Numerical Methods in Engineering
, Vol.
15
, pp.
189
208
.
8.
Sauve´, R. G., 1993, “H3DMAP Version 5.2—A General Three-Dimensional Finite Element Computer Code for Linear and Non-Linear Analyses of Structures,” Ontario Hydro Research Division Report No. 92-256-K, Rev. 2.
9.
Sauve´, R. G., and Dubey, R. N., 1991, “Efficient Shell Elements for Three-Dimensional Non-Linear Structural Dynamic Analysis,” Structural Dynamics: Recent Advances, eds., M. Petyt, H. Wolfe, and C. Mei, Elsevier Applied Science, pp. 264–276.
10.
Sauve´, R. G., Badie, N., and Holt, R., 1989, “Simulation of Fuel Channel Response in CANDU Nuclear Reactors,” Proceedings of the 10th Structural Mechanics in Reactor Technology, Paper No. L08/4, pp. 219–224.
11.
Underwood
P.
,
1983
, “
Dynamic Relaxation
,”
Computational Methods for Transient Analysis
, Vol.
1
, pp.
245
265
.
12.
Wood
W. L.
,
1967
, “
Comparison of Dynamic Relaxation With Three Other Iterative Methods
,”
The Engineer
, Vol.
224
, pp.
683
687
.
This content is only available via PDF.
You do not currently have access to this content.