In all textbooks, when iteration methods are introduced, the iterative formula is always H(x)x+f=0, where f is the external force applied on the system. All methods are stated when f is fixed.
These methods cann't be used directly to the displacement-controlled case, unfortunately. The reason is that the external force f keeps changing during the iteration. In this case, f is determined due to both the controlled displaement and the instant system stiffness, of which the former is fixed but the latter keeps changing during the iteration. As a result, the external force f is not fixed.
In fact, when it comes to ABAQUS UMAT, it is always a problem of fixed-deformation instead of fixed-loading. Therefore, the iterative methods on textbook cann't be used directly.
Who can recommend some proper books on that topic, pls ? :)
references that discuss control methods
Hello,
References 1, 2 and 4 discuss load control, displacement control and arc length control. Reference 4 has a particularly nice discussion of the various techniques. I used reference 4 to write a program using displacement control. You may look at a paper I wrote which provides an algorithm for displacement control (http://people.wallawalla.edu/~louie.yaw/Co-rotational_docs/2Dcorot_trus…).
Reference 3 discusses generalized displacement control.
REFERENCES
1. Crisfield, M. A. (1991). Non-linear Finite Element Analysis of Solids and Structures
Vol 1. Chichester, England: John Wiley & Sons Ltd.
2. M. J. Clarke and G. J. Hancock. A study of incremental-iterative strategies for non-linear
analyses. International Journal for Numerical Methods in Engineering, 29:1365-1391, 1990.
3. Y. B. Yang, L. J. Leu, and Judy P. Yang, Key Considerations in Tracing the Postbuckling
Response of Structures with Multi Winding Loops, Mechanics of Advanced Materials and
Structures, 14:175-189, 2007.
4. McGuire, W., Gallagher, R. H., and Ziemian, R. D., Matrix structural analysis, 2nd Ed.,
Wiley, New York, 2000.
I hope this is what you were looking for.
regards,
Louie