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Displacement Controlled Geometric Nonlinear FEM

Hi I am working on numerical simulation of petroleum pipeline subjected to
seismic hazards. I have developed Geo-Nonlinear FEM code for load
controlled which i have compered with Ansys and it is working fine.
now i would like to apply fault  displacement for this i need to
convert my code to displacement controlled using penalty approach
but it is not converging. i will be very happy if any one can suggest
how i can over come this problem or plz sugest me some book or papre. here I am using Newton-Raphson method 


thanking you



phunguyen's picture

Hi Vasudeo,

 I guess you were trying to pass the snap-back point with standard displacement control that is impossible since the displacement is now decreasing. For this you need arclength controls or path-following methods. You can find them in the books of Prof. Crisfield "Nonlinear  finite elements...". (I am not sure of the title of the book).

Hope it helps.

George Papazafeiropoulos
First Lieutenant
Infrastructure Engineer, Hellenic Air Force
Civil Engineer, M.Sc., Ph.D. candidate

Crisfield's book is named "Nonlinear Finite
Element Analysis of Solids and Structures" and it has volume 1
(essentials) and volume 2 (advanced topics). You will need sections 9.3 and 9.4
of volume 1 (version 2000)

In addition, you may find interesting the paper
"Geometrical Interpretation of the Arc-Length Method" by M.Fafard and
B.Massicotte (Computers and Structures, Vol.46, No.4, pp.603-615, 1993). In
this paper two arc-length methods are presented and compared (the Crisfield and
Ramm methods). Moreover, a more general method is developed, in which
arc-length methods remain as special cases and which also covers
load-controlled and displacement controlled methods. You can modify this
general method according to your needs.

George Papazafeiropoulos
First Lieutenant
Infrastructure Engineer, Hellenic Air Force
Civil Engineer, M.Sc., Ph.D. candidate

yawlou's picture


 You may like to look at an article I wrote here

In the article I have an outline of a displacement control algorithm.  This is done in the context of a geometrically nonlinear 2d truss formulation (using the corotational method).  I also have references at the end of the article.

Displacement control can handle problems of snap through.  However, if snap back or multiple equlibrium path loops are necessary for you to traverse during your nonlinear analysis, then it will be necessary for you to use arc length control or generalized displacement control.

 Arc length methods are very popular, but personally I like generalized displacement control better.  I have implemented it and find it easier to implement.  A really good reference for generalized displacement control is the following:

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.




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