ArcLength integrator

[Kbra]

I am currently conducting static pushover analysis of steel fibre reinforced structures.
My aim is include the degradation part of the pushover curves in order to
capture the SFRC improved toughness.

The Opensees manual describes:
"This command is used to construct a StaticIntegrator object of type
ArcLength. Arc-length methods are used to enable the solution algorithm to
pass limit points, such as maximum and minimum loads, and snap-through and
snap-back responses. At these limit points, the stability of the numerical
system is dependent on whether the analysis is performed under load or
displacement control. In structural analysis, these limit points are
characteristic of cracking of reinforced concrete and of buckling of
shells."

It seems therefore as the Arclength integrator can be applied to include the
degradation part of a pushover curve. However, the manual do not give a
complete describtion of this command and there are several questions marks
added to the explanation.

My questions are:

Nr 1: Is it possible to include the arclength integrator in a static pushover analysis?
Nr 2: If so what kind of test command is recommended?
Nr 3: Have anyone experience with this, and in case know of any examples available?

Thanks

[silvia]

In one of the examples in the examples repository I found the following command:
#integrator ArcLength 0.0075 1.0

as you can see, it was commented out and replaced with another integrator,
but this may be a place to start.

[fmk]

you can replace the integrator in Example3.2.tcl with the following:

integrator ArcLength [expr $dU/2.0] 0.0

the problem with the ArcLength is determining the initial way to go at each new step, i.e. there are two directions to go which will give the same arcLength (forward or back the way we just came) .. if choose wrong can go back the way you just came .. there are a number of ways to choose the initial dirn .. the one in OpenSees is rather simple .. Laura Lowes
and her student Nilanjan at the University of Washington have looked into other schemes and can advise you further.

[Boris]

Take a look at draft lecture notes for more information on general constrain equations for nonlinear FEM equations:

http://sokocalo.engr.ucdavis.edu/~jerem ... node8.html

(some figures are clipped, perhaps use the PDF version for better quality).

you can also try the Hyperspherical constraint, sort of generalized arch -length...

Boris