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Arc length factors in Riks method
Hello,
It would be grateful if someone could explain me how to calibrate arc length increment factors in Static, Riks method in Abaqus.
For a default input in Static, Riks step I get max LPF factor equal 147(this value is probably correct, expected 147.8). Unfortunately, I'm not satisfied in number of increments(the result of 12 increments). The question is: how to calibrate arc length increment factors(initial, minimum, maxium arc length increment and estimated total arc length) to get more accurate results.
I found something about it, quote:
In cases of severe nonlinearity, the Riks method may not converge or may converge to previously obtainted equilibrium configurations. Often such problems are caused by the arc length being to large. If you suspect that this is the problem, look in the message file to find the typical arc lengths used and return the analysis with a smaller maxium arc length.
What are typical arc lengths?
Attached file contains LPF-arc length graph.
| Attachment | Size |
|---|---|
 graph.JPG | 28.69 KB |
Arc length method is quite
Arc length method is quite peculier as both force and displacements are unknown.
To understand this scheme, imagine you're blindfolded and marching along a curved wall (and not allowed to deviate from curve). So, at any isntance you take ur stick and and try to tap in front of you. In this case, the horizontal projection of stick is search radius, and the distance you cover in one step is arc length.
In a similar way arc length works. In abaqus you give initial increment, total arc length (default is 1, works most of the time), and max arc length increment (1E+36 default, if I remember correctly). So specify max arc length (I always start with 1, and I keep an eye on the status file). In status file, LPF and increment in LPF will be printed. If you find it too small, increase the max arc length increment. You can interprete it as
LPF*Applied Load = Current Load
LPF inc * Applied Load = Load Increment.
Hope it helps your purpose.
Kumar
--
The world started with 0, is progressing with 0, but doesn't want 0.
Thank you for your
Thank you for your exceptionaly good explanation.
I have to agree, I found out that total arc length equal to 1 in many cases is the correct value.
Now I feel free to change the factors and more or less I know what I'm doing.
Ł.
Arc length method
Please tell me the alogotithm for E Ramm's arc length method. I am using the following type of algorithm but am not getting the correct result----
u{0}, lamda=0
Fext
n no of steps
Kg (stiffness with u{0})
u1=(Kg)^-1 * Fext'
[L D]=ldl(Kg)
m=det(D)
arc_length=norm(u1)
lamda= 0.1*arc_length/sqrt(u1'*u1+1)
if m<0
lamda=-lamda
end
u=lamda*u1
iterations:
Kg(u{0}+u)
Fint(u{0}+u)
Fres=Fint-lamda*Fext
ur=-inv(Kg)*Fres'
u1=inv(Kg)*Fext
del_lamda=-(u'*ur)/(u'*u1)
del_ur=ur+del_lamda* u1
u==u+del_ur
lamda=lamda+del_lamda
if norm(Fres)<10^-5)
end
u{0}=u{0}+u
if lamda>=2
end
So please help me..Waiting for the solution eagerly .
Thanks
Md Rushdie Ibne Islam
Reference request
Dear "irushdie",
Do you have Ramm's study in electronic format? If yes, could you send it to me by email so that I can help you? My email is gpapazafeiropoulos@yahoo.gr.
Thank you very much in advance.
George
Arc length method
In the following links one can find MATLAB source codes for implementing the arc-length method (Crisfield, 1981 and Fafard & Massicotte, 1993):
http://en.pudn.com/downloads599/sourcecode/math/detail2447809_en.html
http://www.mathworks.com/matlabcentral/fileexchange/44352-arc-length-method
_______________________________________________
George Papazafeiropoulos
First Lieutenant, Infrastructure Engineer, Hellenic Air Force
Civil Engineer, M.Sc., Ph.D. candidate, NTUA
Email: gpapazafeiropoulos@yahoo.gr
Website: http://users.ntua.gr/gpapazaf/