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non-linear buckling

non-linear buckling

non-linear buckling

(OP)
Hello all,

For some time I've been trying to predict the occurance of rotation in a pipeline with an initial curvature, when bent in the opposite (against the initial curvature) direction. My assumption is that when you try to 'straighten' a curved pipe, it will try to rotate 180 degrees at a certain point to find the 'easiest' (i.e. minimal energy) way of bending in the opposite direction. Because the construction will most likely have two equilibrium positions at this snap-through point, I think this is actually a case of non-linear buckling.

I tried to model this problem in Ansys using a half-circular curved pipe (pipe16 element). On one side this pipe was fixed except for roty, which is constrained with a torsional stiffness. On the other side I applied a moment in the direction to 'straighten' the pipe.
To make sure that rotation occurs I added a small imperfection (small fz) perpendicular to the plane of curvature.

Now here is my problem: I tried both normal NR and arclength methods but they don't give proper convergence. Of course I tried modifying timestep sizes, min and max arclength multipliers, bending moment and imperfection location and size but still the solution ends prematurely. Sometimes however the error solution (substep 999999) indicates rotations in the order of 180 degrees, but somehow the arclength method is not able to follow the deflection/force curve.
Therefore I would like to know if you agree with my approach of this problem, and if you can see what I might be doing wrong in modeling it. What I am ultimately looking for is a completed ansys run showing the bending of the pipe until the snap-through point, the actual snap (pipe rotation), and the post-buckling bending of the pipe.

Just to be clear, in reality the pipeline can be several kilometers in length.

I'm using the following settings in ansys:

large deflection
stress stiffening
arc-length method
pipe16 element

I hope that someone can help me. Most probably I forgot some information here so please ask for it.

Thanks very much!


For the proper understanding of the problem, this is my input file (this one is without arclength control):

/config,nres,100000
/clear
/filename,model,0
/prep7

et,1,pipe16
keyopt,1,6,1
R,1,0.2,0.01
MP,EX,1,207E9
MP,prxy,1,0.29
mp,ex,2,1e9
mp,prxy,2,0.29

r=100
k,1,0,0,0

CIRCLE, 1,r,,,180


k,,-r,-r,0
l,4,5,10

DK,5,all,0
DK,4,ux,0
DK,4,uy,0
DK,4,uz,0
DK,4,rotx,0
DK,4,rotz,0

Dl,3,,ux,0
Dl,3,,uz,0
Dl,3,,uy,0

fk,2,mz,2e5
fk,3,fz,10


LSEL,S, , ,       3
LATT,2,1,1, , , ,  
ALLSEL,ALL  

k,100,r,0,20
l,100,2

lesize,4,,,1
lmesh,4

lesize,1,,,10
lesize,2,,,10
lmesh,1
lmesh,2
lmesh,3

ANTYPE,0
NLGEOM,1
NSUBST,50,10000,1   
AUTOTS,1
SSTIF,ON
NEQIT,500
OUTRES,ALL,ALL  
RESCONTRL,DEFINE,ALL,ALL,1

/solve

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