Inducing a Knot to recover large nonlinear rotations on Shells and Beams.

disla

Hi,

According to the ccx manual, in versions prior to and including version 2.7 a knot was introduced as soon as the user applied a rotation or a moment to a node.
That changed later and seems some functionalities were affected. I’m not into the details but there is a workaround to recover some of them.
One can force a Knot to show up in different ways. There are two of them which are particularly easy to set up. (Victor , I think this could be implemented.)

•If the thickness is not the same in all participating elements.
•If the offset is not the same in all participating elements.

Then the BC are applied to the Knot. I have applied this idea to test large rotations on shells and beams and it works for me.
I’m using a benchmark to check performance.
Special attention to orientation on beams.
Some Buckling analysis might be required to anticipate buckling modes that could emerge during the analysis.

Beams can be rotated directly by means of rotation and moment (I mean nonlinear). Shells by rotation. (I’m still searching how to do it directly with moments).

disla

Popular Benchmark Problems for Geometric
Nonlinear Analysis of Shells
K.Y.Sze1*, X.H.Liu1#, S.H.Lo2



Results:



https://we.tl/t-4JbvRCH53m

Victor

Forcing a knot at the loaded end causes it to solve for all angles, unlike the 360/180 degree convergences failures without?

I wonder what the disadvantages of knots are. Maybe they artificially constrain deformation since they supposedly only allow uniform expansion?

disla

It seems it solve the 360/180 problem. I have pushed the number of revolutions of the shell strip example up to ten and the approach is robust. It fails after 8 complete turns.
That’s normal considering there is a lot of deformation involved. I have also try using degrees instead of radians to discard the possibility that the issue came from wrong translation into amplitude, and it also works.

Maybe they artificially constrain deformation

If I understood well the manual the Knot reduces the number of normal vectors and automatically declares a common MPC in between the cloud of nodes.

disla

I have found the way to apply the moment directly to the shell. Not 100% sure if this can be generalized but it works in this case leading to the same result as imposing the rotation.

Example based on Figure 3a. Cantilever to end bending moment S8R.liml
Moments can be distributed across the Knots of the edge in the same way as forces if using the same coefficients.





Amplitude definition for *CLOAD,AMPLITUDE=Moment is required in the custom cards.

Victor

From what I've seen with beam elements, if there's a knot where you apply a moment or rotation constraint, then it uses that instead of mean rotation MPCs. So my guess is this avoids the <90 degree limitation on mean rotation MPCs.

disla

.Nonlinear buckling of long wire (B32R) with initial imperfection under pure torsion using Knot.

disla

Knots (ccx) may be of nice help when applied to the extreme of beams or shell elements but, when they emerge inadvertently in between the spam , they can affect considerably the results.
In between knots make the expanded nodes between elements to lie in a plane that is made rigid. That prevent the nodes form stretching in the plane, stiffening artificially the model.
I have found >100% difference in deflections due to this effect + discontinuous shear stresses.
One way to prevent knots in between curved surfaces/beams is to provide a minimum of the following number of elements in the arc direction.



This assumes same material properties ,no offsets between elements and common orientation.
The video shows the amplified effect of in between knots on beams. Images are better retained in memory

Victor

I guess that's the reason Guido once removed the use of knots in some places like beam ends where they seem better.

On curves like this, I wouldn't consider it a serious problem because with mesh refinement, the angle between elements will go down below the 20 degree threshold for knots and they'll disappear.

But that sphere problem is a worry, where you had a row of knots caused by different thicknesses that wasn't going to disappear with mesh refinement.

disla

like beam ends where they seem better.

I agree. On free ends they could be of big help to impose moments and rotations without noticeable side effects and regarding midspan knots is just a matter of paying attention to refinement to avoid Knots when possible.