Nonlinear Axial Compression (Buckling) of a Cylinder not Converging

Analysis issues
101

Dear All,

With just over 100 replies I would like to thank everyone who contributed to our original topic which was concerning the (non) convergence of nonlinear buckling of a circular cylindrical vessel. Indeed, we are still having convergence issues (we can proceed upto around 90% of the critical buckling load predicted by Donnell’s equation).

I have to agree with @xyont final comments regarding the difficulty in carrying out a nonlinear buckling analysis using elastic material and perfect geometry. Indeed, the reaction force-displacement curve that we obtained using various element types and mesh densities will serve to illustrate that without Riks solver, it seems a futile effort to hassle with elastic and perfect geometry.

image
image900×650 65.4 KB

The only way the buckling path taken from the main solution branch to the other branch can be resolved is by utilizing the Riks solver (NR cannot do it).

Thanks again for all your help, contributions and constructive discussions.
Fethi

102

Some good news regarding the Riks solver: Feature request: Static Riks / arc-length procedure · Issue #165 · Dhondtguido/CalculiX · GitHub

In Abaqus, there are more ways to handle such problematic global instabilities in addition to the arc-length method, such as automatic step-wise stabilization or contact stabilization, dynamic implicit quasi-static procedure or even the dynamic explicit procedure.

3 Likes
103

Juan74 posted the inp.

Wait to face the problem using test data.

1 Like
104

We are working on the composite layering of S8R element, but there’re some problems

As the number of layers increased the model starts to behave differently, here is the result for nonlinear buckling with 2 layers (each 12.5 mm) and plastic material card @xyont

hcpy_1
hcpy_1784×672 50.1 KB

We’ve decided to reduce the lc value of S8R mesh from 256 to 128 as a solution and used applied deformation of 5e3 which is shown below

5e3_deformation
5e3_deformation784×672 16.9 KB

again used 2 layered composite shell section with plastic and elastic material cards

the elastic solution solved 17.9 mm whereas the plastic solution solved 22 mm

Screenshot 2026-10-04 222012
Screenshot 2026-10-04 222012872×554 130 KB

We would appreciate your opinion.

the inp file for 2-layered plastic solution:

**Heading
nonlinear buckling analysis, skirt  with openings and holes under load, shell mesh
*INCLUDE, INPUT=all.msh
*INCLUDE, INPUT=skir_sless_top_LOAD.nam
*INCLUDE, INPUT=base_plate_center_YFIX.nam
*BOUNDARY
Nbase_plate_center_YFIX,1,3
Nskir_sless_top_LOAD,1,2

*Material, Name=S450
*Density
7.8E-09
*Elastic
210000, 0.28
*Expansion, Zero=20
1.1E-05
*Conductivity
14
*Specific heat
440000000
*Plastic
450, 0
495, 0.02
540, 0.05
675, 0.4
**

*SHELL SECTION, ELSET=Eall, COMPOSITE
12.5,,S450
12.5,,S450

** step 1, nonlinear displacement control buckling analysis 
*STEP,NLGEOM,INC=10000
*STATIC
0.02,1,1e-4,0.1 
*BOUNDARY, 
Nskir_sless_top_LOAD,3,3,100
*NODE FILE, OUTPUT=2D
U
*EL FILE
S
*NODE PRINT, NSET=Nskir_sless_top_LOAD
U
*NODE PRINT, NSET=Nbase_plate_center_YFIX, TOTALS=ONLY
RF

*END STEP
105

I guess your problem is again mesh quality. I’m not sure the use of composite material modeling can improve the solution.

This one here achieves 100% load (same as before but with plastic material): https://drive.google.com/file/d/1-U8xHjvbqKqmvNT269CqteeaVmiFkb5H/view?usp=sharing

1 Like