Non-linear Buckling

Tested with CGX 2.19 / CCX 2.19

• Large displacements
• Plasticity
• Buckling with imperfection (a small internal pressure)
• Shell elements

File	Contents
pre.fbd	Pre-processing script for CGX
post.fbd	Post-processing script for CGX
Kasten.inp	CCX input
df.gpl	Gnuplot input for force-displacement curve

Reference solution for elastic limit (without buckling)

Preprocessing

The parameters can be changed in pre.fbd

Parameter	Value	Meaning
lx	100	width in x-direction in mm
ly	100	width in y-direction in mm
lz	150	height in mm
nd	7.8	target node distance in mm
disp	20	displacement in mm

> cgx -b pre.fbd

Geometry and sets

Solving

> ccx Kasten
> monitor.py Kasten

Kasten.inp

Mesh and set definitions

*include,input=all.msh
*include,input=lower.nam
*include,input=upper.nam

Clamping of the upper and lower edge

*boundary
Nlower,1,6
Nupper,1,6

Material definition (elasto-plastic)

*MATERIAL,NAME=Steel
*ELASTIC
210000,.3
*plastic
100,0
200,0.3
300,1
*DENSITY
7.8E-9

Material and shell thickness assignment

*SHELL SECTION,ELSET=Eall,MATERIAL=Steel,offset=0
1

Step 1: Internal pressure (imperfection)

*STEP,nlgeom
*STATIC
*dload
*include,input=all.dlo
*el file
S
*node file
U
*end step

Step 2: Axial compression (prescribed displacement)

*step,nlgeom
*static
0.05,1,,0.05
*boundary
*include, input=disp.inc
*el file
S,PEEQ
*node file
U
*node print,totals=only,nset=Nupper
U,RF
*end step

Postprocessing

> cgx -b post.fbd

Magnitude of the displacement due to pressure application (imperfection). Max. deflection is approximately 10% of the sheet thickness.

Deformed geometry after collapse. The left image shows the result for the parameters as in the files. The right image has double the displacement and a target element size of 3 mm.

Vertical displacement and plastic equivalent strain:

Force-displacement plots. Left: full history, right: detail of transition to collapse. Note that 40 kN is the elastic limit in the linear analysis.