Rohrknie

Thin-Walled Tube

Tested with CGX 2.16 / CCX 2.15

• Modal and static analysis
• Shell and solid model
• Full and half models (symmetry reduction)
• Automatic movie generation in the post-processing
• Application of distributed loads
• Generation of a force-displacement curve

Model-independent files

File	Contents
values.fbd	CGX script, model parameters
geo.fbd	CGX script, geometry plot
post-modal.fbd	CGX-script, Animation of mode shapes
df.gpl	Gnuplot command file for the force-displacement-plot
test.py	Python script to run all simulations

In order to avoid inconsistent use of the individual scripts, top level script files are provided, which contain the calls to pre-processing, solving and post-processing.

Reference for the mass properties

The theoretical mass and cg position are computed to compare with the values obtained by CGX for evaluation of geometric precision in CGX.

Comparison for the paramters given in values.fbd and with C3D20R elements.

Model	File	Volume	x of cg
Reference		55860	41.59
Solid full	solid.fbd	54881	41.15
Solid full (45° sweep)	solid1.fbd	55568	41.48
Solid half	solid-sym.fbd	27440	41.15

Model	File	Area	x of cg
Reference		56807	41.64
Shell full	shell.fbd	55965	41.30
Shell half	shell-sym.fbd	27982	41.30

Properties of the expanded elements

Model	File	Volume	x of cg
Reference		55860	41.59
Shell full, expanded	shell-modal.fbd	55337	41.34
Shell half	shell-sym-modal.fbd	27709	41.37

Modal analysis results for solid/shell and full/reduced model

The mode frequencies for the first two symmetric mode shapes are compared. All models have the same mesh density and consist of a single layer of C3D20R elements (after shell expansion). For the shell models, the reference surface is the outside. This might lead to slightly increased mass.

Mode	Solid full	Solid half	Shell full	Shell half
In-plane bending	337.2	337.2	339.9	350.5
Ovalization	894.7	895.0	898.3	900.7

The animated gifs are created automatically in post-modal.fbd, wich is called by the top level script for the individual models.

The movies contain one and a quarter cycles. This is because the gif movies are just played once on github and then remain static with the last frame displayed.

Full shell model, modal analysis

File	Contents
shell.fbd	CGX script, pre-processing for the shell model
shell-modal.fbd	CGX-script, complete modal analysis of the shell model (including pre-post)
shell-modal.inp	CCX input, modal analysis, shell model

> cgx -b shell-modal.fbd

Half shell model, modal analysis

File	Contents
shell-sym.fbd	CGX script, pre-processing for the shell model with symmetry
shell-sym-modal.fbd	CGX-script, complete modal analysis of the shell model with symmetry (including pre-post)
shell-sym-modal.inp	CCX input, modal analysis, shell model with symmetry

> cgx -b shell-sym-modal.fbd

Full Solid model

File	Contents
solid.fbd	CGX script, pre-processing for the solid model
solid-modal.fbd	CGX-script, complete modal analysis of the solid model (including pre-post)
post-solid-static.fbd	CGX-script, post-processing of the solid static simulation
solid-modal.inp	CCX input, modal analysis, solid model
solid-static.inp	CCX input, static analysis, solid model

Full solid model, modal analysis

> cgx -b solid-modal.fbd

Full solid model, static analysis

In the static analysis we apply a distributed load to the upper end of the tube, without constraining the cross section shape using the *distributing coupling command. The nodes of the lower left end are completely constrained.

The generation of a force-displacement curve is demonstrated.

First, the mesh is generated:

> cgx -b solid.fbd

Solution

The analysis consists of two steps.

1. Full load is applied in negative x-direction, just the final results are written to the results files.
2. The load is increased until it reaches the same value in positive x-direction. The results are written in small intervals for generation of a force-displacement curve

> ccx solid-static
> monitor.py solid-static

Postprocessing:

> cgx -b post-solid-static.fbd

Steps for generation of the force-displacement curve:

1. Extraction of the time history data from the dat-file using the script dat2txt.py.
2. Creating a single file from the displacement history and the force history using the join shell command.
3. Running Gnuplot with the command file df.gpl.

The force-displacement plot is heavily non-linear because of the severe changes of the section moment of inertia due to ovalization. The displacement range for which convergence of the solver can be obtained depends on the element type and the mesh density. Here we use C3D20R elements.

Half solid model, modal analysis

File	Contents
solid-sym.fbd	CGX script, pre-processing for the solid model
solid-sym-modal.fbd	CGX-script, complete modal analysis of the solid model (including pre-post)
solid-sym-modal.inp	CCX input, modal analysis, solid model

> cgx -b solid-sym-modal.fbd