Finite Element Analysis (FEA) is a numerical modelling technique for predicting behaviour of solids, fluids, electromagnetic fields, and heat-flows. Adaptive FEA automatically adjusts its mesh density to provide more accurate results. It's done by calculating FEA error and using it to alter the mesh density until error is reduced to a tolerable limit. This archive contains the following programs for adaptive FEA:
- femgs1 for carrying out linear 2D FEA
- adpgs1 for calculating FEA error and the remeshing parameters
- faopgs2 for adaptive unstructured mesh generation
- plotp for converting mesh, stresses, and error data into encapsulated postscript
Assuming gcc is already installed.
sudo apt update
sudo apt upgrade
sudo apt install gfortran
sudo apt install xpdf ghostscript
git clone https://github.com/SensorAnalyticsAus/adaptiveFEA.git
cd adaptiveFEA/
make distclean
make all
make clean
Following steps will complete a cycle of adaptive FEA
cd ./run
cp ../dot-dat/ex61.dat .
cp ex61.dat input.dat
Run the mesh plotting program to view the input mesh
../plotp
output device is postscript file pltf*.plt
Brightness controll factor [0.]...[1.]
0.7
plot membrane elements ? (t/f)
t
plot element errors or Domain dec? (t/f)
f
plot stress ? (t/f)
f
plot cable elements ? (t/f)
f
plot g strings ? (t/f)
f
number nodes ? (t/f)
t
number elements ? (t/f)
f
element reduction factor ? (0.0 - 1.0)
0.
auto scale ? (t/f)
t
plot single view ? t/f
t
view no 1/2/3/4 ?
1
isoyes = F
pltf1.plt opened
enter the title
Initial Mesh ex61.dat
4.6354998053636374E-310 0.0000000000000000 0.0000000000000000 0.0000000000000000
Convert output plot file to PDF format and view ex61.dat:
ps2pdf pltf1.plt
xpdf pltf1.plt.pdf
../femgs1
Enter the input file (.dat assumed)
ex61
Example rect
0.001000 0.000000
Guass [1] JCC [0]
1
Semi-Band-Width before = 112
Semi-Band-Width reduction Yes[1] No[0]
0
Semi-Band-Width after = 112
F E analysis started with node = 96 and elements = 153
iln = 5
...
...
*** Time for analysis = 0.000000 min or 0 sec ***
*** no of iterations = 0 ***
*** The stresses are stored in ex61.str ***
*** The results of FE are stored in ex61.fem ***
*** renumbered input data file ex6_.dat generated ***
../adpgs1
Enter the input file (.dat assumed)
ex61
Example rect
0.001000 0.000000
opening ex61.str for reading the stresses
-5.27588e+00 2.28607e-01 -2.51780e-01
...
...
nita (percent) from the current mesh = 48.490119
he_min = 0.871135 he_max = 106.717485
Enter your own hmin
1.25
Magnification = 1.4 (hmin = 1.2)
*** Element errors are stored in ex61.err ***
*** Mesh parameters are in ex61.me
*** Adaptivity results are in ex61.adp
../faopgs2
Max of 50000 nodes and 70000 elements can be meshed
***Node para are going to be used***
Enter the project file name (without extension)
ex61
Example rect
0.001000 0.000000
opening ex61.men for reading
cannot open ex61.men opening ex61.me for read
Enter [1] if coarse background mesh is to be refined
1
Enter [1] if mesh post-processing required
1
...
...
*** Mesh Compiled with 1600 Nodes and 3008 Element ***
*** File ex61o.dat with 1600 nodes & 3008 elements has been generated ***
*** Neural net training data saved in ex61.inf ***
../femgs1
Enter the input file (.dat assumed)
ex61o
Example rect
0.001000 0.000000
Guass [1] JCC [0]
1
Semi-Band-Width before = 2620
Semi-Band-Width reduction Yes[1] No[0]
1
...
...
*** Time for analysis = 0.000000 min or 0 sec ***
*** no of iterations = 0 ***
*** The stresses are stored in ex61o.str ***
*** The results of FE are stored in ex61o.fem ***
*** renumbered input data file ex61_.dat generated ***
../adpgs1
Enter the input file (.dat assumed)
ex61o
Example rect
0.001000 0.000000
opening ex61o.str for reading the stresses
1.61877e+00 -3.04040e-02 -4.70029e-01
...
...
nita (percent) from the current mesh = 32.172155
he_min = 0.017925 he_max = 1371.344995
Enter your own hmin
.9
Magnification = 50.2 (hmin = 0.9)
*** Element errors are stored in ex61o.err ***
*** Mesh parameters are in ex61o.me
*** Adaptivity results are in ex61o.adp
cp ex62o.dat input.dat
cp ex62o.str stress.dat
cp ex61o.err error.dat
../plotp
output device is postscript file pltf*.plt
Brightness controll factor [0.]...[1.]
0.7
plot membrane elements ? (t/f)
t
plot element errors or Domain dec? (t/f)
f
plot stress ? (t/f)
t
plot cable elements ? (t/f)
f
plot g strings ? (t/f)
f
number nodes ? (t/f)
f
number elements ? (t/f)
f
element reduction factor ? (0.0 - 1.0)
0.
auto scale ? (t/f)
t
enter 1 2 3 4 5 for sx sy sxy smax smin
3
plot single view ? t/f
t
view no 1/2/3/4 ?
1
isoyes = F
pltf1.plt opened
enter the title
Refined Mesh ex61o.dat Sxy
4.6354998053636374E-310 0.0000000000000000 -22.795900000000000 33.677500000000002
Convert to PDF and view ex61o.dat:
ps2pdf pltf1.plt
xpdf pltf1.plt.pdf
The last step can be repeated to obtain a plot with the error overlay by setting plot element errors or Domain dec? option as 't' and the following option as 'f'.
This folder contains sample dot-dat files for adaptive FEA. A dot-dat file specifies the starting mesh topology, material properties of the structure, boundary conditions, and applied force(s) i.e. load points on the structure for carrying out adaptive FEA. In this regard try.pdf contains information for creating custom dot-dat files. In such files the columns have to be maintained exactly in the same format as of try.dat. For instance the 3rd line of the try dot-dat file comprises first two fields of 6 columns i.e. 2 x 6 columns, followed by 9 fields of 5 columns i.e. 9 x 5 columns (a total of 57 vim columns). Each value must be fully contained within its own column. The FORTRAN graphics program plotp expect input values strictly being within the specified columns.
Other dot-dat files may contain some data fields outside of try.dat populated spaces, such data fields are not read thus can be ignored.
If faopgs2, femgs1, or plotp fail.
- Check dot-dat file is conforming to the expected format.
- Try increasing the
hminvalue in adpgs1 to reduce the number of elements in final mesh.
Full explanation of the adaptive technique can be found in Chapter 5 of Topping and Khan [1]. An earlier version; Khan and Topping [2].
[1]: BHV Topping and AI Khan, PARALLEL FINITE ELEMENT COMPUTATIONS - Chapter 5, Saxe-Coburg Publications
[2]: AI Khan, BHV Topping, Parallel adaptive mesh generation, Computing systems in Engineering 2 (1), 75-101