Adaptive Dynamic Relaxation

About

Dynamic Relaxation (DR) is a niche finite element analysis (FEA) technique which allows form-finding of flexible objects such as roofing sails, elastic-receptacles, robotic masks etc. This archive contains ANSI C and FORTRAN programs for carrying out adaptive DR analysis. This process can be broken down into following steps.

• Specifying a coarse 2D mesh with boundary nodes and out-of-plane loaded nodes.
• Computing the deformed coarse 3D mesh, from the loading, and elemental stresses by DR.
• Conducting adaptive analysis.
• Generating a refined mesh using the meshing parameters computed during adaptive analysis.
• Mapping the refined 2D adaptive mesh to coarse 3D mesh to form the final 3D refined mesh.

Installation

Assuming gcc is already installed.

sudo apt update
sudo apt upgrade
sudo apt install gfortran
sudo apt install okular ghostscript

git clone https://github.com/SensorAnalyticsAus/surf.git
cd surf
make distclean
make all
make clean

Dynamic Relaxation

Copy over a dot-dat file and call it input.dat

cd run
cp ../dot-dat/walldr.dat 
cp walldr.dat input.dat

Initial Mesh: walldr.dat

Run the DR program flat2

../flat2 
 input number of required iterations
1000
 INPUT MASS ADDITION
1000
 INPUT DENSITY
1
 OUTPUT /SLACK LENGTHS T/F
f


 INITIALISE LOAD,MASS,FOR FIRST TIME
  ENERGY AT ITERATION    1    EQUALS       0.13556818E+09
...
...
ENERGY AT PEAK   ITERATION  228    EQUALS       0.46047986E-09
  ENERGY AT ITERATION  229    EQUALS       0.42586760E-10

Plot DR results

cp data.dat input.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)
f
 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
 plot single view ? t/f
t
 view no   1/2/3/4 ?
4
  isoyes =   T
 input vertical angle
30
 input horizontal angle
30
    pltf4.plt     opened 
 enter the title
walldr.dat after DR
   4.6354998053636374E-310   0.0000000000000000        0.0000000000000000        0.0000000000000000

Display DR Output

ps2pdf pltf4.plt
okular pltf4.plt.pdf

Adaptive Analysis

cp data.dat walldr-o.dat
cp stress.dat walldr-o.str
../adpgs1 
Enter the input file (.dat assumed)
walldr-o
Example rect                    
0.007000 0.000000 
opening walldr-o.str for reading the stresses
 1.11530e+05  1.22930e+04  3.18390e+04
...
...
9.17860e+03  1.14650e+05  2.63560e+04

 nita (percent) from the current mesh = 72.263493
 he_min = 1.238584  he_max = 16.746790
Enter your own hmin 
1.25
Magnification =   1.0 (hmin =   1.2)
*** Element errors are stored in walldr-o.err ***
*** Mesh parameters are in walldr-o.me 
*** Adaptivity results are in walldr-o.adp

Mesh Refinement

../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)
walldr-o
Example rect                    
0.007000 0.000000 
opening walldr-o.men for reading 
cannot open walldr-o.men  opening walldr-o.me for read
Enter [1] if coarse background mesh is to be refined
1
Enter [1] if mesh post-processing required
1
The program is to be run without debug

 The No. of p_stack elems = 0
Coarse BG mesh elem no.1 resulted in --> nn = 63 and ne = 94
...
...
Coarse BG mesh elem no.28 resulted in --> nn = 63 and ne = 94

 over all diagonal exchange started 

 overall smoothing started
iln = 10

 Time taken for mesh generation =     0.0000 min



  *** Mesh Compiled with 676 Nodes and 1198 Element *** 
*** File walldr-oo.dat with 676 nodes & 1198 elements has been generated ***
*** Neural net training data saved in walldr-o.inf ***

Map the 2D refined mesh to its 3D geometry

../surfgs1 
Enter the (3D) coarse mesh file name (without extension)
walldr-o
Example rect                    
0.000000 0.000000 
Enter the (2D) refined mesh file name (without extension)
walldr-oo
Example rect                    
0.000000 0.000000 
Dmax = 141.421356
Nq = 77.781746
Higher Nq value can improve the quality of mesh
Enter Nq or RETURN to accept computed value
500
Nq is set to: 500.000000
***input.dat file has been generated***

Plot the adaptive (3D) 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)
f
 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 ?
4
  isoyes =   T
 input vertical angle
30
 input horizontal angle
30
    pltf4.plt     opened 
 enter the title
Adaptive Refined Mesh walldr-oo.dat     
   4.6357120049427339E-310   0.0000000000000000        0.0000000000000000        0.0000000000000000

Display mapped mesh

ps2pdf pltf4.plt
okular pltf4.plt.pdf 

Remarks

Mapping of any 2D unstructured mesh onto a 3D surface is detailed in Khan and Topping [1]. Further information on adaptive DR is available in Topping and Khan [2]. The DR method is outlined in Topping and Khan [3].

References

[1] AI Khan and BHV Topping, Three Dimensional Adaptive Surface Re-Meshing For Large Displacement Finite Element Analysis

[2]: BHV. Topping and AI Khan, PARALLEL FINITE ELEMENT COMPUTATIONS, Saxe-Coburg Publications

[3]: BHV Topping, AI Khan, Parallel schemes for dynamic relaxation, engineering computations Int J Comput Aided Eng Software. v11, 513-548