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Last active Mar 13, 2018
3Dflex.py

3Dflex.py

A script for calculating 3D flexure in python. Converted from GARRY QUINLAN's fortran program 3dflex.f.

This programme calculates the flexure for 3D elastic sheet where the sheet can have one of its 4 edges as a free edge. It uses a finite difference approach to the 3D flexure problem and lets Te, restoring force and ;loading vary in a random fashion. There are many comments written in the program to guide the user through.

INPUT:

The input file is called PAR3DF.DAT. This name is hard wired into the programme. Comments are written next to the input lines on the sample programme.

Further description of the input follows. The first line is youngs modulus and Poissons ratio ( e11 and 0.25). One then starts by setting up a grid with a dimensions chosen by the user (delx) . Some where between 1 to 20 km for the grid size seems sensible depending on the area under study. I have used up to a 100 by 100 grid but at this size it takes a long time to converge ( 1 hr on a Ultra Spare) or about 100,000 iterations.

The second line sets the number of elastic thicknesses needed. If you have say 3 , you start by specifying he whole grid as a base value, say: 1,59,1,59 15 ( the means row 1 to 59 and column 1 to 59 give an elastic thickness = 15 km). If you wanted another region to have a different elastic thickness you would put another in i.e. rows 22 to 26 and column 35 and 36 give Te = 5 km. : 22,26,35,36, 5

Then one specifies the number of loads in the same way the Te’s are specified. The loads are in MPa. So you were going to describe a mountain 2 km high of density 2700 kg/m3 the load is 2700 * 2000 * 9.8 = 5.3 x e07 MPa

Next the restoring force is specified for each grid square. Note that the number you put in is density contrast * g .i.e density contrast * 10 ( approx). A row or column is specified to check for convergence, leave the tolerance level at 1*–06 and set the iteration level to 100,000.

The 2nd last line one can specify one of the boundaries to be broken by putting in a 1 And the last line lets one apply an in-plane stress in units on n/m2.

RUNNING:

`python 3Dflex.py`

Or for 3Dflex.f90

`gfortran 3Dflex.f90 -o 3Dflex & 3Dflex`

OUTPUT:

Is saved as DEF3D.dat

Command line output is:

```   9.99999980E+10  0.250000000
1
1          59           1          59   15.0000000
7
19          21          21          23   41600000.0
21          25          23          25   41600000.0
23          27          25          27   41600000.0
25          27          27          29   41600000.0
29          31          27          29   41600000.0
35          37          23          27   44900000.0
37          39          21          29   44900000.0
10.0000000
59          59
2
1          59           1          59   10000.0000
19          39          21          29   6000.00000
5000
9.99999975E-06
3          57          24          24
1.70000005
0           0           0           0
0.00000000       0.00000000       0.00000000
5          55          24          24
WITHIN TOLERANCE AFTER   3170 ITERATIONS
3170   34378.0391       34377.6992       9.88548982E-06```

Note

A bigger and better library can be found here http://csdms.colorado.edu/wiki/Model:Flexure More resources includes:

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 1.0e11,0.25 Example input. The first line is youngs modulus and Poissons ratio 1 No. of different thicknesses 1,59,1,59,15.0 i.e thickness of Te =5 km 7 no. of different load segments 19,21,21,23,4.16E07 different loads etc... 21,25,23,25,4.16E07 23,27,25,27,4.16E07 25,27,27,29,4.16E07 29,31,27,29,4.16E07 35,37,23,27,4.49E07 37,39,21,29,4.49E07 10.0 delx 59,59 no. of grids of study area in x and y 2 no. of different isostatic restoring forces 1,59,1,59,10000.0 restoring force of seds 19,39,21,29,6000.0 restoring force over volcanoes 5000 max no. of iterartions 1.0E-05 tolerance of convergence 3,57,24,24 row or column used to check convergence 1.7 sor parameter 0,0,0,0 1= broken, 0=contiuous, left, right, bottom, top 0.0,0.0,0.0 end load in x, y and shear: x = up Y= sideways: -ve=compression