Optimizing LS-DYNA input curves

To optimize LS-DYNA input curves, e.g. stress vs. strain data, one solution is to use splines that interpolate a certain number of given points. The coordinates of that points or at least some of them are defined as LS-OPT parameters. Further variables may be defined in the LS-DYNA input file.

To interpolate the supporting points, the perl program cubic_hermite_interpolation.pl is used as preprocessor in LS-OPT: 

$ ------ Pre-processor -------- 

prepro own 
prepro command "../../cubic_hermite_interpolation.pl curve_out.inc" 
prepro input file "supporting_points.txt"	

The variables are defined in preprocessor input file supporting_points.txt.

0 0
<<x1>> <<y1>>
<<x2>> <<y2>>
0.8 <<y3>> 

Each line contains the coordinates of a supporting point, the number of points is arbitrary and the coordinates may be fixed values and LS-OPT variables, respectively.

The program returns the file curve_out.inc that contains the output curve in LS-DYNA format and may be used directly as inlude in the LS-DYNA input file, here in example.key.

*INCLUDE
curve_out.inc 

To ensure that the supporting points are monotonically increasing, constraints have to be defined in LS-OPT on previously defined composite expressions.

$ CONSTRAINT DEFINITIONS
$
constraints 2
move
constraint 'constraint_x2_x1'
lower bound constraint 'constraint_x2_x1' 0.1
constraint 'constraint_y2_y1'
lower bound constraint 'constraint_y2_y1' 1e-06
$

$
COMPOSITE EXPRESSIONS
$
composite 'constraint_x2_x1' {x2-x1}
composite 'constraint_y2_y1' {y2-y1}
$						

Now, an objective has to be defined. In this case we use a Mean Squarred Error composite that compares the displacement test curve test_curve.dat to the computed displacement curves, see http://www.lsoptsupport.com/examples/parameter-identification/history-mse. 

After five iterations, LS-OPT returns a stress vs. strain curve that leads to a displacement curve close to the given test data.

For convenience example files have been prepared and are available for download at the end of this document.