Solution with LS-OPTui

Monto Carlo Analysis Task

1. From the main menu bar select Task → Direct Simulation → Monto Carlo Analysis.

Define the solver

1. Select the Solvers panel.
2. For Solver Package Name choose LS-DYNA.
3. For Command specify the LS-DYNA executable ls971_R4_2 (This name can be different on your computer).
4. For Input File browse the file metal.k.
5. For Name of Analysis Case enter SOLVER_1.
6. Push the Add button.

Statistical Distribution

1. Select the Distribution panel.
2. Choose Normal Type.
3. For Mean enter 200.
4. For Standard Dev enter 20.
5. Type in a Distribution Name, e.g. Y.
6. Push the Add button.

7. Choose Uniform Type.
8. For Lower enter 0.6.
9. For Upper enter 1.4.
10. Type in a Distribution Name, e.g. U_FS.
11. Push the Add button.

12. Choose Uniform Type.
13. For Lower enter 0.
14. For Upper enter 50.
15. Type in a Distribution Name, e.g. P_OFF.
16. Push the Add button.

Change Variable

1. Select the Variables panel. The variables are already defined in the input file metal.k using *PARAMETER (see below) and therefore cannot be deleted.
2. For Type of NAdapt switch the menu to Constant.
3. Change the (start) value of NAdapt to 2.
4. For Type of YIELD switch the menu to Noise Var.
5. Choose Y as the Distribution of the variable YIELD.
6. For Type of FS1 switch the menu to Noise Var.
7. Choose U_FS as the Distribution of the variable FS1.
8. For Type of FS2 switch the menu to Noise Var.
9. Choose U_FS as the Distribution of the variable FS2.
10. For Type of FS3 switch the menu to Noise Var.
11. Choose U_FS as the Distribution of the variable FS3.
12. For Type of PWAVEL switch the menu to Constant.
13. Change the (start) value of PWAVEL to 50.
14. For Type of POFF switch the menu to Noise Var.
15. Choose P_OFF as the Distribution of the variable POFF.

Sampling Panel

1. Select the Sampling Panel.
2. For POINT SELECTION choose Latin Hypercube.
3. For Number of Simulation Points per Case enter 25.

Define the Responses

  Define the maximum percent thinkness reduction

1. Select the Responses panel. 
2. From the possible response types select: D3PLOT.
3. For Parts to be included choose All Parts.
4. For Result Type select Misc.
5. For Component select %_thickness_reduction.
6. And select the Maximum Value.
7. And the maximum value should be taken from time 0 to the current time.
8. For Response Name enter prc_thick_red_max.
9. Push the Add button.

  Define the FLD

10. From the possible response types select: FLD.
11. For Parts to be included choose List of Parts.
12. In the List of Parts enter 1.
13. Push the (Add) > button.

  Repeat the previous steps and create this list of parts:

14. For Sampling locatin select Center surface.
15. For Load curve ID enter 90.
16. For Response Name enter PLD.
17. Push the Add button.

  Define the minimum shell thickness

18. From the possible response types select: D3PLOT.
19. For Parts to be included choose List of Parts.
20. In the List of Parts enter 1.
21. For Result Type select Misc.
22. For Component select shell_thickness.
23. And select the Minimum Value.
24. And the minimum value should be taken from time 0 to the current time.
25. For Response Name enter thick_min.
26. Push the Add button.

Define the objective response

1. Select the Objective panel.
2. From Response select prc_thick_red_max as the objective.
3. For Weight leave the default 1. If you have several objective functions, you may assign weight to each one according to their importance.
   

Define the constraints

1. Select the Constraints panel.
2. Choose the Response per_thick_red_max as constraint.
3. For Lower Bound accept the default -inf.
4. For Upper Bound enter 34.

Run panel

1. Select the Run panel.
2. Push the Run button. (Save the project as com.metal_MC)