Robustness of Metal Forming
Solution with LS-OPTui
Solution with LS-OPTui
Task
Monto Carlo Analysis Task
- From the main menu bar select Task → Direct Simulation → Monto Carlo Analysis.
Solvers
Define the solver
- Select the Solvers panel.
- For Solver Package Name choose LS-DYNA.
- For Command specify the LS-DYNA executable ls971_R4_2 (This name can be different on your computer).
- For Input File browse the file metal.k.
- For Name of Analysis Case enter SOLVER_1.
- Push the Add button.
Distribution
Statistical Distribution
- Select the Distribution panel.
- Choose Normal Type.
- For Mean enter 200.
- For Standard Dev enter 20.
- Type in a Distribution Name, e.g. Y.
- Push the Add button.
- Choose Uniform Type.
- For Lower enter 0.6.
- For Upper enter 1.4.
- Type in a Distribution Name, e.g. U_FS.
- Push the Add button.
- Choose Uniform Type.
- For Lower enter 0.
- For Upper enter 50.
- Type in a Distribution Name, e.g. P_OFF.
- Push the Add button.
Variables
Change Variable
- Select the Variables panel. The variables are already defined in the input file metal.k using *PARAMETER (see below) and therefore cannot be deleted.
- For Type of NAdapt switch the menu to Constant.
Change the (start) value of NAdapt to 2.- For Type of YIELD switch the menu to Noise Var.
- Choose Y as the Distribution of the variable YIELD.
- For Type of FS1 switch the menu to Noise Var.
- Choose U_FS as the Distribution of the variable FS1.
- For Type of FS2 switch the menu to Noise Var.
- Choose U_FS as the Distribution of the variable FS2.
- For Type of FS3 switch the menu to Noise Var.
- Choose U_FS as the Distribution of the variable FS3.
- For Type of PWAVEL switch the menu to Constant.
- Change the (start) value of PWAVEL to 50.
- For Type of POFF switch the menu to Noise Var.
- Choose P_OFF as the Distribution of the variable POFF.
Sampling
Sampling Panel
- Select the Sampling Panel.
- For POINT SELECTION choose Latin Hypercube.
- For Number of Simulation Points per Case enter 25.
Responses
Define the Responses
Define the maximum percent thinkness reduction
- Select the Responses panel.
- From the possible response types select: D3PLOT.
- For Parts to be included choose All Parts.
- For Result Type select Misc.
- For Component select %_thickness_reduction.
- And select the Maximum Value.
- And the maximum value should be taken from time 0 to the current time.
- For Response Name enter prc_thick_red_max.
- Push the Add button.
Define the FLD
- From the possible response types select: FLD.
- For Parts to be included choose List of Parts.
- In the List of Parts enter 1.
- Push the (Add) > button.
Repeat the previous steps and create this list of parts:
| List of Parts: |
|---|
1 |
| 2 |
| 3 |
- For Sampling locatin select Center surface.
- For Load curve ID enter 90.
- For Response Name enter PLD.
- Push the Add button.
Define the minimum shell thickness
- From the possible response types select: D3PLOT.
- For Parts to be included choose List of Parts.
- In the List of Parts enter 1.
- For Result Type select Misc.
- For Component select shell_thickness.
- And select the Minimum Value.
- And the minimum value should be taken from time 0 to the current time.
- For Response Name enter thick_min.
- Push the Add button.
Objective
Define the objective response
- Select the Objective panel.
- From Response select prc_thick_red_max as the objective.
- For Weight leave the default 1. If you have several objective functions, you may assign weight to each one according to their importance.
Contraints
Define the constraints
- Select the Constraints panel.
- Choose the Response per_thick_red_max as constraint.
- For Lower Bound accept the default -inf.
- For Upper Bound enter 34.
Run
Run panel
- Select the Run panel.
- Push the Run button. (Save the project as com.metal_MC)
Com-file
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ Command file "com.metal_MC" $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $ Generated using LS-OPT Version 4.1 $ "Metalforming Analysis Example Problem" $ Author "LS-OPT Class" $ Created on Tue Apr 26 16:29:24 2011 solvers 1 responses 3 $ $ NO HISTORIES ARE DEFINED $ $ $ PROBABILISTIC DISTRIBUTIONS $ distribution 3 distribution 'Y' NORMAL 200 20 distribution 'U_FS' UNIFORM 0.6 1.4 distribution 'P_OFF' UNIFORM 0 50 $ $ DESIGN VARIABLES $ variables 5 Noise variable 'YIELD' distribution 'Y' Noise variable 'FS1' distribution 'U_FS' Noise variable 'POFF' distribution 'P_OFF' Noise variable 'FS2' distribution 'U_FS' Noise variable 'FS3' distribution 'U_FS' $ $ CONSTANTS $ constants 2 Constant 'PWAVEL' 50 Constant 'NAdapt' 2 $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $ SOLVER "SOLVER_1" $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $ $ DEFINITION OF SOLVER "SOLVER_1" $ solver dyna960 'SOLVER_1' solver command "ls971_R4_2" solver input file "metal.k" solver check output on solver compress d3plot off $ ------ Pre-processor -------- $ NO PREPROCESSOR SPECIFIED $ ------ Post-processor -------- $ NO POSTPROCESSOR SPECIFIED $ ------ Metamodeling --------- solver experiment design lhd_generalized solver number experiments 25 $ ------ Job information ------ solver concurrent jobs 1 $ $ RESPONSES FOR SOLVER "SOLVER_1" $ response 'prc_thick_red_max' 1 0 "D3PlotResponse -res_type misc -cmp %_thickness_reduction -select MAX -start_time 0.0000" response 'FLD' 1 0 "DynaFLDg CENTER 1 2 3 90" response 'thick_min' 1 0 "D3PlotResponse -pids 1 -res_type misc -cmp shell_thickness -select MIN -start_time 0.0000" $ $ OBJECTIVE FUNCTIONS $ objectives 1 objective 'prc_thick_red_max' 1 $ $ CONSTRAINT DEFINITIONS $ constraints 1 constraint 'prc_thick_red_max' upper bound constraint 'prc_thick_red_max' 34 $ $ JOB INFO $ analyze monte carlo STOP
Results
Results
Correlation Bars
If we want to find out the most important variable for the maximum thickness reduction, we can just view the correlation of the maximum percent thickness reduction (prc_thick_red_max) with the variables.
Start the LS-OPT Viewer by selecting the Viewer panel and
- Select Correlation Bars.
- From the left side, select Response→prc_thick_red_max.
- choose to show the Correlation.
- This bar diagram shows the correlation coefficients of the maximum percent reduction (prc_thick_red_max) with all the variables and gives the 95% confidence intervals of the estimation at the meantime. Obviously, the variable YIELD is most correlated with the maximum percent thickness reduction.
- We can verify this fact in different ways (also see Correlation Matrix and Scatter Plots).
Correlation Matrix
By viewing the correlation matrix of variables against responses, we can also find out the most correlated variable to the maximum percent thickness reduction.
Open a new Viewer: 
- Restart the LS-OPT Viewer by clicking on the first icon on the menu bar.
- Select Correlation Matrix.
- Disselect Response for Row entities.
- Disselect Variable for Column entities.
- Now we obtain a matrix showing all the correlation coeffients between variables and responses. From the first column we find that the variable YIELD has the largest absolute value of the correlation coffient with the maximum percent thickness reduction, whick coincides with the fact we've seen before.
- We can verify this fact in different ways (also see Correlation Bars and Scatter Plots).
Scatter Plots
A scatter plot shows the sample points on the coordinate plane of two entities (variables, responses).
Restart the Viewer again and
|  |
|
YIELD vs. prc_thick_red_max |
Change the entity to be shown on the x-coordinate.
|
FS1 vs. prc_thick_red_max |
|
FOFF vs. prc_thick_red_max |
|
FS2 vs. prc_thick_red_max |
|
FS3 vs. prc_thick_red_max |
Conclusion: The first plot (YIELD vs. prc_thick_red_max) shows the most linear correlativity among the plots, which means again that YIELD is the most important variable for the maximum thickness reduction.
- We can verify this fact in different ways (also see Correlation Bars and Correlation Matrix).
DYNA Stats
DYNA Stats
Maximum Percent Thickness Reduction
Display the maximum percent thickness reduction of part 1 in LS-PrePost (D3Plot)
- Select the DYNA Stats panel.
- Click on Create button.
- Select Fringe plot for the type of plot.
- Select D3Plot Components →Misc→%_thickness_reduction from the list.
- Check the box of Follow coordinates instead of nodes.
- For part enter 1.
- Go to the next panel.
- For what to plot select Statistic of D3Plot data.
- Choose Max Value as statistic.
- Select Use actual FEA results (Monte Carlo) as analysis method.
- Go to the next panel.
- Give a name to this plot, e.g. prc_thick_red_max.
- Push the Finish button.
- We need to generate the plot after the setup.
- Push the Display button to show the plot.
- This figure shows the maximum value of the maximum percent thickness reduction.
- The minimum occurs at node 15980 (min=-0.346648) and the maximum at node 15833 (max=43.0792).
Sheet Thickness
Display the variation of the sheet thickness of part 1 in LS-PrePost (D3Plot)
It follows the way as usual. Note that:
- By the first step, D3Plot Components →Misc→shell_thickness.
- By the second step, choose Std Dev (Standard deviation) as statistic for this time.
- By the last step, give a name to this plot, e.g. sheet_thick.
- This figure shows the standard deviation of the sheet thickness.
- The maximum occurs at node 16058 (max = 0.0503878).
FLD
Display the FLD of part 1 in LS-PrePost (D3Plot)
It follows the way as usual. Note that:
- By the first step, select D3Plot Components→FLD→maxima_eps1/fldc.
- Choose Provided curve instead of parametrically defined curve.
- For Curve ID enter 90.
By the second step, choose Max Value as statistic for this time.
- By the last step, give a name to this plot, e.g. fld.
- This figure shows the maximum of the FLD maxima surface eps1/fldc.
- The maximum occurs at node 15833 (max = 2.70426).
Download
The complete data set (input and command files) is available for download:
For Linux
For Windows
