Overcoming Convergence Difficulties in ANSYSWorkbench Mechanical, Part I: Using Newton-Raphson Residual Information

padtinc.com /blog/the-focus/overcoming-convergence-difficulties-in-ansys-workbench-mechanical-part-i-using-newton-raphson-residual-information

Ted Harris

Unable to converge. Convergence Failure. Failure to Converge. Never nice words to see when youare trying to get your simulation done.

If youve encountered convergence failures while running nonlinear structural analyses in ANSYSWorkbench Mechanical, this two part series is for you. What is a convergence failure? In a nutshell itmeans that there is too much imbalance in the system. The calculated reaction forces do not matchthe applied loads and even though the program tries hard to make changes to overcome theimbalances, it hasnt been able to do so and stops. If we look at the Force residuals under SolutionInformation, we will see that the solver has been unable to get the force convergence residual, orimbalance force, to drop below the current criterion

Test model example: Newton Raphson Convergence Failure; Solution Stops

We wont spend a lot of time here explaining the Newton-Raphson method, convergence, and residualplots here, since we wrote a Focus article back in 2002 which discusses them in more detail. Thearticle begins on p. 7 at this link:

/blog/wp-content/uploads/oldblog/archive/PADT_TheFocus_08.pdf

The context of that article was Mechanical APDL, but the article is directly relevant since solving in

http://www.padtinc.com/blog/the-focus/overcoming-convergence-difficulties-in-ansys-workbench-mechanical-part-i-using-newton-raphson-residual-informationhttp://www.padtinc.com/blog/wp-content/uploads/oldblog/image_361.pnghttp://www.padtinc.com/blog/wp-content/uploads/oldblog/image_362.pnghttp://www.padtinc.com/blog/wp-content/uploads/oldblog/archive/PADT_TheFocus_08.pdfhttp://www.padtinc.com/blog/wp-content/uploads/oldblog/image_363.pnghttp://www.padtinc.com/blog/wp-content/uploads/oldblog/image_364.pnghttp://www.padtinc.com/blog/wp-content/uploads/oldblog/image_365.pnghttp://www.padtinc.com/blog/wp-content/uploads/oldblog/image_366.png

Workbench Mechanical is done in Mechanical APDL in batch mode.

In crayon terms, we want the purple line to drop below the blue line. When it doesnt and the solver isout of options to keep trying, the solution stops and we get an error message.

Now what? The traditional knobs to turn are to increase the number of substeps, decrease contactstiffness if contact is involved, perhaps add more points to the plasticity curve, etc. But what ifsomething else is the problem? How can we identify where the problem is?

In this part I article we will discuss how to plot the Newton-Raphson residuals as contour plots to seewhere in the model the highest force imbalances are located. Often this is useful information to helpus figure out what is going on so we can take corrective action. First, be aware that we must turn onthe Newton-Raphson residual plots prior to solving. That means you either have to turn them on andre-solve after a convergence failure, knowing that youll get the same failure again, or you need toclairvoyantly (or perhaps just prudently) turn on the residuals prior to attempting the initial solve. Whyarent they on all the time, you ask? Most likely because they slow things down just a bit and alsorequire a bit more disk space than otherwise, although if the solution runs to completion no Newton-Raphson residual plots are saved.

Here is how we turn them on. In the Details view for the Solution Information branch, change theNewton-Raphson Residuals setting from the default of zero to a nonzero number such as 3 or 4. Thatwill continuously save the last 3 or 4 Newton-Raphson residual plots for viewing as contour plots afterthe solution has stopped due to a convergence failure.

After the solution has stopped, the Newton-Raphson residual plots will be available underthe Solution Information branch.

The quantity plotted is actually the square rootof the sum of the squares of the residuals inthe global X, Y, and Z directions. So, the plotsdont show us direction information, but they doshow where the residuals and hence the forceimbalances are the largest. Below is anexample. The region in red shows where theresiduals are the highest. Since this is a modelinvolving contact between two bodies,apparently the contact regions and specificallycontact at the corners of the part on the left is the source of our convergence difficulties.

Newton-Raphson Residual Force Plot for the last attempted equilibrium iteration.

So, how do we use this information? In this case we now suspect that the contact regions, especiallyat the corners of the smaller part, are the problematic areas. Using this information we made twochanges to the model.

First, we changed the Detection Method for the contact elements from Program Controlled (at theelement Gauss points) to Nodal-Normal to Target. Many times when contact problems involve touchingat corners, the robustness of the contact interface can be improved by changing the detection methodfrom Gauss points to nodes.

Second, we reduced the contact stiffness by changing Normal Stiffness from Program Controlled(factor of 1.0) to a Manual setting of 0.2. Reducing the contact stiffness can help with contactconvergence for a lot of problems. Too low of a stiffness value can cause problems too, but in thiscase the resulting penetration is still small so a value of 0.2 seems reasonable. When in doubt, asensitivity study can be performed whereby you make changes to the contact stiffness value whiletracking your results quantities of interest. As with most inputs you can vary, your results of interestshould not be sensitive to contact stiffness.

These two changes allowed our test model to nicely converge for the full amount of load.

Other considerations:

The Newton-Raphson Residual plots are always displayed on the original geometry, not the deflectedgeometry at version 14.0 of ANSYS Mechanical. If the deflections are large this can make it harder toascertain what is causing the high residual values. In those cases, it can be helpful to compare thetotal deformation and stress plots for the unconverged solution, along with those plots for the lastconverged solution, with the 1.0 true scale on the deformation active. This will show the parts in theirdeflected state, and that can help in determining why the residuals are high at certain locations.

We recommend creating at least 3 residual plots (set in the details of Solution Information as describedabove). Sometimes the location of the imbalance can bounce around a bit from equilibrium iteration toequilibrium iteration, so having more than one or two plots to look at can be beneficial in determiningproblem locations.

Conclusion

Summing it up, the Newton-Raphson residual plots are one piece of information we can use todetermine why we are having convergence difficulties. They can give us an indication of where theconvergence difficulties are occurring in the model, and many times we can use that information to helpus know what settings should be modified or what other changes should be made to the model toimprove the convergence behavior.

In part II of this article, well look at how to quickly use ANSYS Mechanical APDL to view the elementsthat have undergone too much deformation.

padtinc.comhttp://www.padtinc.com/blog/the-focus/overcoming-convergence-difficulties-in-ansys-workbench-mechanical-part-ii-quick-usage-of-mechanical-apdl-to-plot-distorted-elements

By Ted Harris October 18, 2012

Overcoming Convergence Difficulties in ANSYS WorkbenchMechanical, Part II: Quick Usage of Mechanical APDL to PlotDistorted Elements

In part I if this series, we saw how to use Newton-Raphson residual plots as an aid to vanquishing convergencedifficulties in ANSYS Workbench Mechanical. In part II, we will see how to quickly launch the ANSYS MechanicalAPDL user interface to plot elements that have undergone too much distortion, thereby resulting in a convergencefailure. Several problems can cause convergence failures, but one that can be particularly frustrating is elementsthat have undergone too much distortion.

Currently there isnt a way to isolate and view elements that have triggered a convergence failure due to too muchdistortion within the Workbench Mechanical user interface. Fortunately we have access to the older ANSYSMechanical APDL interface, which does allow us to select and visualize elements that have undergone too muchdistortion. This can be useful in that it tells us exactly where in the model the elements are failing. Hopefully wecan use this information to take corrective action in Mechanical such as making local mesh modifications, addingmore details to geometry, etc.

So, how do we do this? Rather than try to give a lesson on how to use the Mechanical APDL interface, were justgoing to give the commands needed to be clicked with the mouse or typed in. Were following the K.I.S.S.principal, meaning Keep It Simple, Silly.

The procedure to follow includes these steps:

1. Identify the directory in which our results file resides.

2. Launch ANSYS Mechanical APDL.

3. Point to the results file identified in step 1.

4. Modify the nodal coordinates so they are in the deflected state at the point of convergence failure.

5. Plot those error-causing elements.

We will now go into more detail using a model that has convergence trouble. This model solved successfully forthe first 4 substeps, but on the 5th substep the solution failed to converge. We get this error in the solver output(Solution Information):

*** ERROR *** CP = 2872.649 TIME= 16:29:51 One or more elements have become highly distorted. Excessive

http://www.padtinc.comhttp://www.padtinc.com/blog/the-focus/overcoming-convergence-difficulties-in-ansys-workbench-mechanical-part-ii-quick-usage-of-mechanical-apdl-to-plot-distorted-elementshttp://www.padtinc.com/blog/wp-content/uploads/2012/10/image94.pnghttp://www.padtinc.com/blog/wp-content/uploads/2012/10/image7.pnghttp://www.padtinc.com/blog/wp-content/uploads/2012/10/image8.pnghttp://www.padtinc.com/blog/wp-content/uploads/2012/10/image9.pnghttp://www.padtinc.com/blog/wp-content/uploads/2012/10/image10.pnghttp://www.padtinc.com/blog/wp-content/uploads/2012/10/image11.pnghttp://www.padtinc.com/blog/wp-content/uploads/2012/10/image12.pnghttp://www.padtinc.com/blog/wp-content/uploads/2012/10/image13.pnghttp://www.padtinc.com/blog/wp-content/uploads/2012/10/image14.pnghttp://www.padtinc.com/blog/wp-content/uploads/2012/10/image65.pnghttp://www.padtinc.com/blog/wp-content/uploads/2012/10/image69.pnghttp://www.padtinc.com/blog/wp-content/uploads/2012/10/image73.pnghttp://www.padtinc.com/blog/wp-content/uploads/2012/10/image15.pnghttp://www.padtinc.com/blog/wp-content/uploads/2012/10/image41.pnghttp://www.padtinc.com/blog/wp-content/uploads/2012/10/image81.pnghttp://www.padtinc.com/blog/wp-content/uploads/2012/10/image77.pnghttp://www.padtinc.com/blog/wp-content/uploads/2012/10/image16.pnghttp://www.padtinc.com/blog/wp-content/uploads/2012/10/image21.pnghttp://www.padtinc.com/blog/wp-content/uploads/2012/10/image85.png

distortion of elements is usually a symptom indicating the need for corrective action elsewhere. Try incrementing the load more slowly (increase the number of substeps or decrease the time step size). You may need to improve your mesh to obtain elements with better aspect ratios. Also consider the behavior of materials, contact pairs, and/or constraint equations. If this message appears in the first iteration of first substep, be sure to perform element shape checking.

Looking at the model, we see we have an indenter that is being pressed into a block of material. The indenter issteel and the block is aluminum. Both have nonlinear material properties defined.

Total deformation for the last converged substep looks like this:

The unconverged results show that we have some elements that have large nodal deflections:

So, our error message tells us that one or more elements have become highly distorted. Which elements arethey? The following procedure will show us how to view those for sure, using Mechanical APDL.

Here are each of the 6 steps mentioned above, in detail:

1. Identify the directory in which our results file resides:

We do this from the Workbench window, by clicking on View > Files. Scroll down in the resulting list of files untilyou find file.rst, the ANSYS Result file. The location will be listed in the resulting information, but the text is notselectable. To make it easier, right click on the file.rst row and select Open Containing Folder.

From the top of the resulting Windows Explorer window, select the folder path and right click > copy.

2. Launch ANSYS Mechanical APDL:

Click Start > All Programs > ANSYS 14.0 > ANSYSMechanical APDL Product Launcher. In the resultingwindow, paste in the directory path in the WorkingDirectory box:

Click the Run button at the bottom of the window. The Mechanical APDL user interface will start.

3. Point to the results file identified in step 1:

Click on General Postproc on the left, then Data & File Opts. In the resulting Data and File Options window, clickon the [] button below Read single result file:

You should see the result file, file.rst, available in the resulting window. Click on that file, then click Open. ClickOK in the Data and File Options window.

We need to read in one set of results to load the model into the Mechanical APDL database. Click GeneralPostproc > Read Results > Last Set.

4. Modify the nodal coordinates so they are in the deflected state at the point of convergence failure:

Lets plot the elements so we can see the model (this will show the elements with nodes in the original,undeflected positions). Well just have you type in the command to make the element plot: in the input line nearthe top of the window, type eplot, then return.

The plot will show in the default front view, looking down the global Z axis. Note that if weak springs are on inWorkbench Mechanical, you will see these as line elements pointing away from the model in a few places.

The nodal modification is performed in the preprocessor. Click on the Preprocessor command on the left side ofthe window. Type in this command in the input line to modify the nodal positions to those of the unconverged (lastset) of results:

upgeom,,,,file,rst

Plot the elements again. You should now see the deflected nodal positions.

Using the view controls over on the right side, we can rotate and zoom in. A short cut is to use the right mousebutton to box zoom and Ctrl + Right Mouse Button to rotate the model. Now we can better see where thedeformations are occurring. We still have all elements selected and plotted, so the next step will be to filter theplot to show the error-causing elements.

5. Plot those error-causing elements:

Shape checking of elements consists of two levels, warning and error. The solver will not continue if any elementsexceed the error level. Shape checking is discussed in detail in section 13.1 of the Theory Reference in theANSYS Help. We have the ability to plot both warning level elements and error level elements, using thisprocedure:

On the left side of the window, click on Meshing > Check Mesh > Individual Elm > Plot Warning/Error Messages.

With all boxed checked, this is the resulting plot in the front view. Good elements are displayed in blue, warning elements in yellow,and error or failed elements are shown in red.

When the elements are very highly distorted, their surfaces cant always be displayed and it looks like there is ahole in the model. This wont always happen depending on how highly distorted the elements are, viewingdirection, etc..

If we uncheck the Good Elements (blue) box, then only the warning and error elements are displayed.

When you are done viewing the elements, click on the Quit button near the top, and exit without saving to get outof Mechanical APDL.

So what does all this tell us? For this model, the elements below the indenter body are experiencing too muchdeformation (red elements). Some elements in the indenter body are at the warning level but not the error level(yellow elements). The fix could be to apply the load more gradually (more substeps), refine the mesh at thislocation, or maybe a combination of both. In this case we also changed the Workbench Mechanical shapechecking from Standard to Aggressive Mechanical.

ANSYS Penetration Model

Overcoming Convergence Difficulties in ANSYS Workbench Mechanical, Part I: Using Newton-Raphson Residual InformationOther considerations:ConclusionOvercoming Convergence Difficulties in ANSYS Workbench Mechanical, Part II: Quick Usage of Mechanical APDL to Plot Distorted Elements