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Newton-Raphson Residuals (2)

As a follow up to the previous post, here's my slightly different take of the Newton-Raphson Residuals.

The help manual shows a nice gradually decreasing stiffness curve (similar to Figure 1). It didn't match what I learned in school or Wikipedia where the algorithm was used to find the root. By rephrasing the question as finding the root for the Newton-Raphson Residual (External - Internal Force), one then gets to Figure 2.

The Octave/Matlab script used to create the above plots can be found here.

Newton-Raphson Residues

When doing non-linear analysis, it is good practice to indicate you would like to save the Newton-Raphson Residualsbefore the analysis is started. It can go a long way in troubleshooting when/if the solution doesn't converge later. You may do so by specifying how many youngest residuals you wish to keep. I personally like to keep 3 to see if it is consistent. Also, increase "Identify Element Violations" toggle to 1 to locate any mangled elements.


Number of Residuals & Identify Distorted Elements
ANSYS now spends a bit of time & resource saving the residuals as it solves each iteration (see below). If you specify only 3 (as suggested above), only the youngest 3 residuals are saved with successive overwriting of the older files. The process is highlighted in the output file below:

file.out showing when residual files are saved
If later ANSYS spouts out colorful language disguised as WARNING or ERROR, you would then see the following objects under Solution Informati…

Magnetic Forces Between Two Permanent Magnets

Magnetic Field of 2 Cylindreical Permanent Magnets
Background & Model Setup Many years back, part of my MS degree required me to do some modeling of some permanent magnets to get magnetic stiffness and magnetic flux. The code is based on the work done then. Other related ANSYS resources I found:
CozyWork's 2D single magnet model. Ansys Help archive. Newer Ansys v18 has much of it undocumented.  K&J Magnetics has a really cool website calculator that computes the magnetic force of a few simple cases. The ANSYS script below computes the magnetic force between two magnets of N52, 10 mm diameter, 5 mm thick magnets. It is assumed the magnets have relative permeability of 1.05 and Coercive Force of >11.2 kOe (>89,1267 A/m).

The model consists of the two cylindrical shaped magnets at a small distance from each other. Surrounding them is another cylinder that represents the air. Both are polarized in the positive Z direction thus the magnets will be in attraction.

Side View …

Hello World!

My original inspiration for this blog was Peter Budgell's tips and tricks web page that was hand coded in HTML back in 1998. I unfortunately only discovered it relatively recently. It is enlightening though some of it is a bit dated. As Peter wrote:

"I find that writing these pages improves my own insight, encourages me to learn more, and helps me broaden the number of things I consider in setting up and post-processing finite element models"
I'm not as seasoned as many analyst but I hope some of the post would be useful to others.