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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.