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Does this curve only apply for systems of 1 degrees of freedom or also multiple degrees of freedom?

Does this curve only apply for systems of 1 degrees of freedom or also multiple degrees of freedom?

(OP)
Illustration of how the Newton-Raphson Method works; is it only valid for one degree of freedom or multiple degrees of freedom?

RE: Does this curve only apply for systems of 1 degrees of freedom or also multiple degrees of freedom?

In the case of a 3d response surface a similar approach is used, with the first step being to find the local gradient vector at your current location. I think. Best place to read up on it is Matlab's help files.

Cheers

Greg Locock

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RE: Does this curve only apply for systems of 1 degrees of freedom or also multiple degrees of freedom?

(OP)
I was thinking each DOF has its own curve, and that they are solved together using matrices. Am I wrong?

RE: Does this curve only apply for systems of 1 degrees of freedom or also multiple degrees of freedom?

I think the FEA is solving all three directions simultaneously, sure each direction will have a different slope ... you're looking at a 4D surface.

RE: Does this curve only apply for systems of 1 degrees of freedom or also multiple degrees of freedom?

A very interesting resource discussing N-R method for single and multi DOF cases is K.J. Bathe’s lecture 10 in "Finite Element Procedures for Solids and Structures". You can find it on MIT OpenCourseWare website. His book ("Finite Element Procedures") is also great but it skips the multi DOF case.

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