Question about the Newton Raphson Method
Question about the Newton Raphson Method
(OP)
Hi all,
I have got a question about the way the NR method works. I am reading lots of books but I cannot figure it out.
Let's consider the non linear graph of the picture(http://nptel.ac.in/courses/105108072/mod07/image/l...). My question is: does the solver already know the equation of that non linear curve, before starting the iterative procedure? If not:
My first guess is the origin of the coordinate system. Then I apply a load equal to the load step. Using linear equations, I obtain the tangent. I intersect the tangent with the horizontal line of equation y=Load Step.
Now??? How can I project the point on the horizontal line down to the non linear curve if we do not know the equation of that curve?
On the other hand, if the solver already knows the equation of the non linear curve, then how has it calculated it? And why do we need an iterative procedure to get the displacement at y= load step when we know the equation of the curve? Cannot the solver replace y=Load step into the non linear equation?
Thanks very much
I have got a question about the way the NR method works. I am reading lots of books but I cannot figure it out.
Let's consider the non linear graph of the picture(http://nptel.ac.in/courses/105108072/mod07/image/l...). My question is: does the solver already know the equation of that non linear curve, before starting the iterative procedure? If not:
My first guess is the origin of the coordinate system. Then I apply a load equal to the load step. Using linear equations, I obtain the tangent. I intersect the tangent with the horizontal line of equation y=Load Step.
Now??? How can I project the point on the horizontal line down to the non linear curve if we do not know the equation of that curve?
On the other hand, if the solver already knows the equation of the non linear curve, then how has it calculated it? And why do we need an iterative procedure to get the displacement at y= load step when we know the equation of the curve? Cannot the solver replace y=Load step into the non linear equation?
Thanks very much





RE: Question about the Newton Raphson Method
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RE: Question about the Newton Raphson Method
So I do not originally have the non linear curve. You are saying that:
I start with a certain value of F and d (on the picture (0;0)). I apply the force equal to the load step (on the picture the force F): now, as you say, I cannot calculate the d from F (where F is the force equal to the load step amplitude), so I have to use linear assumptions to get what the d would be if F was applied linearly. Now I have got the point (d1; F). So I have got the point on the horizontal line. Now I can calculate the real Force which is associated to d1 through the use of non linear equations because, as you say, I can obtain F from d. In this way I obtain the projection of the point (d1,F) on the non linear curve. And then I can restart. Is it correct?
Thanks
RE: Question about the Newton Raphson Method
prex
http://www.xcalcs.com : Online engineering calculations
http://www.megamag.it : Magnetic brakes and launchers for fun rides
http://www.levitans.com : Air bearing pads
RE: Question about the Newton Raphson Method
Given F, find d ...
first estimate is based on the initial slope (d1)
but then you find the slope at d1 is much lower than the initial slope
and when you evaluate the function for d1 you get F1<F
so you can extrapolate the slope at d1 to F and get d2
evaluate, extrapolate, repeat ...
another day in paradise, or is paradise one day closer ?
RE: Question about the Newton Raphson Method
I am sorry, but there is something which I don't get.
You are saying that there is a way through which I can go from d to F with non linear equations? I thought FEA software could work only with linear equations. So the solver can deal with non linear equation when it goes from d to F, but it cannot do that when it goes from F to d?
RE: Question about the Newton Raphson Method
TTFN (ta ta for now)
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RE: Question about the Newton Raphson Method