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ptc-51162021-Visitor
1-Visitor
May 24, 2013
Question

Radau , second order integration with non-linear system of ode

  • May 24, 2013
  • 4 replies
  • 3374 views

Hello everyone,

I have a system of 3 non linear equations second order differential.

I'm using radau solving the following system : d/dt (phi) = f(phi)

But i would like to solve the system d²/dt²(phi)= f(phi) instead.

My f(phi) is a three dimensionnal vector with non linear . coupled phi's

For example (i've removed sensitive data and simplified problem)

ptc+question.PNG

How would you format D(u,Y) ? I've tried with the other solvers but it didn't solve. I'm stuck with Radau.

4 replies

A
AlanStevens19-Tanzanite
19-Tanzanite
May 24, 2013

What are the initial conditions for the three components of dYdu?

Alan

A
AlanStevens19-Tanzanite
19-Tanzanite
May 24, 2013

Attached is an example using Odesolve, with arbitrary initial first derivative values. Your system is very stiff!!

(The default integrator is BDF/Adams, but you can right-click on Odesolve and choose Radau if you want).

Alan

P
ptc-51162021-VisitorAuthor
1-Visitor
May 24, 2013

Ok thanks for the tip.

I've replaced the equations with the real system.and it's saying too many initial conditions. And doesn't solve.

I have 6 IC's

W
Werner_E25-Diamond I
25-Diamond I
May 24, 2013

On the RHS of your equations you forgot to write the parameter parenthesis G2(t) - you simply wrote G2, etc.

P
ptc-51162021-VisitorAuthor
1-Visitor
May 24, 2013

Ok , it's working in the first sheet.

However when i'm transferring the method back to the second field. I have an error on G0 (too many IC's)

ptc+question.PNG

Here is the full sheet...

It's very long and it's at the end.

W
Werner_E25-Diamond I
25-Diamond I
May 24, 2013

If you use only the result of the symbolic evaluation (the euqations itself) you get past this error, but you get a new one.

It only works if u.end is under 0.25, otherwise you get the following error :

Plate2.png

P
ptc-51162021-VisitorAuthor
1-Visitor
May 24, 2013

If you use the Radau solver it does work. i have to compute u.end till tlast which is around 0.35. And solves.

Is there a way to get past this error without copying the whole thing equations again and again?

I'm making this CAD as a routine check for deflections compared with other FE softwares

I have a few steps after the solving and it's a bit annoying to have this.

The bdf/radau signal diverge? Let me check that out.

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