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L
lferreira1-Visitor
1-Visitor
April 4, 2018
Solved

ODE Illegal context

  • April 4, 2018
  • 4 replies
  • 8911 views

Hello,

 

I am trying to solve a differential equation for a clamped Circular Kirchhoff-Love plate.

 

Why am I getting this error in my displacement function w(r)?

 

 

Best answer by Werner_E

So we can't use w(0)=0 as initial conditions as I did and you need to provide a new fourth condition.

How about w''(0)=0 ?

 

Bild.png

EDIT: I am not into mechanics myself so I am not sure but maybe Chapter 4 here

http://imechanica.org/files/4_Bending%20of%20plates.pdf

can help you to find two reasonable additional initial conditions.

 

4 replies

V
24-Ruby IV
ValeryOchkov24-Ruby IV
24-Ruby IV
April 4, 2018

Attach please the Mathcad Prime sheet!

L
lferreira1-VisitorAuthor
1-Visitor
April 4, 2018

Sorry, the .prt with the embedded sheet is attached.

F
Fred_Kohlhepp23-Emerald I
23-Emerald I
April 4, 2018

Probably because you're trying to solve a fourth order differential equation

Capture.PNG

L
lferreira1-VisitorAuthor
1-Visitor
April 4, 2018

Oh, so what are the restrictions when trying to solve differential equations?

L
LucMeekes23-Emerald IV
23-Emerald IV
April 5, 2018

Here's the full solution for any value of q, D and R(adius of the disk):

LM_20180405_Ode1.png

So with that we should be able to continue as follows:

LM_20180405_Ode2.png

This function is large, but that does not prevent us from using it:

LM_20180405_Ode3.png

And we can even see what it does (or would do) for values of r beyond the size of the disk R:

LM_20180405_Ode4.png

Success!
Luc

 

Notice! However that my result differs from the one your picture, when I subtract them I don't get 0:

LM_20180405_Ode5.png

So far I wasn't able to locate where I went wrong.

L
LucMeekes23-Emerald IV
23-Emerald IV
April 4, 2018

I get this:

LM_20180404_Ode.png

Too few initial conditions...{also when the second is correctly written as w'(1000)=0}

You must add two (it's a fourth order).

 

I can't open you .prt file.... What are values for q and D ?

 

Luc

-
-MFra-21-Topaz II
21-Topaz II
April 4, 2018

Hi,

I have chosen Adams/BDF,

fourthorder.jpg

L
lferreira1-VisitorAuthor
1-Visitor
April 4, 2018
53 seconds ago

The thing is, when r=0 -> center of the plate in cylindrical coordinates , I don't know the value, in fact, that's the value I will be looking for, because it will be the maximum deflection of the circular plate.

 

What I know is that at the edge of the circular plate (r=1000) my deflection is 0, as well as my angle (clamped)

W
Werner_E25-Diamond IAnswer
25-Diamond I
April 4, 2018

So we can't use w(0)=0 as initial conditions as I did and you need to provide a new fourth condition.

How about w''(0)=0 ?

 

Bild.png

EDIT: I am not into mechanics myself so I am not sure but maybe Chapter 4 here

http://imechanica.org/files/4_Bending%20of%20plates.pdf

can help you to find two reasonable additional initial conditions.

 

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