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Thread Subject:
Help to solve system of 2 coupled elliptic PDEs (orthotropic cylinder with body forces)

Subject: Help to solve system of 2 coupled elliptic PDEs (orthotropic cylinder with body forces)

From: Philip

Date: 9 Mar, 2009 15:39:02

Message: 1 of 4

Hello all,
I'm an undergraduate student engaged in my final year project, and I've been trying for a term to solve some equations. With my project deadline in a week, and my supervisor away at a conference, I need some results and am getting desperate.

My problem is this:
I have an orthotropic cylinder experiencing body forces.

Governing Equations of the form:

[A+B]*r*u_rz + C*u_z + D*r*v_zz + B*r*v_rr + r*Z=0

D*u_r + D*r*u_rr - r*B*u_zz + [A-B]*r*v_rz + E*u/r + r*R=0

Where r and z are my independant variables.
u and v are my dependant variables, with derivatives wrt r and z denoted by underscores.
A-E are constants.
Z and R are the body force terms, which are scalar functions of r and z for which I have no analytical solution, but which I can compute numerical values for.

Boundary conditions are:
at r=b and r=c:
C*u_r + B*u/r + A*v_z = 0

at z=0
v=0

at z=d
A*u_r + B*u/r + C*v_z = 0

My approach so far has been to try and learn to use the PDE toolbox GUI, pdetool, to find a numerical solution, but I haven't been able to make my equations fit the form:

-div(c11*grad(u1)) - div(c12*grad(u2)) + a11*u1 + a12*u2 = f1
-div(c21*grad(u2)) - div(c22*grad(u2)) + a21*u1 + a22*u2 = f2

My main problem is that I have first derivatives of u and v that I can't find a way to generate from -div(c*grad(u)).
My second problem is that I don't even know if the pde toolbox will allow me to call the algorithm I need for computing the body forces as part of the governing equations.

Any help anyone can give me would make me immensely grateful, whether by direct solution of my equations or by pointing me towards a generic solution for orthotropic cylinders under body forces, and I'll be happy to give credit in my report.

Regards,
Phil

Subject: Help to solve system of 2 coupled elliptic PDEs (orthotropic

From: vedenev

Date: 9 Mar, 2009 16:03:10

Message: 2 of 4

You can specify du/dx like items in f. x, y, sd, u, ux, uy, and t -
is prdefiende symbols that can be used in f. ux is du/dx. Use
pdenonlin in this case.

-----------------------------------------
Maxim Vedenev, MATLAB Custom Programming
vedenev@ngs.ru
http://simulations.narod.ru/

Subject: Help to solve system of 2 coupled elliptic PDEs (orthotropic

From: Rune Allnor

Date: 9 Mar, 2009 16:04:06

Message: 3 of 4

On 9 Mar, 16:39, "Philip " <philip.ke...@balliol.ox.ac.uk> wrote:
> Hello all,
> I'm an undergraduate student engaged in my final year project, and I've been trying for a term to solve some equations. With my project deadline in a week, and my supervisor away at a conference, I need some results and am getting desperate.
>
> My problem is this:
> I have an orthotropic cylinder experiencing body forces.

No, it isn't. Your problem is that you are unable to
manage your time. Call or email your supervisor at the
conferenceand ask for help.

Rune

Subject: Help to solve system of 2 coupled elliptic PDEs (orthotropic

From: Philip

Date: 11 Mar, 2009 12:08:01

Message: 4 of 4

> You can specify du/dx like items in f. x, y, sd, u, ux, uy, and t -
> is prdefiende symbols that can be used in f. ux is du/dx. Use
> pdenonlin in this case.

Thank you, Dr Vedenev, that was extremely helpful.

I have 2 more questions though:

1. Can I call an m-file in f? I have a non-analytic solution for the body forces which would need to be calculated at each node as a function f(x,y).

2. How do ux and uy work in the system case? I need u1x, u1y and u2y, is that how they are entered?

Regards,
Phil

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