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 + [AB]*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.
AE 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
