| Author | Message | ||
     Fernando Buezas (fernandob) Member Username: fernandob Post Number: 10 Registered: 02-2007 |
Dear Mr Nelson. I'm working in the following problem: del2(w) = u del2(u)- lambda*w= 0 in a unitary rectangular domain. The boundary condition to impose are: 1) w = 0 2) dx(w)= 0, on x=0,1 and 3) dyy(w)+ k1 * dxx(w) = 0 4) dy(dyy(w) + k2*dxx(w)) = 0, on y = 0,1 where k1 and k2 are constants. How I could formulate the conditions 3 and 4? Thank you for your cooperation. F Buezas | ||
| Jerry Brown (jerrybrown11743) Member Username: jerrybrown11743 Post Number: 39 Registered: 03-2004 |
This is apparently a plate on an elastic foundation with two clamped edges and two free edges. I have a similar problem. The plate is not on an elastic foundation and it takes into account the in-plane stresses due to bending. But it has the same boundary conditions. I have not found a way to handle those particular boundary conditions with FlexPDE. See "System of 4th order nonlinear equations" in this forum. Please let me know if you get any good ideas. | ||
| Jerry Brown (jerrybrown11743) Member Username: jerrybrown11743 Post Number: 40 Registered: 03-2004 |
Also see "Bending of plate" in this forum. | ||
| Robert G. Nelson (rgnelson) Moderator Username: rgnelson Post Number: 997 Registered: 06-2003 |
Take a look at the way this fourth-order equation is derived, and see if there is some intermediate stage at which a meaningful split of variables can be made in terms of bending angles, moments, or some other tangible quantity that might make a more amenable split of the equations than simply del2(w)=u. | ||
| Jerry Brown (jerrybrown11743) Member Username: jerrybrown11743 Post Number: 41 Registered: 03-2004 |
I agree that finding a different way to split the variables is the best bet. However, my efforts in that direction have not been successful. It's a fascinating puzzle and I intend to take another run at it soon. Fernando, I'm sure you have a good reference on plate theory or you wouldn't have known about boundary condition (4). But, for what it may be worth, I've found "Theory of Plates and Shells" by Timoshenko and Woinowsky-Krieger to be especially helpful. |