Centre of polar surface plot in MATLAB

Hi,

I'm working on a project to model the displacement of a circular trampoline when a load is applied to an arbitrary patch.

I've used pol2cart to wrap initially rectangular arrays into a circle. The displacement for each point in the mesh is calculated by iteration, as an average of the four adjacent points from the previous iteration:

displace_new(rad,ang) = (displace_old(rad+1,ang) + displace_old(rad-1,ang) + displace_old(rad,ang+1) + displace_old(rad,ang-1))/4;

I've got some additional code to set the perimeter displacement to zero, 'stitch' the edges together smoothly, and account for a rip in the trampoline across which stress can't be transferred, which all seems to work nicely.

However, I'm having issues transmitting the displacement across the centre of the circle - as you can see from the screenshots it's behaving like a rectangular surface that's been wrapped around in a circle rather than a true circular surface.

I've been told it should be possible to sort out the centre just by setting the displacement of all the zero-radius (rad=1) points to the mean of all the points one step outwards (rad=2):

if rad == 1 displace_new(rad,ang) = mean(displace_old(rad+1,:)); end

but this isn't working for me - what am I doing wrong?

Thanks in advance!

[Curtis Garner]

It looks like your 'center' edge on your rectangle is being constrained more than it should be. What method are you using to enforce that all of these point have the same vertical displacement?

[DGM]

If you're assuming that your rectangular representation has uniform density, then that would mean that the center of the trampoline is excessively heavy (and probably excessively stiff), simply due to the mesh density. That's just a guess.

EDIT: I totally fell for that.