[Gmsh] calculating deformation under own weight

[Florin Andrei]

Consider a simple object, like a thick round flat disk, laying down on 
its back on 3 small equidistant support points. Disk diameter about 300 
mm, thickness about 50 mm. Due to gravity, the disk will sag a little 
around the supports.

Assume the disk is rigid enough that sagging is infinitesimal, maybe 1 
micron or less. The disk is made of a very rigid material, homogeneous, 
no holes (such as a solid slab of ceramic). Density and Young's modulus 
are known, and are typical for ordinary ceramic, glass or amorphous 
materials (medium density, high stiffness).

How would you calculate sagging in every point on the top face of the disk?

I'm learning Gmsh specifically to solve this problem. So far I've made a 
3D mesh describing the shape of the disk. That was easy. What are the 
next steps?

I assume I'll have to describe gravity somehow, like a force pulling 
down every point of the mesh, deduced from density. Then the 3 support 
points at the bottom will have to be included as constraints 
(immovable). And then the model will have to take into account real 
numbers for Young's modulus. I assume GetDP will be involved somehow.

I'm not asking for a full solution, but I would appreciate an outline of 
the steps I need to take. Then I can print out documentation, lock 
myself in the basement and learn. :)

Some background info:

I have no prior experience with real FEA software. However, I've a 
degree in physics and while in college I wrote many programs (in Pascal 
and C) describing vibrating strings and membranes by means of discrete 
elements - like rudimentary FEA, but homegrown. So I understand the 
general theory, but I need to learn the practical aspects of this FEA 
environment.

If need be, I can write small scripts and programs in a variety of 
languages for auxiliary tasks, but I'd prefer to use Gmsh / GedDP for 
the "heavy lifting".

I'm doing this as a hobby.

-- 
Florin Andrei
http://florin.myip.org/