[Getdp] Linear Elasticity Examples

[Christophe Geuzaine]

m.fenner at gmx.net wrote:
> Dear Christophe,
> 
> I rerecently discovered the linear elasticity examples in the wiki -
> and immediately ran into a few problems with the 3D-example.
> 
> 1. the ukulele.geo produces a number of errors when loading. The
> variables in the Layers command are missing:
> 
> Error   :
> '/cygdrive/d/MF/Programme/FEM/Problems/Elasticity-01/parts.geo', line
> 15 : Unknown variable 'Peg'
> 
> Nevertheless a mesh can be generated with a few parts of the ukulele
> missing. Next I completed the ukulele by assigning the missing
> variables at random.
> 
> I tried both meshes with the .pro files but neither gives a solution:
> 
> 
> GetDP   : Warning   : Generated system is of dimension zero .. GetDP
> : Warning   : No equations in linear system

Seems like I forgot to put the "parts.geo" file in the wiki. Should be 
fixed now.

> 
> 2. I also tried a simple model (rectangular beam). I fix the bottom
> face of the beam and apply a transverse force  either at the top
> surface or a top edge without further constraints. The solver is
> hardly converging, just stopping at NB_Max_Iter. The solution gives
> an "S"-shaped displacement as if there was a z=0 constraint on the
> top surface. Despite the warning in the Wiki to use the exmples and
> operators at own risk: Do you have an idea about where this goes
> wrong? (I shall attach the files.)

Actually, it looks good to me: you impose a zero displacement on the 
face z=0 and a force along the x-axis direction on the face z=0.05. This 
will lead to an S-shaped deformation.

To speed up the convergence, just increase the size of the incomplete LU 
factorization (used as a preconditionner for GMRES). You can have a look 
at the sample solver.par file I've added in the wiki for an example.

> 
> Another question:
> 
>> From the Elasticity_3D.pro file I assume that the non standard D1
>> and D2 operators also work with the Lanczos algorithm. Is that
>> right? I am quite interested in mechanical Eigenmodes.
>> ohyeahq at yahoo.co.jp has sent a patch for the Lanczos functionality
>> recently. But I fear that it shall take me ages to set up all the
>> stuff (cygwin, GSL, LAPACK ...) required - not to speak of
>> implementing the patch and building my own binaries. Do you intend
>> to implement this patch into a distribution soon? I guess I'd
>> rather wait for that.

Not sure when we will distribute a new binary. But since the patch is 
merged in the main tree, I would recommend that you compile the nightly 
source archive (http://geuz.org/getdp/src/). Cygwin is actually pretty 
easy to install, and it provides precompiled packages for GSL and LAPACK 
(just select them in the cygwin installer, along with gcc and g77).

Best,

Christophe

-- 
Christophe Geuzaine
Applied and Computational Mathematics, Caltech
geuzaine at acm.caltech.edu - http://geuz.org