Re: [Getfem-users] other element types

[Roman Putanowicz]

> Dear All,
> 
> I recently thought about using the following structural elements:
> 
> * 1D: Euler-Bernoulli or Timoshenko beam
> * 2D: axially symmetric continuum elements
> * 1D: axially symmetric flat plate (like an axially symmetric beam)
> 
> Before I start working on any of these elements. Maybe there is somebody who
> already implemented any of these. (Like the truss element in a recent email.)
> Or somebody has a few hints for me e.g. how to implement axial symmetry in 
> general.
> Christian Fischer
Hello,

Continuing the thread about implementation of axisymmetric problems.

I have prepared quick and dirty example of calculation of system matrix
for heat conductivity problem in a cylinder (in attachment).

In this case element conductivity matrix is

 S = 2 * pi \int_(Le)  k * (dH/dr)^T * dH/dr * r dr

where Le - element length
      H - matrix of shape functions
(I use notation from J.E. Akin Finite Element Analysis with Error Estimators,
 -- there was just a calculated example I could refer to).
(the trick there is to multiply differential equation by r to remove
 1/r from the left hand side ).


The example illustrates the use of mesh_fem_global_function.
In this case the global function f(r) = r.

It is not needed in this example but for complete implementation one could
also implement calculation of gradient and Hessian of this function (to be
honest I haven't figured this yet :).

I hope that the code will be of any help.

Regards

Roman

-- 
Roman Putanowicz, PhD  < address@hidden  >
Institute for Computational Civil Engng (L-5)
Dept. of Civil Engng, Cracow Univ. of Technology
www.l5.pk.edu.pl, tel. +48 12 628 2569, fax 2034

cyl_heat.cxx
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