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Re: [Getfem-users] other element types
From: |
Roman Putanowicz |
Subject: |
Re: [Getfem-users] other element types |
Date: |
Wed, 14 Jul 2010 08:26:05 +0200 |
User-agent: |
Mutt/1.5.13 (2006-08-11) |
> 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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