How to assembly a stiffness matrix ?

[Francesco]

I have a structure ( i.e. a crane ). I split the structure in a certain
number of simple elements ( shaft or beam ).
For each element i can build a local stiffness matrix of 12x12 element.
Then i need to assembly this little matrixes in the big structure
matrix. Dimension of the structure matrix is equale to: ( number of
nodes x 6 ). nodes are cross point between elements.

Each element matrix has a specifical location in the big matrix.

How i can assembly the big structure matrix, starting by the single
element matrix ?
What i want to input is only the dimension of the structure matrix and
the data of each single element matrix. The big structure matrix should
be calculated by Mathematica.

Thanks in adavance for help and sorry for my very bad english

Regards,

Francesco

[Oliver Ruebenkoenig]

Ciao Francesco,

we have a lot of open source tools to do that in mathematica.
You can download the software from:
http://www.imtek.de/simulation/mathematica/IMSweb/index.html

If you have questions you might want to join the mailing list under:
http://elmo.imtek.uni-freiburg.de/mailman/listinfo/ims

To you question:
I have a data structure imsMakeElementMatrix and imsAssemble. You fill all
the element matrices with imsMakeElementMatrix and put them into the
imsAssemble command and done you are. The online documentation can be seen
here:
http://www.imtek.de/simulation/mathematica/IMSweb/imsTOC/Numerics%20and%20Algor$

If you are into finite elements you might enjoy some of our application
examples at:
http://www.imtek.de/simulation/mathematica/IMSweb/imsTOC/Application%20Examples$

For transient problems I can recommend model order reduction. Assume you
have a high dimensional system of equations (say 30000 DOFs) you may be
able to find an approximate system of ( say 20 DOFs !!! ) that has very
much the same behaviour and then time integrate that ( which is of course
_very_ fast ) in the last step you do a re-projection to the original
system. For online documentation have a look at:
http://www.imtek.de/simulation/mathematica/IMSweb/imsTOC/Application%20Examples$

Please note: The online documentation is slightly dated - some 4 weeks or
so and not all documentation has all the nice pictures inside...

We also have some tools to input for example ANSYS generated stuff (mesh,
element files and so on ) into mathematica.

Nice export to povray and VTK script are possible.

Does this help?

Oliver

Oliver Ruebenkoenig, <rueb...@imtek.de>
Phone: ++49 +761 203 7385

[Francesco]

Thanks a lot, i'm reading just now documentation and it seems a very
rich package !

Regards,

Francesco

Oliver Ruebenkoenig ha scritto:

[car...@colorado.edu]

One of my FEM courses teaches that subject. The chapter devoted to
the assembly process is

http://www.colorado.edu/engineering/Aerospace/CAS/courses.d/IFEM.d/IFEM.Ch25.d/IFEM.Ch25.index.html

The rudiments are explained in Chapter 3 and 4 of the same Notes.