Release date |
1999-12-19 |
Author: |
Moritz
Beck, moritz@moritz-beck.de |
Purpose: |
Generation
of stiffness matrix for displacement method in civil engineering (plain
systems) |
License
and Copyright: |
This
software is freeware, it should be used and copied freely. Manipulating and
changes at the source code are prohibited. |
By using
your link-Software (e.g. the TI-GRAPHLINK-Software) the groupfile kmat.89g
should be transmitted to the calculator. Note: all files need to get in a
folder “statik2d” (check box “Retain folder”).
Firstly
this software was developed on my TI89, but it’s also tested on my girl friends
TI92 an it should do its task on the TI92+.
While
learning the displacement method for solving complex static systems (plain
systems) I was told to think about bars with inconsistences between the end of
the bar and a node. Stiffness matrixes for various inconsistences should be
generated by using the four general matrixes for bars, stable fixed at the
node.
The reason
for implementing a algorithm for this: I’m lacy, to lacy to generate it by
myself.
I trust at
your knowledge about the displacement method in the following details,
reffering to the lecture of Prof. Möller, institute of statics in civil
engineering (http://rcswww.urz.tu-dresden.de/~statik) at the Dresden Technical
University (http://www.tu-dresden.de).
Used Signs:
i,k |
node at beginning of a bar/ end of a bar |
ik,ki |
beginning/ end of a bar |
|
Stiffness matrix at start of a bar (ik),
caused by a displacement of the end of the bar (ki) |
|
similar to the last, caused by the
displacement of the node at the beginning of the bar |
|
Displacement of the beginning of a bar |
|
Forces at the node k |
|
Forces at end of the bar |
|
Forces at end of the bar, caused by extern
forces, should be calculated outside the displacement method |
|
local coordinates |
|
global vectors |
|
Transformation matrix to convert local to
global coordinates |
A static
system will be solved by solving by the follwing linear Equations:
My
Intention by developing the kmat-package was the generation of stiffness
matrixes with any inconsistences. There were three forms possible, in each
coordinate one (three coordinates: x1, x2, angle3). So there were 82=64
combinations of inconsistences? Some of them are nonsens, e.g. x1 at beginning
and end of a bar, others ar possible, e.g. a link.
kmat(bar,
displaced-node, inconsistence-at-start, angle-at-start, inconsistence-at-end,
angle-at-end)
This
function generates the stiffness matrix, e.g. with your given values.
kmat
– parameters
bar |
At which
end of the bar? ik (beginning)=0, ki (end)=1 |
displaces-node |
Which
node will be displaced? i=0, k=1 |
inconsistence-at-start |
Inconsistences
are coded as octal numbers, the summary of numbers will be the combination of
incostistences between bar and node: 1=x1
(force along the bar), 2=x2 (force across the bar), 3=x3 (Momentum) d.h.
0=fixed at the node |
angle-at-start |
Which
angle has the inconsistence to the local coordinates? default=0 |
inconsistence-at-end |
similar
to ~at-start |
angle-at-end |
similar
to ~at-start |
Example
kmat(0,0,0,0,0,0)
returns the K(ik,i) stiffness matrix of a fixed bar
kmat(0,1,0,0,7,0)
no fixing at the end of the bar => matrix = 0
kmat(0,0,4,0,4,0)
=> ideal framework bar
My software
is very slowly. The TI89 works hard and takes some time (up to 10sec) for calculating.
This
Version is the first public one, all the fomer versions were to gracy to make
it public here.
my girl
friend Kerstin, my fellow students and friends Matthias, Tobi, Olaf, Sylvia,
encouraging me to develop some Software.