#
Sample FElt Problems

## Simply-supported beam with spring support

Our first example is a simple four node, three element problem that
simulates a simply-supported beam with a spring in the middle for additional
support. The spring is modeled by a truss element. The input file for
this problem looks like this. If we ran this file
through felt then the output would look like this.

The wrench in this example is modeled by 307 constraint strain triangular
elements (plane stress assumption). This model was easily constructed in
velvet by laying down fourteen boundary markers (one at each corner) and
then letting FElt's Geompack based triangle generation ability do the
rest. The nodes and elements that were generated were assigned whatever
constraint and material were active at the time of the generation, in this
case free and steel. To finish up the problem definition all we had to
do was to change the constraint on the pinned nodes and the force on the
node at the point where the force was being applied. Note that we could
also have generated this problem outside of velvet using corduroy and
this input file. From the input, corduroy generates
the nodes and elements section of a FElt file so all we would have to do
is edit the result and add some material properties, constraints, and forces.
The final main velvet
window for this problem illustrates several of velvet's basic
capabilities for problem rendering and definition that we then used to help
illustrate exactly what was going on in the problem. The different colors
on the nodes represent different constraints and forces applied to the
nodes. In this case, we have assigned the color red to the pin constraint,
green to the free constraint, and blue to the horizontal force. When these
objects are assigned to a given node, that node is colored with the
appropriate color. Velvet's drawing tools have also been used to produce
the dimensioning lines. These tools allow you to draw arbitrary figures
and text right onto the main problem canvas and do not affect the mathematics
of the problem in any way. Besides aiding in understanding the problem
as you work with it in velvet, the drawing tools and object coloring can
also be very helpful if you want to dump the main drawing area (as either
a PostScript file or as an XWD) for inclusion in some kind of report or
presentation.

If we select solve from the problems/analysis menu the default output for
this problem will be a text window containing the exact same ASCII based
results that felt would produce for this model. In a problem this large,
this kind of output is not very useful so we would probably rather make
use of some ov velvet's more powerful post-processing options. We can
generate a color contour plot of the stress
in the x direction
by selecting plot stresses from the post-processing menu (other components
of stress would also be available by changing the settings in the conturing
control dialog box, also available from the post-processing menu). We
could also do the same thing for a
displacement component (in this case the x component). These color
contour plots can be saved in either PPM or EPS format. Another useful
kind of output for a large problem like this is a
wireframe drawing of the displaced shape.
Velvet can save these wireframe drawings in either PostScript format
or as an XWD.

## Transient analysis of a two-dimensional frame

For a transient analysis problem like this frame
example, felt can generate both tabular
output or ASCII based time-displacement plots.
In velvet, you can get the same tabular output as in felt, but the
time-displacement plots are graphical and can
be saved in PostScript format for easy hardcopy rendering. Animation of
transient analysis problems is also available in velvet. The
animation window in velvet gives you easy control over the
speed and direction (forward or reverse) of the animation.
The forcing function in this example
was a periodic ramp with period 0.4 seconds constructed using a simple
fmod() statement. This kind of construction is just one example of FElt's
powerful input syntax that allows you to describe
time-dependent forcing functions or boundary conditions as either analytic
functions of time or as a series of discrete time, value pairs.

## Modal analysis of a two-dimensional frame

The modal analysis capabilities in FElt allow you to calculate the
eigenvalues (natural frequencies) and eigenvectors (mode shapes) of
a FElt problem. This example input file for a simple
two-dimensional frame when run through
felt will produce a simple table of eigenvalues
and eigenvectors. If we solve the problem in velvet we can also draw
the actual mode shapes corresponding to the
eigenvectors. The controls for this kind of output allow you to flip
through each mode one at a time. You can also save each mode shape plot
as either an XWD or PostScript file.

## Static thermal analysis of a plate

Static thermal analysis involves basically the same mathematical procedure
and roughly the same kinds of output as static structural analysis.
In this example we have a rectangular plate,
insulated top and bottom. The left-most edge is held at a fixed temperature
of 100 degrees and the other three are exposed to a free stream temperature
of 50 degrees. The output from felt for this problem
consists of a table of nodal temperatures at thermal equilibrium. If we
had solved the problem in velvet then we could also have generated
a color contour plot of temperature by selecting
plot displacements (temperature is the single displacement DOF in a thermal
analysis problem) from the post-processing menu (note the very coarse
contouring that results from the very coarse mesh in this plot).

## Transient heat transfer in a one-dimensional rod

With this example we are modeling transient
heat transfer in a one-dimensional
rod. The rod is modeled as two elements. The right end of the rod is
insulated and the left end is held at a fixed temperature so we
only consider convection over the length-wise surface. The initial
temperature at all three nodes is 25 degrees. At time t=0+, node 1
is raised to 85 degrees and maintained there. Note that along with the
standard tabular and plotted result the
output from felt for this problem also includes print-outs of th mass
and stiffness matrices. Just like for transient structural analysis,
the output from velvet for this kind of problem replaces the ASCII
based plot with a graphical one.