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.

Wrench

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.