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Modeling and Solution Techniques 163

5.3 Substructures (Superelements)
Another very useful technique for analyzing very large FEA models of mechanical sys-
tems is to apply the concept of substructures or superelements (SEs). Substructuring is a
process of analyzing a large structure as a collection of (natural) components. The FEA
models for these components are called substructures or superelements (SEs). The physical
meaning of a substructure is simply a finite element model of a portion of the structure.
Mathematically, it presents a boundary matrix which is condensed by eliminating the inte-
rior points and keeping only the exterior or boundary points of the portion of the structure.
In other words, instead of solving the FEA system of equations once, one can use partitions
of the matrix so that larger models can be solved on relatively smaller computers. More
details of the theory and implementations of the substructures or SEs can be found in the
documentation of the FEA software packages.
Figure 5.3 shows an FEA model of a truck used to conduct the full vehicle static or
dynamic analysis. The entire model can have several millions of DOFs that can be beyond
the capabilities of some computers. Using the substructuring technique, one can build the
FEA model for each subsystem first (such as the cab, chassis, steering system, suspension
system, payload, and so on) and then condense the FEA equations to smaller ones relating
only to DOFs on the interfaces between the subsystems and residing on a residual struc-
ture (e.g., the chassis). The condensed system is much smaller than the original system and
can be solved readily.
The advantages of using the substructuring technique are

• Good for large problems (which will otherwise exceed your computer capabilities)
• Less CPU time per run once the SEs have been processed (i.e., matrices have been
condensed and saved)
• Components may be modeled by different groups
• Partial redesign requires only partial reanalysis (reduced cost)
• Efficient for problems with local nonlinearities (such as confined plastic deforma-
tions) which can be placed in one SE (residual structure)
• Exact for static deformation and stress analysis

FIGURE 5.3
An FEA model of a truck analyzed using substructures.