The Use of Condensation Techniques for Solving Dynamics Problems

The advent of large computer systems for structural analysis has sometimes led to the use of little-understood approximation techniques which can lead to undetected errors. For example, for dynamic analysis, only dynamic degrees of freedom at the points of significant mass and moment of inertia are needed, which allows a large degree of freedom problem to be condensed to a more manageable, smaller size. This paper explains the theory behind such condensation techniques, illustrates their use, and outlines numerical techniques for efficiently generating the condensed equations. Three examples of condensation are given to illustrate the approximation involved and the error that can be expected.