# Guyan Reduction (Static Condensation)

A Finite Element reduction technique which is used in the dynamic solution of very large problems having a large number of degrees of freedom where we often desire only a small percentage of the frequency and mode shapes. Guyan reduction is essentially a substructuring method which reduces the problem to a smaller one by relating certain degrees of freedom to certain others by means of constraint equations, thereby reducing the size of the problem. The degrees of freedom that are retained in the final solution are called 'masters' ('slaves' for those eliminated) and are, associated with large amounts of mass and inertia concentrations. Accuracy of the dynamic solution (natural frequencies, mode shapes) is largely dependent on the selection of the master degrees of freedom both in terms of number and direction.

**See also: **Finite Element Method.

**Subjects: ** Mechanical Engineering