Chapter 7: Gap Condition in Mode Superposition Transient

This information is a supplement to Mode-Superposition Method in the Theory Reference and describes the theory behind the gap condition feature.

A "quasi-linear" analysis variation is available with the mode-superposition method. This variation allows interfaces (gaps) between any of the master DOFs and ground, or between any pair of master DOFs. If the gap is initially closed, these interfaces are accounted for by including the stiffness of the interface in the stiffness matrix, but if the gap should later open, a force is applied in the load vector to nullify the effect to the stiffness. If the gap is initially open, it causes no effect on the initial solution, but if it should later close, a force is again applied in the load vector.

The force associated with the gap is:

(7–1)

where:

= gap stiffness (input as STIF, GP command)

and

= displacement across gap (must be master degrees of freedom)

= initial size of gap (input as GAP, GP command)

This mode-superposition method with a gap definition (GP command) adds an explicit term to the implicit integration procedure. An alternate procedure is to use the full method, modeling the linear portions of the structure as superelements (using the CMS method) and the gaps as gap elements. This latter procedure (implicit integration) normally allows larger time steps because it modifies both the stiffness matrix and load vector when the gaps change status.

The load vector, which must be converted to modal coordinates (Equation 14–141) at each time step, is given by