# Linear Gap

Linear gap is the simplest contact form used in Nastran simulations.

Linear gap can solve a large class of problems, such as hole bearing, heel-toe interaction and fitting contacts. Linear does not include friction, large displacements and material non-linearity. CGAP contact elements (node-to-node defined in the FEM environment) run in both linear static (SOL101) and non-linear analysis (SOL106).

- Displacement criteria: no penetration (MPC displacement > =0)
- MPCFORCE criteria: compressive force only (MPC force < =0)

The equation for the gap displacement can be written as:

Uygap = Uyopening – Uyclosing + Uyinitial

Rearranging in MPC format and setting Uyclosing as the dependent (first) term:

Uyclosing – Uyopening + Uygap – Uyinitial = 0

The Nastran commands to use for linear gaps are the following:

SPOINT (scalar point definition) is used to define the U_{gap} and
U_{init} :

SPOINT 55 155

The SUPORT entry specifies reference degrees-of-freedom for rigid body motion, and it
puts SPOINT 55 (U_{gap}) in the R-set for iteration:

SUPORT 55 0

SPC selects a single-point constraint set to be applied and defines the initial gap
opening = .05 (U_{init}):

SPC 101106 155 0 .05

MPC entry: (equations of motion: Uy3 – Uy2 + U_{gap} – U_{init} =
0)

$ SID G1 C1 A1 G2 C2 A2

MPC 101106 3 2 1.0 2 2 -1.0

$ G3 C3 A3 G4 C4 A4

55 0 1.0 155 0 -1.0

- PARAM, CDITER (integer) maximum number of iterations to determine open/closed
- PARAM, CDPRT (yes/no) print iteration history of constraint violations
- PARAM, CDPCH (yes/no) punches DMIG, CDSHUT entries for final solutions
- DMIG, CDSHUT: input vector of initial open/closed state of gaps (default = all closed)